18.2: Tracking Infectious Diseases
-
- Last updated
- Save as PDF
Learning Objectives
- Explain the research approaches used by the pioneers of epidemiology
- Explain how descriptive, analytical, and experimental epidemiological studies go about determining the cause of morbidity and mortality
Epidemiology has its roots in the work of physicians who looked for patterns in disease occurrence as a way to understand how to prevent it. The idea that disease could be transmitted was an important precursor to making sense of some of the patterns. In 1546, Girolamo Fracastoro first proposed the germ theory of disease in his essay De Contagione et Contagiosis Morbis , but this theory remained in competition with other theories, such as the miasma hypothesis, for many years (see What Our Ancestors Knew ). Uncertainty about the cause of disease was not an absolute barrier to obtaining useful knowledge from patterns of disease. Some important researchers, such as Florence Nightingale, subscribed to the miasma hypothesis. The transition to acceptance of the germ theory during the 19th century provided a solid mechanistic grounding to the study of disease patterns. The studies of 19th century physicians and researchers such as John Snow, Florence Nightingale, Ignaz Semmelweis, Joseph Lister, Robert Koch, Louis Pasteur, and others sowed the seeds of modern epidemiology.
Pioneers of Epidemiology
John Snow (Figure \(\PageIndex{1}\)) was a British physician known as the father of epidemiology for determining the source of the 1854 Broad Street cholera epidemic in London. Based on observations he had made during an earlier cholera outbreak (1848–1849), Snow proposed that cholera was spread through a fecal-oral route of transmission and that a microbe was the infectious agent. He investigated the 1854 cholera epidemic in two ways. First, suspecting that contaminated water was the source of the epidemic, Snow identified the source of water for those infected. He found a high frequency of cholera cases among individuals who obtained their water from the River Thames downstream from London. This water contained the refuse and sewage from London and settlements upstream. He also noted that brewery workers did not contract cholera and on investigation found the owners provided the workers with beer to drink and stated that they likely did not drink water. 1 Second, he also painstakingly mapped the incidence of cholera and found a high frequency among those individuals using a particular water pump located on Broad Street. In response to Snow’s advice, local officials removed the pump’s handle, 2 resulting in the containment of the Broad Street cholera epidemic.
Snow’s work represents an early epidemiological study and it resulted in the first known public health response to an epidemic. Snow’s meticulous case-tracking methods are now common practice in studying disease outbreaks and in associating new diseases with their causes. His work further shed light on unsanitary sewage practices and the effects of waste dumping in the Thames. Additionally, his work supported the germ theory of disease, which argued disease could be transmitted through contaminated items, including water contaminated with fecal matter.
Snow’s work illustrated what is referred to today as a common source spread of infectious disease, in which there is a single source for all of the individuals infected. In this case, the single source was the contaminated well below the Broad Street pump. Types of common source spread include point source spread, continuous common source spread, and intermittent common source spread. In point source spread of infectious disease, the common source operates for a short time period—less than the incubation period of the pathogen. An example of point source spread is a single contaminated potato salad at a group picnic. In continuous common source spread, the infection occurs for an extended period of time, longer than the incubation period. An example of continuous common source spread would be the source of London water taken downstream of the city, which was continuously contaminated with sewage from upstream. Finally, with intermittent common source spread, infections occur for a period, stop, and then begin again. This might be seen in infections from a well that was contaminated only after large rainfalls and that cleared itself of contamination after a short period.
In contrast to common source spread, propagated spread occurs through direct or indirect person-to-person contact. With propagated spread, there is no single source for infection; each infected individual becomes a source for one or more subsequent infections. With propagated spread, unless the spread is stopped immediately, infections occur for longer than the incubation period. Although point sources often lead to large-scale but localized outbreaks of short duration, propagated spread typically results in longer duration outbreaks that can vary from small to large, depending on the population and the disease (Figure \(\PageIndex{2}\)). In addition, because of person-to-person transmission, propagated spread cannot be easily stopped at a single source like point source spread.
Florence Nightingale’s work is another example of an early epidemiological study. In 1854, Nightingale was part of a contingent of nurses dispatched by the British military to care for wounded soldiers during the Crimean War. Nightingale kept meticulous records regarding the causes of illness and death during the war. Her recordkeeping was a fundamental task of what would later become the science of epidemiology. Her analysis of the data she collected was published in 1858. In this book, she presented monthly frequency data on causes of death in a wedge chart histogram (Figure \(\PageIndex{3}\)). This graphical presentation of data, unusual at the time, powerfully illustrated that the vast majority of casualties during the war occurred not due to wounds sustained in action but to what Nightingale deemed preventable infectious diseases. Often these diseases occurred because of poor sanitation and lack of access to hospital facilities. Nightingale’s findings led to many reforms in the British military’s system of medical care.
Joseph Lister provided early epidemiological evidence leading to good public health practices in clinics and hospitals. These settings were notorious in the mid-1800s for fatal infections of surgical wounds at a time when the germ theory of disease was not yet widely accepted (see Foundations of Modern Cell Theory ). Most physicians did not wash their hands between patient visits or clean and sterilize their surgical tools. Lister, however, discovered the disinfecting properties of carbolic acid, also known as phenol (see Using Chemicals to Control Microorganisms ). He introduced several disinfection protocols that dramatically lowered post-surgical infection rates. 3 He demanded that surgeons who worked for him use a 5% carbolic acid solution to clean their surgical tools between patients, and even went so far as to spray the solution onto bandages and over the surgical site during operations (Figure \(\PageIndex{4}\)). He also took precautions not to introduce sources of infection from his skin or clothing by removing his coat, rolling up his sleeves, and washing his hands in a dilute solution of carbolic acid before and during the surgery.
Link to Learning
John Snow’s own account of his work has additional links and information.
This CDC resource further breaks down the pattern expected from a point-source outbreak.
Learn more about Nightingale’s wedge chart here.
Exercise \(\PageIndex{1}\)
- Explain the difference between common source spread and propagated spread of disease.
- Describe how the observations of John Snow, Florence Nightingale, and Joseph Lister led to improvements in public health.
Types of Epidemiological Studies
Today, epidemiologists make use of study designs, the manner in which data are gathered to test a hypothesis, similar to those of researchers studying other phenomena that occur in populations. These approaches can be divided into observational studies (in which subjects are not manipulated) and experimental studies (in which subjects are manipulated). Collectively, these studies give modern-day epidemiologists multiple tools for exploring the connections between infectious diseases and the populations of susceptible individuals they might infect.
Observational Studies
In an observational study, data are gathered from study participants through measurements (such as physiological variables like white blood cell count), or answers to questions in interviews (such as recent travel or exercise frequency). The subjects in an observational study are typically chosen at random from a population of affected or unaffected individuals. However, the subjects in an observational study are in no way manipulated by the researcher. Observational studies are typically easier to carry out than experimental studies, and in certain situations they may be the only studies possible for ethical reasons.
Observational studies are only able to measure associations between disease occurrence and possible causative agents; they do not necessarily prove a causal relationship. For example, suppose a study finds an association between heavy coffee drinking and lower incidence of skin cancer. This might suggest that coffee prevents skin cancer, but there may be another unmeasured factor involved, such as the amount of sun exposure the participants receive. If it turns out that coffee drinkers work more in offices and spend less time outside in the sun than those who drink less coffee, then it may be possible that the lower rate of skin cancer is due to less sun exposure, not to coffee consumption. The observational study cannot distinguish between these two potential causes.
There are several useful approaches in observational studies. These include methods classified as descriptive epidemiology and analytical epidemiology. Descriptive epidemiology gathers information about a disease outbreak, the affected individuals, and how the disease has spread over time in an exploratory stage of study. This type of study will involve interviews with patients, their contacts, and their family members; examination of samples and medical records; and even histories of food and beverages consumed. Such a study might be conducted while the outbreak is still occurring. Descriptive studies might form the basis for developing a hypothesis of causation that could be tested by more rigorous observational and experimental studies.
Analytical epidemiology employs carefully selected groups of individuals in an attempt to more convincingly evaluate hypotheses about potential causes for a disease outbreak. The selection of cases is generally made at random, so the results are not biased because of some common characteristic of the study participants. Analytical studies may gather their data by going back in time (retrospective studies), or as events unfold forward in time (prospective studies).
Retrospective studies gather data from the past on present-day cases. Data can include things like the medical history, age, gender, or occupational history of the affected individuals. This type of study examines associations between factors chosen or available to the researcher and disease occurrence.
Prospective studies follow individuals and monitor their disease state during the course of the study. Data on the characteristics of the study subjects and their environments are gathered at the beginning and during the study so that subjects who become ill may be compared with those who do not. Again, the researchers can look for associations between the disease state and variables that were measured during the study to shed light on possible causes.
Analytical studies incorporate groups into their designs to assist in teasing out associations with disease. Approaches to group-based analytical studies include cohort studies, case-control studies, and cross-sectional studies. The cohort method examines groups of individuals (called cohorts) who share a particular characteristic. For example, a cohort might consist of individuals born in the same year and the same place; or it might consist of people who practice or avoid a particular behavior, e.g., smokers or nonsmokers. In a cohort study, cohorts can be followed prospectively or studied retrospectively. If only a single cohort is followed, then the affected individuals are compared with the unaffected individuals in the same group. Disease outcomes are recorded and analyzed to try to identify correlations between characteristics of individuals in the cohort and disease incidence. Cohort studies are a useful way to determine the causes of a condition without violating the ethical prohibition of exposing subjects to a risk factor. Cohorts are typically identified and defined based on suspected risk factors to which individuals have already been exposed through their own choices or circumstances.
Case-control studies are typically retrospective and compare a group of individuals with a disease to a similar group of individuals without the disease. Case-control studies are far more efficient than cohort studies because researchers can deliberately select subjects who are already affected with the disease as opposed to waiting to see which subjects from a random sample will develop a disease.
A cross-sectional study analyzes randomly selected individuals in a population and compares individuals affected by a disease or condition to those unaffected at a single point in time. Subjects are compared to look for associations between certain measurable variables and the disease or condition. Cross-sectional studies are also used to determine the prevalence of a condition.
Experimental Studies
Experimental epidemiology uses laboratory or clinical studies in which the investigator manipulates the study subjects to study the connections between diseases and potential causative agents or to assess treatments. Examples of treatments might be the administration of a drug, the inclusion or exclusion of different dietary items, physical exercise, or a particular surgical procedure. Animals or humans are used as test subjects. Because experimental studies involve manipulation of subjects, they are typically more difficult and sometimes impossible for ethical reasons.
Koch’s postulates require experimental interventions to determine the causative agent for a disease. Unlike observational studies, experimental studies can provide strong evidence supporting cause because other factors are typically held constant when the researcher manipulates the subject. The outcomes for one group receiving the treatment are compared to outcomes for a group that does not receive the treatment but is treated the same in every other way. For example, one group might receive a regimen of a drug administered as a pill, while the untreated group receives a placebo (a pill that looks the same but has no active ingredient). Both groups are treated as similarly as possible except for the administration of the drug. Because other variables are held constant in both the treated and the untreated groups, the researcher is more certain that any change in the treated group is a result of the specific manipulation.
Experimental studies provide the strongest evidence for the etiology of disease, but they must also be designed carefully to eliminate subtle effects of bias. Typically, experimental studies with humans are conducted as double-blind studies, meaning neither the subjects nor the researchers know who is a treatment case and who is not. This design removes a well-known cause of bias in research called the placebo effect, in which knowledge of the treatment by either the subject or the researcher can influence the outcomes.
Exercise \(\PageIndex{2}\)
- Describe the advantages and disadvantages of observational studies and experimental studies.
- Explain the ways that groups of subjects can be selected for analytical studies.
Clinical Focus: Part 3
Since laboratory tests had confirmed Salmonella , a common foodborne pathogen, as the etiologic agent, epidemiologists suspected that the outbreak was caused by contamination at a food processing facility serving the region. Interviews with patients focused on food consumption during and after the Thanksgiving holiday, corresponding with the timing of the outbreak. During the interviews, patients were asked to list items consumed at holiday gatherings and describe how widely each item was consumed among family members and relatives. They were also asked about the sources of food items (e.g., brand, location of purchase, date of purchase). By asking such questions, health officials hoped to identify patterns that would lead back to the source of the outbreak.
Analysis of the interview responses eventually linked almost all of the cases to consumption of a holiday dish known as the turducken—a chicken stuffed inside a duck stuffed inside a turkey. Turducken is a dish not generally consumed year-round, which would explain the spike in cases just after the Thanksgiving holiday. Additional analysis revealed that the turduckens consumed by the affected patients were purchased already stuffed and ready to be cooked. Moreover, the pre-stuffed turduckens were all sold at the same regional grocery chain under two different brand names. Upon further investigation, officials traced both brands to a single processing plant that supplied stores throughout the Florida panhandle.
Exercise \(\PageIndex{3}\)
- Is this an example of common source spread or propagated spread?
- What next steps would the public health office likely take after identifying the source of the outbreak?
Key Concepts and Summary
- Early pioneers of epidemiology such as John Snow, Florence Nightingale, and Joseph Lister, studied disease at the population level and used data to disrupt disease transmission.
- Descriptive epidemiology studies rely on case analysis and patient histories to gain information about outbreaks, frequently while they are still occurring.
- Retrospective epidemiology studies use historical data to identify associations with the disease state of present cases. Prospective epidemiology studies gather data and follow cases to find associations with future disease states.
- Analytical epidemiology studies are observational studies that are carefully designed to compare groups and uncover associations between environmental or genetic factors and disease.
- Experimental epidemiology studies generate strong evidence of causation in disease or treatment by manipulating subjects and comparing them with control subjects.
Footnotes
- John Snow. On the Mode of Communication of Cholera. Second edition, Much Enlarged . John Churchill, 1855.
- John Snow. “The Cholera near Golden-Wquare, and at Deptford.” Medical Times and Gazette 9 (1854): 321–322. http://www.ph.ucla.edu/epi/snow/chol...densquare.html .
- O.M. Lidwell. “Joseph Lister and Infection from the Air.” Epidemiology and Infection 99 (1987): 569–578. www.ncbi.nlm.nih.gov/pmc/arti...00006-0004.pdf.


8.10: Herbert Hoover and the Politics of the Depression
-
- Last updated
- Save as PDF
As the Depression spread, public blame settled on President Herbert Hoover and the conservative politics of the Republican Party. But Hoover was as much victim as perpetrator, a man who had the misfortune of becoming a visible symbol for large invisible forces. In 1928 Hoover had no reason to believe that his presidency would be any different than that of his predecessor, Calvin Coolidge, whose time in office was marked by relative government inaction, seemingly rampant prosperity, and high approval ratings.
Coolidge had decided not to seek a second term in 1928. A man of few words, “Silent Cal” publicized this decision by handing a scrap of paper to a reporter that simply read: “I do not choose to run for president in 1928.” The race therefore became a contest between the Democratic governor of New York, Al Smith, whose Catholic faith and immigrant background aroused nativist suspicions and whose connections to Tammany Hall and anti-Prohibition politics offended reformers, and the Republican candidate, Herbert Hoover, whose all-American, Midwestern, Protestant background and managerial prowess during World War I endeared him to American voters. 7
Hoover epitomized the “self-made man.” Orphaned at age nine, he was raised by a strict Quaker uncle on the West Coast. He graduated from Stanford University in 1895 and worked as an engineer for several multinational mining companies. He became a household name during World War I when he oversaw voluntary rationing as the head of the U.S. Food Administration and, after the armistice, served as the director-general of the American Relief Association in Europe. Hoover’s reputation for humanitarian service and problem solving translated into popular support, even as the public soured on Wilson’s Progressive activism. Hoover was one of the few politicians whose career benefited from wartime public service. After the war both the Democratic and Republican parties tried to draft him to run for president in 1920. 8
Hoover declined to run in 1920 and 1924. He served instead as secretary of commerce under both Harding and Coolidge, taking an active role in all aspects of government. In 1928, he seemed the natural successor to Coolidge. Politically, aside from the issue of Prohibition (he was a “dry,” Smith a “wet”), Hoover’s platform differed very little from Smith’s, leaving little to discuss during the campaign except personality and religion. Both benefited Hoover. Smith’s background engendered opposition from otherwise solid Democratic states, especially in the South, where his Catholic, ethnic, urban, and anti-Prohibition background were anathema. His popularity among urban ethnic voters counted for little. Several southern states, in part owing to the work of itinerant evangelical politicking, voted Republican for the first time since Reconstruction. Hoover won in a landslide, taking nearly 60 percent of the popular vote. 9
Although Hoover is sometimes categorized as a “business president” in line with his Republican predecessors, he also embraced an inherent business progressivism, a system of voluntary action called associationalism that assumed Americans could maintain a web of voluntary cooperative organizations dedicated to providing economic assistance and services to those in need. Businesses, the thinking went, would willingly limit harmful practice for the greater economic good. To Hoover, direct government aid would discourage a healthy work ethic while associationalism would encourage the self-control and self-initiative that fueled economic growth. But when the Depression exposed the incapacity of such strategies to produce an economic recovery, Hoover proved insufficiently flexible to recognize the limits of his ideology. And when the ideology failed, so too did his presidency. 10
Hoover entered office on a wave of popular support, but by October 1929 the economic collapse had overwhelmed his presidency. Like all too many Americans, Hoover and his advisors assumed—or perhaps simply hoped—that the sharp financial and economic decline was a temporary downturn, another “bust” of the inevitable boom-bust cycles that stretched back through America’s commercial history. Many economists argued that periodic busts culled weak firms and paved the way for future growth. And so when suffering Americans looked to Hoover for help, Hoover could only answer with volunteerism. He asked business leaders to promise to maintain investments and employment and encouraged state and local charities to assist those in need. Hoover established the President’s Organization for Unemployment Relief, or POUR, to help organize the efforts of private agencies. While POUR urged charitable giving, charitable relief organizations were overwhelmed by the growing needs of the many multiplying unemployed, underfed, and unhoused Americans. By mid-1932, for instance, a quarter of all of New York’s private charities closed: they had simply run out of money. In Atlanta, solvent relief charities could only provide $1.30 per week to needy families. The size and scope of the Depression overpowered the radically insufficient capacity of private volunteer organizations to mediate the crisis. 11
By 1932, with the economy long since stagnant and a reelection campaign looming, Hoover, hoping to stimulate American industry, created the Reconstruction Finance Corporation (RFC) to provide emergency loans to banks, building-and-loan societies, railroads, and other private industries. It was radical in its use of direct government aid and out of character for the normally laissez-faire Hoover, but it also bypassed needy Americans to bolster industrial and financial interests. New York congressman Fiorello LaGuardia, who later served as mayor of New York City, captured public sentiment when he denounced the RFC as a “millionaire’s dole.” 12


6.5: Bone Formation and Development
By the end of this section, you will be able to:
- Explain the function of cartilage
- List the steps of intramembranous ossification
- List the steps of endochondral ossification
- Explain the growth activity at the epiphyseal plate
- Compare and contrast the processes of modeling and remodeling
In the early stages of embryonic development, the embryo’s skeleton consists of fibrous membranes and hyaline cartilage. By the sixth or seventh week of embryonic life, the actual process of bone development, ossification (osteogenesis), begins. There are two osteogenic pathways—intramembranous ossification and endochondral ossification—but bone is the same regardless of the pathway that produces it.
Cartilage Templates
Bone is a replacement tissue; that is, it uses a model tissue on which to lay down its mineral matrix. For skeletal development, the most common template is cartilage. During fetal development, a framework is laid down that determines where bones will form. This framework is a flexible, semi-solid matrix produced by chondroblasts and consists of hyaluronic acid, chondroitin sulfate, collagen fibers, and water. As the matrix surrounds and isolates chondroblasts, they are called chondrocytes. Unlike most connective tissues, cartilage is avascular, meaning that it has no blood vessels supplying nutrients and removing metabolic wastes. All of these functions are carried on by diffusion through the matrix. This is why damaged cartilage does not repair itself as readily as most tissues do.
Throughout fetal development and into childhood growth and development, bone forms on the cartilaginous matrix. By the time a fetus is born, most of the cartilage has been replaced with bone. Some additional cartilage will be replaced throughout childhood, and some cartilage remains in the adult skeleton.
Intramembranous Ossification
During intramembranous ossification , compact and spongy bone develops directly from sheets of mesenchymal (undifferentiated) connective tissue. The flat bones of the face, most of the cranial bones, and the clavicles (collarbones) are formed via intramembranous ossification.
The process begins when mesenchymal cells in the embryonic skeleton gather together and begin to differentiate into specialized cells (Figure \(\PageIndex{1}\) a ). Some of these cells will differentiate into capillaries, while others will become osteogenic cells and then osteoblasts. Although they will ultimately be spread out by the formation of bone tissue, early osteoblasts appear in a cluster called an ossification center .
The osteoblasts secrete osteoid , uncalcified matrix, which calcifies (hardens) within a few days as mineral salts are deposited on it, thereby entrapping the osteoblasts within. Once entrapped, the osteoblasts become osteocytes (Figure \(\PageIndex{1}\) b ). As osteoblasts transform into osteocytes, osteogenic cells in the surrounding connective tissue differentiate into new osteoblasts.
Osteoid (unmineralized bone matrix) secreted around the capillaries results in a trabecular matrix, while osteoblasts on the surface of the spongy bone become the periosteum (Figure \(\PageIndex{1}\) c ). The periosteum then creates a protective layer of compact bone superficial to the trabecular bone. The trabecular bone crowds nearby blood vessels, which eventually condense into red marrow (Figure \(\PageIndex{1}\) d ).
Intramembranous ossification begins in utero during fetal development and continues on into adolescence. At birth, the skull and clavicles are not fully ossified nor are the sutures of the skull closed. This allows the skull and shoulders to deform during passage through the birth canal. The last bones to ossify via intramembranous ossification are the flat bones of the face, which reach their adult size at the end of the adolescent growth spurt.
Endochondral Ossification
In endochondral ossification , bone develops by replacing hyaline cartilage. Cartilage does not become bone. Instead, cartilage serves as a template to be completely replaced by new bone. Endochondral ossification takes much longer than intramembranous ossification. Bones at the base of the skull and long bones form via endochondral ossification.
In a long bone, for example, at about 6 to 8 weeks after conception, some of the mesenchymal cells differentiate into chondrocytes (cartilage cells) that form the cartilaginous skeletal precursor of the bones (Figure \(\PageIndex{2}\) a ). Soon after, the perichondrium , a membrane that covers the cartilage, appears Figure \(\PageIndex{2}\) b ).
As more matrix is produced, the chondrocytes in the center of the cartilaginous model grow in size. As the matrix calcifies, nutrients can no longer reach the chondrocytes. This results in their death and the disintegration of the surrounding cartilage. Blood vessels invade the resulting spaces, not only enlarging the cavities but also carrying osteogenic cells with them, many of which will become osteoblasts. These enlarging spaces eventually combine to become the medullary cavity.
As the cartilage grows, capillaries penetrate it. This penetration initiates the transformation of the perichondrium into the bone-producing periosteum. Here, the osteoblasts form a periosteal collar of compact bone around the cartilage of the diaphysis. By the second or third month of fetal life, bone cell development and ossification ramps up and creates the primary ossification center , a region deep in the periosteal collar where ossification begins (Figure 6.17 c ).
While these deep changes are occurring, chondrocytes and cartilage continue to grow at the ends of the bone (the future epiphyses), which increases the bone’s length at the same time bone is replacing cartilage in the diaphyses. By the time the fetal skeleton is fully formed, cartilage only remains at the joint surface as articular cartilage and between the diaphysis and epiphysis as the epiphyseal plate, the latter of which is responsible for the longitudinal growth of bones. After birth, this same sequence of events (matrix mineralization, death of chondrocytes, invasion of blood vessels from the periosteum, and seeding with osteogenic cells that become osteoblasts) occurs in the epiphyseal regions, and each of these centers of activity is referred to as a secondary ossification center (Figure 6.17 e ).
How Bones Grow in Length
The epiphyseal plate is the area of growth in a long bone. It is a layer of hyaline cartilage where ossification occurs in immature bones. On the epiphyseal side of the epiphyseal plate, cartilage is formed. On the diaphyseal side, cartilage is ossified, and the diaphysis grows in length. The epiphyseal plate is composed of four zones of cells and activity (Figure \(\PageIndex{3}\)). The reserve zone is the region closest to the epiphyseal end of the plate and contains small chondrocytes within the matrix. These chondrocytes do not participate in bone growth but secure the epiphyseal plate to the osseous tissue of the epiphysis.
The proliferative zone is the next layer toward the diaphysis and contains stacks of slightly larger chondrocytes. It makes new chondrocytes (via mitosis) to replace those that die at the diaphyseal end of the plate. Chondrocytes in the next layer, the zone of maturation and hypertrophy , are older and larger than those in the proliferative zone. The more mature cells are situated closer to the diaphyseal end of the plate. The longitudinal growth of bone is a result of cellular division in the proliferative zone and the maturation of cells in the zone of maturation and hypertrophy.
Most of the chondrocytes in the zone of calcified matrix , the zone closest to the diaphysis, are dead because the matrix around them has calcified. Capillaries and osteoblasts from the diaphysis penetrate this zone, and the osteoblasts secrete bone tissue on the remaining calcified cartilage. Thus, the zone of calcified matrix connects the epiphyseal plate to the diaphysis. A bone grows in length when osseous tissue is added to the diaphysis.
Bones continue to grow in length until early adulthood. The rate of growth is controlled by hormones, which will be discussed later. When the chondrocytes in the epiphyseal plate cease their proliferation and bone replaces the cartilage, longitudinal growth stops. All that remains of the epiphyseal plate is the epiphyseal line (Figure \(\PageIndex{4}\)).
How Bones Grow in Diameter
While bones are increasing in length, they are also increasing in diameter; growth in diameter can continue even after longitudinal growth ceases. This is called appositional growth. Osteoclasts resorb old bone that lines the medullary cavity, while osteoblasts, via intramembranous ossification, produce new bone tissue beneath the periosteum. The erosion of old bone along the medullary cavity and the deposition of new bone beneath the periosteum not only increase the diameter of the diaphysis but also increase the diameter of the medullary cavity. This process is called modeling .
Bone Remodeling
The process in which matrix is resorbed on one surface of a bone and deposited on another is known as bone modeling. Modeling primarily takes place during a bone’s growth. However, in adult life, bone undergoes remodeling , in which resorption of old or damaged bone takes place on the same surface where osteoblasts lay new bone to replace that which is resorbed. Injury, exercise, and other activities lead to remodeling. Those influences are discussed later in the chapter, but even without injury or exercise, about 5 to 10 percent of the skeleton is remodeled annually just by destroying old bone and renewing it with fresh bone.
Diseases of the...
Skeletal System
Osteogenesis imperfecta (OI) is a genetic disease in which bones do not form properly and therefore are fragile and break easily. It is also called brittle bone disease. The disease is present from birth and affects a person throughout life.
The genetic mutation that causes OI affects the body’s production of collagen, one of the critical components of bone matrix. The severity of the disease can range from mild to severe. Those with the most severe forms of the disease sustain many more fractures than those with a mild form. Frequent and multiple fractures typically lead to bone deformities and short stature. Bowing of the long bones and curvature of the spine are also common in people afflicted with OI. Curvature of the spine makes breathing difficult because the lungs are compressed.
Because collagen is such an important structural protein in many parts of the body, people with OI may also experience fragile skin, weak muscles, loose joints, easy bruising, frequent nosebleeds, brittle teeth, blue sclera, and hearing loss. There is no known cure for OI. Treatment focuses on helping the person retain as much independence as possible while minimizing fractures and maximizing mobility. Toward that end, safe exercises, like swimming, in which the body is less likely to experience collisions or compressive forces, are recommended. Braces to support legs, ankles, knees, and wrists are used as needed. Canes, walkers, or wheelchairs can also help compensate for weaknesses.
When bones do break, casts, splints, or wraps are used. In some cases, metal rods may be surgically implanted into the long bones of the arms and legs. Research is currently being conducted on using bisphosphonates to treat OI. Smoking and being overweight are especially risky in people with OI, since smoking is known to weaken bones, and extra body weight puts additional stress on the bones.
Interactive Link
Watch this video to see how a bone grows.


8.6: Photon Used to Create Mass
proton hits proton, creates proton-antiproton pair
Particles other than the photon can also create particles. A particle of any type can carry enough energy to create particles similar to or different from itself. Each such creation must not only follow momenergy conservation laws of special relativity, but is also subject to the law of conservation of total electric charge and other conservation laws, as described in elementary particle physics.
Any energetic particle can create other particles
This is not a textbook of particle physics, but our examples include interactions between common particles. Here are brief descriptions of some of them.
Electron
Electrons form the outer structure of every atom and rattle around in approximately \(99.99999999999\) percent of its volume. The mass of the electrons of an atom, however, accounts for only about one two-thousandth of its mass or less. The electron carries a negative "elementary" electrical charge. Every accepted theory of particle physics treats the electron itself as an elementary particle - it is not made up of anything more fundamental. The positron is the antiparticle of the electron, with the same mass but a positive elementary charge. When positron and electron meet, sooner or later they mutually annihilate, yielding two or more high-energy photons (gamma rays). This will be the fate of the positron and one of the electrons in the polyelectron discussed in Section \(8.5\) soon after they begin to orbit one another.
Proton
The proton (Greek for "the first one’") is, with the neutron, the most massive constituent of atomic nuclei. The sirnplest atom, hydrogen, in its most abundant form has a single proton as nucleus. The proton has a positive charge equal in magnitude to that of the electron, but a mass almost two thousand times as great as that of the electron. As far as we know the proton is stable; experiments have shown its lifetime to be greater than \(10^{31}\) years - very much longer than the current age of the universe (about \(10^{10}\) years). Particle physicists postulate that protons (and neutrons) are composed of still-moreelementary particles called quarks. The antiproton, antiparticle of the proton, has mass equal to that of the proton but negative unit charge. When it encounters a proton, the two particles annihilate, sometimes creating gamma rays but more often other particles not listed in this box.
Neutron
The neutron (from Latin neuter - "neither’" ; neither positively nor negatively charged) is similar to the proton but has no charge and has slightly greater mass. It is a constituent of all nuclei except for the most abundant form of elementary hydrogen. When not in a nucleus, the neutron decays into a proton, electron, and neutrino with half-life of about 10 minutes.
Photon
The photon, the quantum of light, has zero mass. Its properties are described in Section 8.4.
Neutrino
There are several kinds of neutrinos, all of which appear to have zero mass and to move at light speed. The neutrino (ltalian for "little neutral one"’) has no charge and interacts only weakly with ordinary matter: Neutrinos of certain energies can pass through a block of lead one light-year thick with only a \(50-50\) chance of being absorbed! An immense flux of neutrinos passes continually through our bodies without injuring us. "Ten million trillion \(\left[10^{19}\right]\) neutrinos will speed harmlessly through your brain and body in the time it takes to read this sentence. By the time you have read this sentence, they will be farther away than the moon."
Threshold energy defined
Figure \(\PageIndex{1}\) shows "the creation of a proton-antiproton pair by a proton in the presence of another proton." "The antiproton has mass equal to that of the proton but carries a negative unit charge (Box 8-1). The interaction shown leaves all four resulting particles moving along together. The resulting particles stay together when the incoming particle has the lowest energy that can create the additional pair. This minimum energy is called the threshold energy. We don’t want the four particles to move apart after the creation. If they did, we would have to supply the incoming particle with additional kinetic energy. It would have to carry an energy greater than the threshold energy. We discuss here the threshold energy of the incoming proton.
Magnitudes of the momenergy vectors displayed in Figure \(8-9\) are expressed in " "natural units" for the proton, namely the mass of the proton itself, \(1.67 \times 10^{-27}\) kilograms or \(938.27 \mathrm{MeV}\) . This time the numbers are not all integers: the momentum of the system has a value equal to the square root of 48, or \(6.928\) proton masses.
"Efficiency" of particle production
The creation of a proton - antiproton pair by a PROTON requires a total of eight proton units of energy to create two proton units of mass. In contrast the creation of an electron-antielectron pair by a PHOTON requires a total of only four electron units of energy to create two electron units of mass. Why is the photon process so much more efficient (in units of mass of the struck particle) than the proton process? Answer: The photon is annihilated in the creation process. In contrast, the incoming proton is not annihilated; the bookkeeper must keep the incoming proton on the payroll, providing momenergy after the collision to keep the proton in step with the other three particles. This after-collision momenergy of the proton is not available to be applied to other products of the collision. Therefore a proton of given total energy can create less mass than a photon of the same energy when each strikes a stationary target.
1


4.8: Transcultural Nursing Care Models
Cultural Competence Models
- Burchum JLR; Cultural competence: Evolutionary dimension.
- Campinha-Bacote J; Cultural competence in providing health care services: Culturally adequate care model.
- Cross T., Bazron B; Dennis K., Isaacs M.; Towards a culturally adequate care process: Effective services for minority children with emotionally serious illness.
- Kim-Godwin YS; Clarke PN & Barton L.; Providing culturally adequate public care model.
- Leininger MM; The differences in cultural care and the theory of universality.
- Leininger M; Cultural care theory and ethnocentric research method.
- Leininger M; Evaluation of culture care for appropriate and adequate practices.
- Orque M.; Orque’s ethnic/cultural system: Conceptual framework for ethnic nursing care.
- Pacquiao DF; Cultural competence in ethical decision making.
- Papadopoulos I. & Lees S; Training culturally competent researchers.
- Purnell LD. & Amp; Paulanka BJ; Ppur model for cultural competence.
- Suh EE; Cultural competence model through evolutionary concept analysis.
- Wells M; Beyond cultural competence: a model for individual and institutional cultural development [ 4 , 46 ].
Cultural Assessment Models
- Giger JN. & Davidhizar RE; Transcultural nursing; Evaluation and intervention
- Spector RE; Cultural difference in health and disease.
Cultural Assessment Guidelines
- Andrews MM; Culturally adequate nursing care.
- Andrews MM; History of health and cultural competence in physical examination.
- Bloch B; Bloch’s assessment guide for ethnic/cultural diversity.
- Boyle JS & Andrews MM; Andrews/Boyle assessment guide.
- Spector RE; Cultural care: guidelines for inheritance, assessment and health traditions [ 4 , 46 ].
The conceptualization of the cultural competence model in nursing has emerged after 1989. Leininger, Campinha-Bacote, Giger and Davidhizar, Orque, Purnell and Paulanka, Spector, Andrews and Boyle are regarded as the pioneers contributing to the accumulation of the relevant data. Orque is a leading figure in developing a cultural model for nursing with “the conceptual framework of the ethnic system”. The use of nursing theories and models in nursing researches offers unparalleled contribution to the health care system through the practices of the nurse as a professional. Cultural competence models developed by nurse researchers can be transferred not only to nursing but also to other disciplines.
Leininger describes transcultural nursing as a branch of nursing or nursing school based on comparative research and analysis of different cultures which provides cultural universalism and cultural independence in nursing care and focuses on comparative studies and analyzing differences in cultures around the world in a respectful manner in view of health, illness, care, beliefs and values [ 3 , 5 , 13 ].
The aims of transcultural nursing are to provide sensitive and effective nursing care to meet the cultural needs of individuals, families and groups, to integrate transcultural concepts, theories and practices into nursing education, research and clinical applications, to improve transcultural nursing knowledge, and to incorporate this knowledge into nursing practice.
The International Nurses Association (ICN) invited the nurses from the World Health Organization (WHO) member countries to work on adaptable models to their communities at the 1989 Seoul Conference. The studies conducted in Turkey show that the nurses need to have classification lists and guidelines to be used in care, and thus a more systematic care will be provided in less time for individual patients and more data will be collected. In Turkey internationally developed models and classification systems in nursing care are translated into Turkish, or new guidelines specific to clinics are developed and used. These include NANDA’s diagnosis, Gordon’s Functional Health Patterns, NIC, NOC and Daily Living Activities and the OMAHA system [ 55 ].
The use of transcultural nursing models, classification systems and guidelines is becoming widespread. These models focus on the relationship of nursing to concepts and theories related to life, health, disease and society, facilitate organizing their thoughts, and provide a common language among professional members.
While there has been an increased awareness of the importance of cultural care and collecting cultural data in recent years in Turkey, no models or guides have been developed in Turkey [ 55 ].
These Models
Leininger’s Sunrise Model
The “Culture Care Diversity and Universality” theory developed by Leininger in 1960, the first nurse who made the first work in this field and received the title of anthropologist, is the first theory developed in the field of transcultural nursing and still used worldwide. This theory focuses on exploring different and universal cultures and providing comparative care. It adopts a multi-factorial approach affecting health and care such as environmental conditions, ethnography, language, gender, class, racism, social structuring, belief, politics, economics, kinship, technology, culture and philosophy. This model includes technological, religious and philosophical, kinship and social factors, cultural values and lifestyle, political and legal, economic and social factors [ 50 ], which have been used in many studies in the west and in other countries since 1960 (Figure 4.8.1).
Narayanasamy’s ACCESS Model
Narayanasamy described the model in 1998 with the letters ACCESS (Assessment, Communication, Cultural negotiations and Compromise, Establishing respect, Sensitivity and Safety) to form the framework of cultural care practices [ 42 ] (Table 1).
| Transkültürel Hemşirelik | |
|---|---|
| Assessment | Culturally focusing on the patient’s life style, beliefs and practices related to health |
| Communication | Awareness of the variety of verbal and nonverbal reactions |
| Cultural Negotiation and Compromise | Becoming more aware of the other people’s cultures and exploring their problems as well as understanding the patient’s opinion, |
| Respect | Describing therapeutic relationship relevant to the patient’s cultural beliefs and consensus values |
| Sensitivity | Applying the sensitive care model to culturally different groups |
| Safety | Making the patient feel safe in the culturally sensitive care |
Table 1: Narayanasamy’s ACCESS model (1998).
Reference: [ 2 ].
Giger and Davidhizar’s Trans-cultural Assessment Model
The model developed in 1988 was first published in 1990. This model is a tool developed to assess cultural values and their effects on health and disease behavior [ 33 ] (Figure 4.8.2).
Purnell’s Cultural Competence Model
This ethnographic model created to promote cultural understanding of people’s status in the context of health promotion and illness is based on ethical perspectives of individual, family and community. It can be used in primary, secondary and tertiary protection stages [ 56 ] (Figure 4.8.3).
Nurses’ Competence to Provide Trans-cultural Care
- Having the ability to understand complex cultural dimensions,
- Assuming a holistic approach to care instead of biophysical approach,
- Showing efforts to reach rapidly increasing cultural beliefs and activities that are unique to distinct groups and individuals
- Being able to change the idea of believing that individuals’ own race is superior to others,
- Being able to make cultural evaluations,
- Developing communicative and scientific language skills,
- Being able to deal with cultural differences in real terms and make interpretations,
- Being able to use appropriate cultural teaching techniques
- Compromising cultural beliefs and studies with the general state of provision of health care,
- Respecting for the sociocultural diversity of women, newborn babies and their families [ 8 , 57 ].


1.14: A Kiss Is Just a Kiss - The Impossibility of Sexual Communication
-
- Last updated
- Save as PDF
Learning Objectives
- Recognize that the conventional view that sex as a form of communication is false and misleading.
Watch this video or scan the QR code to learn more about sexual communication in relationships.
“The Impossibility of Sexual Communication” does not mean communication about sex or about feelings is impossible and I will address that at the end. I am simply claiming at the beginning that communication by means of sex is impossible.
Regardless of almost all the most recent popular beliefs and articles on the topic, sex (or any touching) is not a form of communication! It does not communicate love, care, concern, tender feelings, or anything. (One can imagine a Bert Reynolds or Richard Pryor movie scene where either of them meets some beautiful, but insecure, woman who very soon asks him to show her he cares about her — by making love to her. Surely Reynolds or Pryor would be able to give the camera one of their most devilish, gleaming smirks. I would claim that the absurdity of the request as a demonstration of caring or love is not diminished by occurring instead on the third or eighth date or on the wedding night or thereafter.) Neither is bad sex or no sex a communication of lack of love, lack of concern, lack of tender feelings, or whatever. Sex is not an expression of anything, let alone of love. Further, I think it is risky and potentially harmful to believe that it is.
How one touches another is probably a matter of both inborn and early personality and early learning that continues to develop to some extent through one’s lifetime. How you are touched as a child and how your parents teach you to touch pets and other people will probably have a great deal of bearing on how you touch others, both sexually and non-sexually as an adult. In regard specifically to sex, what you learn about style or technique and in some cases even your goals, point of view, or intentions for sex will depend a lot on what you read and hear and on what your partner(s) teaches you — perhaps in direct verbal teaching, but possibly even more so by response to your efforts. If one has the proper curiosity, if one has the proper sensitivity to different ways of touching and being touched, caressed, and massaged, if one has the proper attitude of at least wanting to please the other person, and the sensitivity or sense to look for clues to their response, if one learns by being with someone who is demonstrably (and therefore educationally) responsive and positively reinforcing to your touching them in pleasing ways, then one is likely to learn more pleasing “technique” — that is, personal style. With the wrong inborn personality, bad early training, lack of knowledge, and/or not particularly instructive or responsive partner(s), one’s natural touch is not likely to be or appear particularly loving, regardless of how one feels about their partner or what one intends. And various combinations of inborn and developed personality and training will help cause someone to be that much “better” or “worse” a lover, along with whatever their feelings or intentions are at any given time with any given partner. It is not just your feelings or intentions alone that determine what sort of lover you are or what sort of touch you have.
This is not to say there is a standard set of directions for how to make love to every person or to any given person each time. Different people like different things; some people like different things at different times. But also, different people learn different things and have different instincts about touching. Some people will be more gentle, others more rough; some more responsive to their partner’s needs than others; some more responding to their partner’s actions, some more communicative or demonstrative about what they enjoy; some will be more open to change; others, more desirous of certain patterns; some will have a lighter touch, others will be more forcefully massaging, others able to vary their touch; some will be clumsy and fumbling, others very smooth; some will be comfortable and comforting. And this is apart from what they are thinking and how they feel about their partner.
Whatever one’s ability to please or displease one’s partner probably says too little in general to signal communication either of love or of the lack of it. Selfish playboy seducers or selfish playgirl seductresses —with only the moment and their own desires on their minds may have little love for their partner, but their actions might be quite gentle and stimulating. And on the other hand, there are certainly plenty of people who love others but who have little idea of how to please their loved one sexually, and who therefore may appear in bed either to be rough, unloving, insensitive, or stupid, though none of those may be the case.
A tender kiss is not necessarily a sign of tender feelings. It may be just the way, for whatever reason, that person kisses. Some people kiss better than others. They might be able to send a shiver down the spine of almost anyone they kiss; more people who kiss them might enjoy it better. At a charity kissing booth, they might make lots more money than anyone else. But that is not a sign in any way that they are feeling particularly loving toward, or in love with, whom they kiss. And it does not mean that in general, they are more loving than anyone who does not kiss as well. Kissing and touching are arts. They depend on knowledge, sensitivity to the moment and to one’s own and the other person’s textures and pressures, positioning, timing, etc.
How one touches, kisses, manipulates, or has intercourse is not necessarily any sort of sign of any inner feeling. It is simply a sign of how that person makes love to you at that moment, given the way you kiss, play with, caress, respond to, and have intercourse with him or her. And since there is no guarantee or even a social convention that kissing, touching, or making love in a certain way is a sign of loving feelings, it does not have to be. A person might kiss you (in a certain way) for any number of reasons. The reason they have might not be that they are intending to tell you they love you. You’re taking it that way would be your misunderstanding, not their lying or even (intentionally) deceiving you. Someone might kiss you out of gratitude, lust, loneliness, friendly affection, simple fondness, pity, experimentation, a test of how you will react, to say good night, because they think you expect or want them to, or whatever.
Taking tender (or however), pleasant, “loving” gestures as a sign of loving feelings and being correct about it is still not understanding communication. Communications are messages a communicator tries to send, not just anything someone thinks they perceive is being said or sent, even if the content, of what they infer or mistakenly think is being said, is true.  When you are right it is because you are perceptive, not because the other person has (intentionally) told you anything; and when you are wrong, it is because you made an error, not because they made an error or lied to you. If someone tries to hide pain from you, for example, but you can tell anyway that they are in pain, it is not because they have told you about their pain, but because you were perceptive enough to discover it for yourself. Communication involves some sort of intention, by the teller, to convey meaning in some sort of conventional manner. Communication involves both an intention (to make something known) and convention (as a means of expressing it). Any action can be a sign of things — babies can signify pain by crying — but such non-conventional signs can often signify almost anything (in the baby’s case, hunger, thirst, pain, overtiredness, gas, wet diapers, being too hot or too cold, loneliness, boredom…), and therefore they are not communication in the normal sense. The meteorologist can forecast the weather from certain signs, but that is not because nature is communicating with him. A baseball batter may guess what pitch a pitcher with bad telegraphing habits is about to pitch to him, but the pitcher is certainly not trying to tell, nor in the normal sense telling, the batter what pitch he is going to throw as if they had met beforehand and fixed the game. One cannot tell whether his or her partner has cooked one’s favorite meal because he or she has wrecked the car or has some other bad news, has no other food in the house, wants that meal themself, has good news, is feeling loving, or just thought it was time to have it again. Actions like those can be a sign of anything or nothing and therefore are not communication at all.
A person who would rely only on such non-conventional signs is very likely to end up in trouble. For example, a person who assumes his spouse no longer loves him because she no longer often kisses him might not find out until he has made damaging accusations (or actions) that something outside the relationship is simply troubling her or that she does not feel well. Likewise, a girl who thinks she is loved because she is kissed or gently touched or made love to in a nice way may be quite drastically mistaken. There are an abundant number of short stories and television and movie plots where mistaken or misinterpreted “communications” cause harm. Many of these are simply reflections of the kinds of mistakes that occur in real life.
One more argument that “loving” body language is not communication is the following one: Consider the baseball pitcher who telegraphs his pitches. Suppose he, either purposely or unintentionally, telegraphs the pitch that he does not throw. Say, he telegraphs fastball but throws the slider. If the batter has read the telegraphed signal and sets for the wrong pitch and strikes out, he may have been fooled or deceived, or he may have deceived himself — but he was not lied to. He could have no grounds and would appear crazy or a fool, to claim to the press later that he had struck out because the pitcher had lied to him about what he was going to throw. But if reading such signals is communication, he would have been lied to if the pitcher had intentionally telegraphed the wrong pitch. But even in reality, if a pitcher intentionally telegraphs a wrong pitch to a batter, the pitcher is only trying to trick or deceive the batter, not lie to him. (All lies may be tricks or deceptions, but not all tricks or deceptions are lies.) Hence, reading such signals or making them is not communicating.
Regarding “loving” body language: if a person tells someone he loves them when he knows he does not, this is lying. But kissing a person one does not love (such as out of sympathy or pity, as a very polite way of saying good night, just out of lust or loneliness or appreciation, or simple fondness) is not lying, nor is it even necessarily deceiving them. In this day and age of so much casual sex, one who reads love into every kiss might even be guilty of self-deception. Now, it would be self-contradictory to tell someone you love them but you do not love them.
But there is no contradiction in tenderly kissing someone and then telling them you do not love them and you want them to understand you did it because you just wanted to kiss them, because you feel affection but not love for them, because you were drunk, because you felt lustful, because you meant it as a good night gesture, or because you just wanted to be friends. Since this would not be a contradiction, a kiss cannot mean love.
It seems to me that it is terribly important that people understand what sex means both to themself and to the other person, preferably before engaging in it, if they want to have a better chance of avoiding harmful misunderstandings. And the best way to find out what it means to each other is to discuss it in words . Then you are actually communicating what sex means to you — how you feel about it, why you want to have it, why you think it is right to have it with that person now, how you think you are likely to respond tomorrow to having it today, how you feel about the person, what you expect, want, or think about the relationship, etc. Such a discussion might give a better understanding than guessing about body language, particularly guessing in the dark. Sexual intimacy for most people, even in this day and age, is still a very important kind of experience, and it can be devastating if one later finds out it did not have the kind of meaning or importance for the other person that it did for you and that you thought it had and wanted it to have for him or her.
When I taught classes and discussed love as a philosophy topic, I often said that I thought there was nothing wrong in asking someone after a kiss why they kissed you, particularly the first time or on a first date. Two students in the past have objected to the idea. One, a former sailor said, “hell, you don’t need to ask and spoil the mood. When you came off the ship in a port and all those girls were standing around saying ‘hey, sailor, you want to have a good time?’ you knew there was no love involved on either side. The only point is you are also trying not to get money involved either, though that is what she wants.” Maybe so, but such a case is hardly the normal circumstances for a first kiss, caress, or passion with someone you are going out with; I had not exactly been (nor am I now) talking about dates between sailors and wharf- walkers. The other student said that asking for the reason for a kiss even on a date would spoil the mood, ruin the romance, be embarrassing, and cost you any further kisses, sex, or loving responses. I replied that happened sometimes but was rarer than the times it helped you gain an understanding of each other and made it even more desirable and nice. He just shook his head and said he could not imagine his ever asking anything like that at such a time. Then it happened to him. He came into class one day and said a girl he went out with over the weekend kissed him and asked him why he had kissed her, what it had meant to him. I and the rest of the class were very interested in his reply and what happened. But he said he was so flabbergasted by the fact she had asked him that the only thing he could think to say was to ask whether she had taken my course. She hadn’t. (Had never kissed me either.)
At any rate, kissing or holding hands or even more intimate sex can be for any number of motives and can mean almost anything.   But whether they do or not, at least you will not be deceiving yourself into thinking it has a meaning that is in no way intended. And you will avoid any accidental misunderstandings. There may not be anything wrong with two particular, mature people making love with each other with both knowing they are doing so simply because they want to and have had a nice time together and are in the mood and that it portends nothing in terms of commitment for either in the future (assuming also there is nothing else in their circumstances, such as one of them having venereal disease or being married to someone who does not deserve being cheated on, etc., that would make the act wrong). But there is something wrong (all other things being equal) with it when one thinks it means much more to the other than it actually does. And it may be easily prevented if they discuss the matter ahead of time, particularly if both are honest.
Of course, a perceptive person takes more than the other person’s word into account, since perhaps they are lying or perhaps (and this can be quite likely with less experienced people) deceiving themselves about what it means to them. A naive, innocent young person may be more vulnerable to, and later hurt by, being loved and left than they honestly think they will be. Discussion is still better than no discussion; at least it can help prevent unintentional misunderstanding, and it may help uncover deception or self-deception before (more) harm is done.
Sometimes people think sex is the only way they can show concern or loving feelings, but this is false. You can always tell someone you love them and how you feel about them, even in difficult or complicated cases. At the very least, even if you are not good at describing your feelings, you could describe to them how you would like to act, rather than acting that way without talking. Saying you would like to kiss or cuddle or make love to someone tells as much (or more) than does trying to kiss them, hug them, or actually kissing them or hugging them. Suppose you have certain desires for another, but desires you feel would best not be acted upon or fulfilled. It seems to me that rather than simply stifling or ignoring such desires and saying nothing to the other person, one might, at an appropriate time, simply verbally express the desire by saying something like: “gee, I really would like to (go to the dance with you, kiss you, play tennis with you, discuss politics with you, make love to you, etc.) but I don’t think I ought to (or cannot now) because ….” This way the other person can at least know that you care about them in certain ways. Sometimes that is important. They may thank you for your comments or say they feel the same way, or they may disagree about the correctness of abstinence. They may even say that they do not feel the same way, at least not at this time. They could also, if they are not nice or understanding, get angry or hostile, but this probably will not usually happen; if it did, it might show you they were not “made in heaven” for you anyway.
Of course, talking is not necessarily romantic even if you are telling someone how much you love them (especially if you do not say it very well), but romance is not always (or perhaps ever) communication. The two are different and may be appropriate at different times. Sometimes, it is more appropriate to communicate, and sometimes it is more important to be romantic, to touch, and/or to be passionate. The point is not to confuse romance, touching, or passion with communication.
There have been a number of girls I have loved in the sense of having passionate, romantic attractions toward, and with whom I got along very well and satisfyingly in many ways, but with whom the sexual activity of varying degree would have been a bad idea for various reasons, even though desired. It was often very important to talk about this with them or at least to talk around the subject in such a way as to make each others’ feelings and intentions known. This often added much to the relationship. If you love someone or miss someone or want someone, but know that having them would not be for the best for each other, there is nothing wrong, and there can be something beautiful, in telling them that, rather than in just ignoring the desires or pretending to the other that those desires are non-existent.
One of my closest and fondest loves was a girl who was already engaged to someone when I met her. We never kissed. But we spent hours talking and walking. We knew how we felt about each other because of the things we said to each other. That knowledge enriched our relationship and our lives. We probably would have married each other, had she not already been committed to another, whom she also loved; and he and she were very good for each other. Our relationship took nothing away from their commitment and their relationship. Her other love and marriage to him took nothing away from our friendship or our feelings for each other.
Some of the closest people are those who have grown old loving each other but behaving simply as loving friends because they were committed (at least to be faithful sexually) to others or because sexual activity of whatever sort might not have been right for some other reason. Still, they could communicate (verbally – by telling or writing) to each other their feelings without trying to do it by making a pass, kissing, or having any degree of sex. Just as sex is not a form of communication about feelings and concerns, words about those feelings and concerns can be a communication without sex. And it can be an important and enriching communication.
One example is Stephen Thayer’s “Close Encounters”: “…touch is the most powerful of all the communication channels — and the most carefully guarded and regulated” (Thayer, 1988). Thayer then goes on to point out five categories of touching: functional-professional (where “touch must be devoid of personal messages”), social- polite (e.g., handshake), friendship- warmth, love-intimacy, sexual-arousal. However, I believe it is not the kind of touch that communicates or carries a message, but the social, verbal, and/or logical aspects of the circumstances in which the touch occurs. A woman patient of a male gynecologist, during a breast examination, for example, would, of course generally be upset and draw back if the doctor, while touching her, said “You know I find you very exciting.” But it would be just as shocking and upsetting if he said it before he touched her. It is not the manner of his touch, but the inappropriateness of his remarks and the uncertainty of what his actions and intentions will be in that kind of vulnerable situation that is upsetting. Or suppose after a normal, professional breast examination, a doctor thinks he may have missed or ignored something. The appropriate action would be to schedule another appointment, not to mention it to the woman at a party they both happen to attend and suggest she let him check her breasts again in a back bedroom. Not because his touch might be any different but because the circumstances or social/emotional “logic” of the situation is meaningful. Or consider a neck massage; it could be given by a professional masseuse, a physical therapist, a nurse, a fellow co-worker (or even a stranger) who sees someone in obvious discomfort huddled over a computer, a lover, one’s mother, or whatever. The massage itself may be indistinguishable whether given by one person or by another; it is the circumstances in which it is given, and the understood relationship between the people, that contributes to the emotional “feeling”, or non-feeling accompanying the massage.  Yet his touch (of her neck) may be the same as when he hopes to sexually arouse her. And the way she responds to the massage will have to do with the context in which it occurs, and with how she feels at the time. Even in the bedroom, if she is angry with him about something, or feeling particularly dispassionate, she may not even be relaxed by his neck massage, let alone aroused. It is not the way someone touches you that means anything in the way communication does; it is the appropriateness of touch in the context of a given situation and in the context of the relationship (at that moment) between the touchers that is important. Even being hit by someone does not, by itself without a context or an accompanying verbal message, tell you why they hit you or what it means. They could even have mistaken you for someone else or assumed incorrectly that you did something terrible.
Of course, touch can be meaningful in a given context; but it is meaningful in the sense of “significant” or “important” or just “highly irregular or unusual”, or “terribly inappropriate”, not in the sense of conveying any specific message. If a stranger were to try to feel a woman’s breasts for lumps or if her doctor were to caress her breasts rather than medically examine them, it would be meaningful in the former sense, not the latter. If she says “What is the meaning of this!” or “What are you doing!”, she is expressing indignation or moral outrage at what he is doing, not at how he is doing it. And she is certainly not simply asking a literal question. But such a sense or use of meaning is not peculiar to touching. If a teacher were to be intentionally teaching French in the class he is supposed to be teaching geometry, that would be meaningful and questionable in the same way.
Touch can also be beneficial, right, reassuring, or otherwise appropriate — it can be meaningful in a good way. Thayer’s article points out a number of such possible situations. But whether touching is right or beneficial or not depends on the circumstances and the consequences. It depends on a number of factors, but communication — what the touch means, which by itself is nothing — is not one of them.
Key Takeaways
- Since sex is neither necessary nor sufficient for love, sex cannot communicate love. Insofar as one thinks that sex is a sign of love, one is inferring it, and might be right or wrong. Incorrect inferences are not miscommunications nor signs of lies.
- There is nothing inconsistent about having sex with someone and telling him or her you are not in love with them. Although disappointing, it is not a sign of lying nor necessarily even a sign of deceit.
- While some people may never be willing to have sex with someone they do not love, that is not guaranteed, and at best shows that sex for them implies they love their partner, but it is not the same as a communicated pronouncement or declaration of love.
Key Terms
- Communication involves a conventional mutually understood (even if imperfectly on various occasions) means of trying to convey ideas or information from one person to another, through some kind of language or symbolism or gestures that have a common meaning. Communication is a complex concept, which distinguishes it from sex.
Review Questions
- Question : What about kissing and touching are arts?
- Question : Why is communication by means of sex impossible? What are the reasons sex is not a form of communication?


2 .
Pair up with another person and teach them how to properly walk with a cane.
3 .
Choose a partner and practice placing each other in common patient positions, including supine (back), Fowler’s (supine, head of the bed raised), orthopneic (tripod pose), prone (stomach), lateral (side-lying), and Sim’s (semiprone). Discuss what feels comfortable or uncomfortable, what parts of the body feel like pressure points, and what you can do to relieve the pressure during position changes.
4 .
Review the competency checklists for this chapter and have a peer or instructor assess your performance of the tasks. You can find the checklists on the Student resources tab of your book page on openstax.org.


10.11: Proficiency Exam
Proficiency Exam
For the quadratic equations in the following problems, specify the values of \(a, b\), and \(c\).
\(2y^2 - 3y + 10 = 0\)
- Answer
-
\(a=2,b=−3,c=10\)
\(10b^2 = 3b\)
- Answer
-
\(a=10,b=−3,c=0\)
For the following problems, use the zero-factor property to solve each quadratic equation.
\((3x+5)(x−1)=0\)
- Answer
-
\(x = -\dfrac{5}{3}, 1\)
\(3b(2b−1)=0\)
- Answer
-
\(b = 0, \dfrac{1}{2}\)
\((a - 8)^2 = 0\)
- Answer
-
\(a=8\)
For the following problems, solve each quadratic equation by factoring.
\(4x^2 - 16 = 0\)
- Answer
-
\(x=−2,2\)
\(y^2 - 12y + 32 = 0\)
- Answer
-
\(y=4,8\)
\(a^2 - 5a = 14\)
- Answer
-
\(−2,7\)
\(6a^2 = 10 - 11a\)
- Answer
-
\(a = -\dfrac{5}{2}, \dfrac{2}{3}\)
\(2x^2 = -2 - 5x\)
- Answer
-
\(x = -2, -\dfrac{1}{2}\)
\(x^3 - 25x = 0\)
- Answer
-
\(x=0,−5,5\)
For the following problems, solve each quadratic equation by extraction of roots.
\(c^2 = 81\)
- Answer
-
\(c=−9,9\)
\(x^2 = 15\)
- Answer
-
\(x = -\sqrt{15}, \sqrt{15}\)
\(3a^2 - 18 = 0\)
- Answer
-
\(a = -\sqrt{6}, \sqrt{6}\)
\((x - 5)^2 = 1\)
- Answer
-
\(x=4,6\)
\((y + 11)^2 - 9 = 0\)
- Answer
-
\(y=−8,−14\)
\(y^2 - 25z^2 = 0\) for \(y\).
- Answer
-
\(y=−5z,5z\)
\(6a^2 - 18b^2c^2\) for \(a\)
- Answer
-
\(a = \pm bc\sqrt{3}\)
For the following problems, solve each quadratic equation using the quadratic formula.
\(x^2 - 6x - 16 = 0\)
- Answer
-
\(x=−2,8\)
\(y^2 - 2y - 7 = 0\)
- Answer
-
\(y = 1 + 2\sqrt{2}\)
\((m + 2)^2 - 5 = 0\)
- Answer
-
\(m = -2 \pm \sqrt{5}\)
\((x + b)^2 = c^2\)
- Answer
-
\(x = -b \pm c\)
\((x+1)(x+4)=6\)
- Answer
-
\(x = \dfrac{-5 \pm \sqrt{33}}{2}\)
\(5z^2 - 5z - 5 = 2z^2 - z\)
- Answer
-
\(z = \dfrac{2 \pm \sqrt{19}}{3}\)
\(2m^2 = 5m\)
- Answer
-
\(m = 0, \dfrac{5}{2}\)
For the following problems, solve each quadratic equation by completing the square.
\(x^2 + 6x - 8 = 0\)
- Answer
-
\(x = -3 \pm \sqrt{17}\)
\(2x^2 + 7x - 12 = 0\)
- Answer
-
\(x = \dfrac{-7 \pm \sqrt{145}}{4}\)
The product of two consecutive odd integers is 143. What are they?
- Answer
-
11 and 13 or −11 and −13
A study of the air quality by an environmental group suggests that t years from now the level of carbon monoxide in the air, in parts per million, will be given by the quadratic equation
\(A = 0.4t^2 + 0.1t + 3.1\)
where \(A\) represents the amount of carbon monoxide in the air.
a) What is the level, in parts per million, of carbon monoxide in the air now?
b) How many years from now will the level of carbon monoxide be at 18.1 parts per million?
- Answer
-
(a) 3.1
(b) 6 years from now
The length of a rectangle is 6 inches longer than the width of the rectangle. Find the dimensions of the rectangle if the area is 112 square feet.
- Answer
-
width: \(\dfrac{-1 + \sqrt{1793}}{4}\)
length: \(\dfrac{1 + \sqrt{1793}}{4}\)
For the following problems, construct the graphs of the following equations.
\(y = x^2 - 3\)
- Answer
-
\(y = (x + 1)^2\)
- Answer
-
\(y = (x-2)^2 + 3\)
- Answer
-
For the following problems, write the equation that corresponds to each graph.
- Answer
-
\(y = (x-2)^2 + 1\) or \(y = x^2 - 4x + 5\)
- Answer
-
\(y = -(x + 3)^2 - 2\) or \(y = -x^2 - 6x - 11\)


Hess' Law and Enthalpy of Formation
Skills to Develop
- Calculate enthalpies of reactions using Hess' Law
- Define "standard state"
What is Hess' Law?
Hess' Law is an early statement of the law of conservation of energy (1840). It says that the heat liberated by a process doesn't depend on how the process happens (only on the starting and ending states: in other words, it's a state function). Now we know we should really use enthalpy for this, not heat, because enthalpy is a state function, so this is true, while heat is a process. Hess' Law lets us break a reaction or process into a series of small, easily measured steps, and then we can add up the ΔH of the steps to find the change in enthalpy of the whole thing. Hess' law is a great way to think about chemical processes and make predictions. We'll see lots of applications of Hess' law, but right now let's start with finding reaction enthalpies using standard enthalpies of formation.
Standard Enthalpies of Formation
Standard enthalpies of formation help us predict reaction enthalpies for many reactions if the products and reactants are well-studied, even if the specific reaction is new. To do this, we imagine that we take the reactants and separate them into their pure elements in a standard state . The standard state is the element in its most stable form at room temperature and atmospheric pressure. Then we take the elements and recombine them to make the products. The reaction enthalpy is equal to the difference in the enthalpies of these processes.
Example
Let's look at a specific example. Here are some enthalpies of formation (in kJ/mol of reaction):
\[C(s) + O_{2}(g) \rightarrow CO_{2}(g)\; \Delta H_{f} = -394\; kJ$$
$$C(s) + 2H_{2}(g) \rightarrow CH_{4}(g)\; \Delta H_{f} = -75\; kJ$$
$$2H_{2}(g) + O_{2}(g) \rightarrow 2H_{2}O(l)\; \Delta H_{f} = -572\; kJ\]
Let's use these enthalpies of formation to calculate the enthalpy of combustion for 1 mol of methane. The reaction we want is
$$CH_{4}(g) + 2O_{2}(g) \rightarrow CO_{2}(g) + 2H_{2}O(g)$$
If we reverse a reaction, we change the sign on ΔH, and if we multiply the reaction by a constant coefficient, we multiply ΔH by the same coefficient. Let's combine the formation constant equations so they add up to the reaction we want:
| CH 4 (g) | → | C(s) + 2H 2 (g) | ΔH f = 75 kJ |
| C(s) + O 2 (g) | → | CO 2 (g) | ΔH f = -394 kJ |
| 2H 2 (g) + O 2 (g) | → | 2H 2 O(l) | ΔH f = -572 kJ |
That's almost right but we're missing the state of the water:
\[H_{2}O(l)\rightarrow H_{2}O(g)\; \Delta H=44\; kJ\]
The full set is
| CH 4 (g) | → | C(s) + 2H 2 (g) | ΔH f = 75 kJ |
| C(s) + O 2 (g) | → | CO 2 (g) | ΔH f = -394 kJ |
| 2H 2 (g) + O 2 (g) | → | 2H 2 O(l) | ΔH f = -572 kJ |
| 2H 2 O(l) | → | 2H 2 O(g) | ΔH f = 88 kJ |
| CH 4 (g) + 2O 2 (g) | → | CO 2 (g) + 2H 2 O(g) | ΔH = ? |
Note that everything but the desired reaction cancels. Now we just add up the enthalpies of each step, and we find that the enthalpy of combustion of 1 mole of methane is -803 kJ.
General Procedure for Hess' Law Calculations
Determine the equation for the desired process (the process for which you want to know the enthalpy change). Break it into steps for which you can look up the enthalpy changes. This probably means steps like formation from elements, and changes of state. (Later, we'll include other processes like ionization, etc) Arrange the steps so that everything cancels out leaving just the desired reaction. Make sure the coefficients on equations are correct (multiply the equation and ΔH by a constant if needed) and that all the components are in the correct state (like the example above, we had to convert from liquid water to gaseous water). Then just add it up!
Outside Links
- Khan Academy: Enthalpy of Formation (12 min)
- Khan Academy: Hess's Law and Reaction Enthalpy Change (16 min)
- Khan Academy: Hess's Law Example (12 min)
- CrashCourse Chemistry: Enthalpy (11 min)


19.15: Spectroscopy of Aldehydes and Ketones
-
- Last updated
- Save as PDF
Objectives
After completing this section, you should be able to
- identify the region of the infrared spectrum in which the carbonyl absorption of aldehydes and ketones is found.
- identify the region of the infrared spectrum in which the two characteristic C$\ce{-}$H absorptions of aldehydes are found.
- use a table of characteristic absorption frequencies to assist in the determination of the structure of an unknown aldehyde or ketone, given its infrared spectrum and other spectral or experimental data.
- identify the region of a proton NMR spectrum in which absorptions caused by the presence of aldehydic protons and protons attached to the α ‑carbon atoms of aldehydes and ketones occur.
- identify two important fragmentations that occur when aliphatic aldehydes and ketones are subjected to analysis by mass spectrometry.
Key Terms
Make certain that you can define, and use in context, the key term below.
- McLafferty rearrangement
Study Notes
The appearance of a strong absorption at 1660–1770 cm −1 in the infrared spectrum of a compound is a clear indication of the presence of a carbonyl group. Although you need not remember the detailed absorptions it is important that you realize that the precise wavenumber of the infrared absorption can often provide some quite specific information about the environment of the carbonyl group in a compound. Notice how conjugation between a carbonyl group and a double bond ( α , β ‑unsaturated aldehyde or ketone or aromatic ring) lowers the absorption by about 25–30 cm −1 .
You may wish to review the McLafferty rearrangement and the alpha cleavage in Section 12.3.
IR Spectra
Ketones
The carbonyl (C=O) stretching vibration band of saturated aliphatic ketones appears at:
- Aliphatic ketones 1715 cm -1
- α , β ‑unsaturated (enone) 1685-1666 cm -1
Figure 8. shows the spectrum of 2-butanone. This is a saturated ketone, and the C=O band appears at 1715.
Aldehyde
In the IR spectra of an aldehyde, a peak usually appears around 2720 cm -1 and often appears as a shoulder-type peak just to the right of the alkyl C–H stretches.
H–C=O stretch 2830-2695 cm -1
C=O stretch
- Aliphatic aldehydes 1740-1720 cm -1
- α , β ‑unsaturated aldehydes (enones) 1710-1685 cm -1
Figure 9. shows the spectrum of butyraldehyde.
1 H NMR Spectra
Hydrogens attached to a carbon adjacent to the sp 2 hybridized carbon in aldehydes and ketones are deshielded due the anisotropy created by the C=O bond and usually show up at 2.0-2.5 ppm.
Aldehyde hydrogens are highly deshielded, appearing far downfield at 9-10 ppm, due the anisotropy created by the pi electrons of the C=O bond, and induction caused by the highly electronegative oxygen atom.
The 1 H NMR spectra of 2-methylpropanal is shown below. The methyl groups, (H b ), show up at 1.1 ppm. The -CH- group is moved downfield due to effect an adjacent aldehyde group (2.4 ppm). The chemical shift of aldehyde hydrogen is highly deshielded (9.6 ppm). Splitting pattern is determined by (N+1) rule: H a is split into two peaks by H b (#of proton=1). H b has the septet pattern by H a (#of proton=6). H c has one peak. (Note that H c has doublet pattern by H b due to vicinal proton-proton coupling.)
13 C NMR Spectra
Aldehydes and ketones have distinctive 13 C NMR peaks which appear in the range 190 to 215 ppm range. Very few types of carbons absorb in this range so the presence of 13 C peak around 200 ppm is considered evidence for a carbonyl group.
Mass Spectra
Aldehydes and ketones generally give moderately intense signals due to their molecular ions, \(\ce{M^+}\). Thus the determination of the molecular weight of a ketone by mass spectroscopy usually is not difficult. Furthermore, there are some characteristic fragmentation patterns that aid in structural identification. These are:
- Formation of the molecular ion:
- \(\alpha\) cleavage to form an acylium ion. This is usually the base peak in the mass spectra.
- A common fragmentation pattern for larger carbonyl compounds is a transfer of \(\gamma\) hydrogen with \(\beta\) cleavage called the McLafferty rearrangement:
The mass spectrum of 2-hexanone shows a 'McLafferty fragment' at m/z = 58, while the propene fragment is not observed because it is a neutral species (remember, only cationic fragments are observed in MS). The base peak in this spectrum is an acylium ion formed after alpha cleavage is at m/z = 43. The molecular ion peak is at m/z =100.
Electronic Absorption Spectra
The absorption at 277 nm for 2-butanone is an n → pi ∗ transition, and with 3-buten-2-one, this absorption shifts to longer wavelengths (324 nm). There is also an intense absorption band for 3-buten-2-one at 219 nm, which is a pi →pi ∗ transition. With 2-butanone a corresponding absorption occurs at 185 nm, which is out of the range of the spectrometer used to take the spectra.
Exercise \(\PageIndex{1}\)
What are the masses of all the components in the following fragmentations?
- Answer
-
Exercise \(\PageIndex{2}\)
A mixture was separated into three fractions: A, B, and C. Elemental analysis reveals that the fractions are structural isomers with the following composition: 69.72% C, 11.70% H, and 18.58% O. The IR spectra for all fractions show several moderate bands around 2950 cm -1 , and a strong band near 1700 cm -1 . The proton and 13 C NMR spectra for each fraction are shown below. Give the common name and draw the bond-line structure for each fraction and correlate the NMR signals with their respective atoms.
- Answer
-


9.3: Points on a common circle
Recall that the diameter of a circle is a chord that passes thru the center. If \([XY]\) is the diameter of a circle with center \(O\), then \(\measuredangle XOY = \pi\). Hence Theorem 9.2.1 implies the following:
Suppose \(\Gamma\) is a circle with the diameter \([AB]\). A triangle \(ABC\) has right angle at \(C\) if and only if \(C \in \Gamma\).
Given four points \(A, B, A'\), and \(B'\), construct a point \(Z\) such that both angles \(AZB\) and \(A'ZB'\) are right.
- Hint
-
Construct the circles \(\Gamma\) and \(\Gamma'\) on the diameters \([AB]\) and \([A'B']\) respectively. By Corollary \(\PageIndex{1}\), any point \(Z\) in the intersection \(\Gamma \cap \Gamma'\) will do.
Let \(\triangle ABC\) be a nondegenerate triangle, \(A'\) and \(B'\) be foot points of altitudes from \(A\) and \(B\) respectfully. Show that the four points \(A, B, A'\), and \(B'\) lie on one circle. What is the center of this circle?
- Hint
-
Note that \(\measuredangle AA'B = \pm \dfrac{\pi}{2}\) and \(\measuredangle AB'B = \pm \dfrac{\pi}{2}\). Then apply Corollary \(\PageIndex{2}\) to \(\square AA'BB'\).
If \(O\) is the center of the circle, then \(\measuredangle AOB \equiv 2 \cdot \measuredangle AA'B \equiv \pi\). That is, \(O\) is the midpoint of \([AB]\).
Assume a line \(\ell\), a circle with its center on \(\ell\) and a point \(P \not\in \ell\) are given. Make a ruler-only construction of the perpendicular to \(\ell\) from \(P\).
- Hint
-
Guess the construction from the diagram. To prove it, apply Theorem 8.2.1 and Corollary \(\PageIndex{1}\).
Suppose that lines \(\ell\), \(m\) and \(n\) pass thru a point \(P\); the lines \(\ell\) and \(m\) are tangent to a circle \(\Gamma\) at \(L\) and \(M\); the line \(n\) intersects \(\Gamma\) at two points \(X\) and \(Y\). Let \(N\) be the midpoint of \([XY]\). Show that the points \(P, L, M\), and \(N\) lie on one circle.
We say that a quadrangle \(ABCD\) is inscribed in circle \(\Gamma\) if all the points \(A, B, C\), and \(D\) lie on \(\Gamma\).
- Hint
-
Denote by \(O\) the center of \(\Gamma\). Use Corollary \(\PageIndex{1}\) to show that the point lie on the circle with diameter \([PO]\).
A nondegenerate quadrangle \(ABCD\) is inscribed in a circle if and only if
\(2 \cdot \measuredangle ABC \equiv 2 \cdot \measuredangle ADC.\)
- Proof
-
Since \(\square ABCD\) is nondegenerate, so is \(\triangle ABC\). Let \(O\) and \(\Gamma\) denote the circulcenter and circumcircle of \(\triangle ABC\) (they exist by Exercise 8.1.1 ).
According to Theorem 9.2.1 ,
\(2 \cdot \measuredangle ABC \equiv \measuredangle AOC\).
From the same theorem, \(D \ni \Gamma\) if and only if
\(2 \cdot \measuredangle ADC \equiv \measuredangle AOC,\)
hence the result.
Let \(\Gamma\) and \(\Gamma'\) be two circles that intersect at two distinct point: \(A\) and \(B\). Assume \([XY]\) and \([X'Y']\) are the chords of \(\Gamma\) and \(\Gamma'\) respectively, such that \(A\) lies between \(X\) and \(X'\) and \(B\) lies between \(Y\) and \(Y'\). Show that \((XY) \parallel (X'Y')\).
- Hint
-
Apply Corollary \(\PageIndex{2}\) twice for \(\square ABYX\) and \(\square ABY'X'\) and use the transversal property ( Theorem 7.3.1 ).