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Хімічний зв'язок є результатом складної взаємодії електронів та ядер атомів і описуються квантовою механікою. Кількість речовини
51
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Хімічні властивості
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До хімічних властивостей відноситься здатність реагувати з іншими речовинами, а також схильність до розкладу. Хімічні властивості речовини залежать не лише від кількісного та якісного складу, тобто з яких і скількох атомів хімічних елементів вона складається, але й від хімічної структури молекул речовини (структура ізомерія) та від просторової конфігурації молекул (конформація та стереоізомерія). Хімічні реакції
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Енергія Хімічні закони закон збереження маси речовини, закон збереження енергії, закон Авогадро, закон діючих мас, закон сталості складу, закон об'ємних відношень газів,
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Термодинамічна фаза Термодинамі́чна фа́за — термодинамічно рівноважний стан речовини, відмінний за своїми фізичними властивостями від інших станів тієї ж речовини. Різні фази мають різні упаковки молекул (для кристалічних фаз, різні кристалічні ґратки), і, отже, різні значення коефіцієнта стисливості, коефіцієнта теплового розширення та інші сприйнятливості. Крім того, різні фази можуть мати різні електричні (сегнетоелектрики), магнітні (феромагнетики), та оптичні властивості (наприклад, твердий кисень). Зелена хімія
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Метою зеленої хімії є зменшення забруднення та його запобігання вже на початку планування хімічних технологій тощо. Важливими принципами зеленої хімії є принцип економії атомів та проведення хімічних реакцій у воді для зменшення використання органічних розчинників. Історія хімії Нобелівська премія з хімії
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Єдиним хіміком, котрий отримав дві Нобелівські премії з хімії (в 1958 та 1980 роках) був Фредерік Сенгер. Ще двоє отримали по дві Нобелівські премії з різних дисциплін — Марія Кюрі (з фізики в 1903 році та з хімії в 1911 році) та Лайнус Полінг (з хімії в 1954 році та миру в 1962 році). За всю історію вручення Нобелівської премії, її отримали тільки 4 жінки: Марія Кюрі, Ірен Жоліо-Кюрі, Дороті Ходжкін та Ада Йонат. Хімія в Україні Див. також Українські хіміки
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Значну роль у розвитку хімічних наук за нових часів в Україні мали наукові товариства природознавців, які існували в Харкові, Києві та Одесі. Математично-природописно-лікарська секція НТШ у Львові з 1897 видавала збірки, в яких були статті з хімії та української хімічної термінології.
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Визначними вченими у Харківському університеті були Олександр Данилевський (фізіологічна хімія) та Володимир Палладін (біохімія), а досліди з органічної хімії провадили Олександр Ельтеков і Костянтин Красуський. Перший підручник фізіологічної хімії Олексія Ходнєва з Харківського університету вийшов 1847 року.
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Широко розвинув цю галузь хімії Антон Володимирович Думанський, який 1912 року почав викладати в Київському університеті колоїдну хімію та видав тоді монументальну монографію про колоїдні розчини. У ділянці органічної хімії в Київському університеті працювали Петро Петрович Алексєєв і Микола Андрійович Бунге та світової слави Сергій Миколайович Реформатський, який відкрив реакцію утворення β-гідроксикислот при допомозі цинк-органічних сполук, що згодом стала носити його ім'я (реакція Реформатського). У 1867–1889 роках Володимир Олександрович Кістяковський працював у галузі біохімії над обміном вуглеводів, зокрема глікогену.
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У 1872—1910 роках В. Радзішевський досліджував різні питання загальної та фармацевтичної хімії; важливі також праці з фізичної хімії С. Толлочка в 1905—1935 роках, а з органічної хімії — Віктора Кемули і Е. Ліннемана.
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Цей останній, працюючи в 1913—1934 роках у Дніпрі, заснував там Інститут фізичної хімії і створив основи електронної хімії і каталізу. Визначним українським біохіміком у Віденському університеті наприкінці XIX століття був І. Горбачевський, який 1882 року синтезував сечову кислоту з сечовини та гліцину. Радянський період
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Більшість наукових праць велася далі в університетах та політехнічних інститутах, хоч пізніше роль основних дослідів з хімії перебрали новозасновані інститути АН УРСР, які нині й репрезентують найвищий рівень хімічної науки в Україні. Вони диспонують більшими засобами для наукової праці і співпрацюють з університетами, політехнічними інститутами та іншими дослідними осередками, подекуди координуючи їхню працю у визначених завданнях. Див. також Хімічна промисловість Періодична система Алфавітний список хімічних елементів Закон збереження маси речовини Закон сталості складу Палегеохімія Бази даних з хімії Примітки Література
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— Івано-Франківськ: Фоліант, 2015. — 361 с., іл. Опейда Й. О. Математичне та комп'ютерне моделювання в хімії: підручник / Й. О. Опейда. — Вінниця: ДонНУ, 2015. — 388 с.
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Бібліотека науково-навчальної літератури хімічного факультету Московського державного університету. «Химики и химия» — офіційний сайт журналу хіміків-ентузіастів. Природничі науки Надпопулярні статті
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Відстань між вершинами А і В— довжина найкоротшого шляху, що сполучає їх. Діаметр множини , що лежить в метричному просторі з метрикою — величина . Діаметр конічного перетину - пряма лінія, що є геометричним місцем середини усіх паралельних хорд даного конічного перетину.
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Символ порожньої множини, на відміну від символу діаметра, схожий на Ø (перекреслена велика літера «О»).
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Див. також Гідравлічний діаметр Еквівалентний діаметр тіла Кутовий діаметр Штангенциркуль, мікрометр — інструменти для вимірювання діаметрів Ератосфен, який обчислив діаметр Землі 240 року до н. е. Елементарна геометрія Довжина Кола
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"path": null }
В оберненому вигляді це співвідношення дає точне вираження метра через визначальні константи c і : 1 м = c = Сутність цього висновку формально зводиться до варіанту визначення, який був до того прийнятий Резолюцією 1 XVII Генеральної конференції з мір і ваг 1983 року:
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"path": null }
Для практичних цілей у лабораторіях метр порівнюють із довжиною хвилі певного випромінювання.
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Ідеї встановлення десяткової системи для одиниць вимірювання висловлювалася ще в XVII ст., однак шлях до її практичного втілення відкрили тільки революційні події у Франції. Ідея секундного маятника
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Такий маятник продемонстрував Християн Гюйгенс. Довжина цього маятника близька до сучасного визначення метра. Однак, незабаром з'ясувалося, що довжина секундного маятника залежить від місця на Землі: французький астроном Жан Рішер встановив, що вона відрізняється в Парижі й в Каєнні, Французька Гвіана на 0,3 %.
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"path": null }
Порівняння з паризьким меридіаном
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Окрім тієї вигоди, що таке рішення було доступним для французьких геодезистів, була перевага ще й у тому, що частина відстані від Дюнкерка до Барселони (близько 1000 км, тобто одна десята від загальної відстані) могла прокластись від початкової до кінцевої точок, розташованих на рівні моря, а якраз ця частина знаходилась посередині чверті кола, де вплив форми Землі, що не є правильною сферою, був би найменшим. Ідея прив'язати одиницю вимірювання довжини до довжини меридіана була не новою: аналогічно раніше були визначені морська миля і льє.
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Де Борда був завзятим ентузіастом десяткової системи. Ідея маятникового стандарту йому не подобалася, оскільки секунда не є десятковою одиницею. 7 квітня 1795 Національний конвент ухвалив закон про введення метричної системи у Франції й доручив комісарам, до числа яких входили Ш. О. Кулон, Жозеф-Луї Лагранж, П.-С. Лаплас та інші вчені, провести роботи з експериментального визначення одиниць довжини і маси. Нововизначена величина отримала назву «метр справжній і остаточний» ().
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Водночас комісія вирахувала значення метра зі старих даних. Розбіжність між новими й старими даними становила 0,03 %. Цікаво, що у сучасних одиницях це метра.
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Вигода від її застосування була настільки очевидною, що і після усунення Наполеона від влади запровадження метричних одиниць продовжилось: 1816: Бельгія і Нідерланди
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Точніші вимірювання Франсуа Араго і Жана-Батіста Біо на початку XIX ст. з'ясували, що еталон не зовсім точно відповідає визначенню метра через довжину меридіана. Попри розбіжність, метр архіву залишився практичним стандартом. Коли у 1867 році виникла ідея встановлення міжнародної системи мір, саме еталон архіву був взятий за одиницю довжини. У 1872 Міжнародна метрична комісія, враховуючи, що запроваджену «природну» одиницю неможливо знову точно відтворити, вирішила перейти по одиниці, відтворюваної архівним метром.
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", 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Було виготовлено 34 міри. У міри № 6 ця довжина виявилась найближчою до довжини архівного метра, і I Генеральна конференція з мір і ваг 1889 постановила вважати її міжнародним прототипом метра; його залишено для зберігання в Міжнародному бюро мір і ваг у Севрі (побл. Парижа). У Франції залишилось ще 4 міри, а решту було розподілено жеребкуванням між країнами, що їх замовили.
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Криптоновий стандарт Розвиток науки у XX ст. створив потребу і можливість точнішого визначення метра. Зокрема, прецизійність спектроскопічних інструментів стала достатньою для визначення одиниці довжини через довжину хвилі світла. XI Генеральна конференція мір і ваг 1960 року прийняла таке визначення метра:
180
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Світловий еталон метра повернув метру характер природної міри та, як показали подальші дослідження, підвищив точність його відтворення у 100 разів, що мало дуже важливе значення для сучасного приладобудування та точного машинобудування. За допомогою світлового еталона можна забезпечити точність відтворення метра щонайменше 10−9 (замість 10−7 з допомогою штрихової міри). Стандарт 1983 року
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Уведення нового, простішого визначення метра спрощує розуміння його фізичного змісту, це визначення зручне для навчальних цілей, але для відтворення розміру метра, створення його еталону доцільно й нині використовувати визначення, прийняте XI ГКМВ.
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Останні зміни
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Пропоноване нове визначення метра, повністю еквівалентне чинному, у резолюції сформульоване так: Метр, позначення м, є одиницею довжини; його величина встановлюється фіксацією чисельного значення швидкості світла у вакуумі точно рівної , коли вона виражена одиницею SI м·с−1. XXV ГКМВ, що відбулася у 2014 році, ухвалила рішення продовжити роботу з підготовки нової ревізії SI, включно з перевизначенням метра, й попередньо намітила закінчити цю роботу до 2018 року, щоб замінити чинну SI оновленим варіантом на XXVI ГКМВ того ж року.
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1 фм приблизно відповідає розміру атомного ядра. Атоми хімічних елементів мають розмір в діапазоні від 100 до 200 пм, або, в нанометрах, від 0,1 до 0,2 нм. Фізики використовують також одиницю ангстрем, Ǻ, що дорівнює 10−10 м, тобто: 1 Ǻ = 100 пм = 0,1 нм. Співвідношення з іншими одиницями довжини Англійська (Американська) система мір Міжнародні морські одиниці довжини Давньоруські міри довжини Астрономічні одиниці довжини Жарґонізм
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Див. також Похідні одиниці: фм, пм, нм, мкм, мм, см, км Міжнародна система одиниць SI Префікси SI Порядки величин (довжина) Тіто Лівіо Бураттіні Виноски Джерела Наказ Міністерства економічного розвитку та торгівлі України від 25.08.2015 № 914. Про затвердження визначень основних одиниць SI, назв та визначень похідних одиниць SI, десяткових кратних і частинних від одиниць SI, дозволених позасистемних одиниць, а також їх позначень та Правил застосування одиниць вимірювання і написання назв та позначень одиниць вимірювання і символів величин.
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Підручник /За заг. ред. В. В. Тарасової. — К.: Центр навчальної літератури, 2006. — 264 с. Посилання
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Фізичні одиниці Одиниці довжини Основні одиниці SI
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Біологія встановлює загальні закономірності, властиві життю в усіх його проявах. Історія становлення і розвитку Термін «біологія» вперше вжив 1797 р. німецький професор анатомії Теодор Руз (1771–1803), пізніше 1800 р. термін застосував професор Дерптського університету Фрідріх Бурдах (1776–1847), а 1802 р. — Жан Батист Ламарк (1744–1829) Лудольф Тревіранус (1779–1864).
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У процесі поступового розвитку й збагачування новими фактами біологія перетворилася в комплекс наук, що досліджує закономірності, властиві істотам із різних боків. Деякі з цих наук представляють самостійні дисципліни — анатомія, фізіологія, гістологія, біохімія, мікробіологія тощо.
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Теоретичний фундамент біології заклало еволюційне вчення Дарвіна, клітинна теорія Шванна і целюлярна патологія Рудольфа Вірхова.
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", 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Важливу значність для розвитку біології мали твори Арістотеля (384—322 до н. е.).
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Одне з головних досягнень цієї доби — створення системи класифікації рослин і тварин (Карл Лінней, 1735). Воднораз переважали умоглядні теорії про розвиток і властивості істот (самозародження, преформації тощо).
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Серед досягнень біології клітинна теорія (Теодор Шванн, 1839), відкриття закономірностей спадковості (Грегор Мендель, 1865). До фундаментальних змін у біології призвело еволюційне вчення Чарльза Дарвіна (1859).
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Із другого боку, прагнення до цілісного, синтетичного пізнання живої природи призвело до поступу наук, які вивчають певні властивості живої природи на всіх структурних рівнях її організації (генетика, систематика, еволюційне вчення тощо). Разючих успіхів від 1950-х років досягла молекулярна біологія, яка розкрила хімічні основи спадковості (будова ДНК, генетичний код, матричний принцип синтезу біополімерів). Учення про біосферу (В. І. Вернадський) розкрило масштаби геохімічної діяльності живих організмів, їхній нерозривний зв'язок із неживою природою. Практичну значність біологічних досліджень і методів (а також генної інженерії, біотехнології) для медицини, сільського господарства, промисловості, розумного використання природних ресурсів й охорони природи та проникнення в ці дослідження ідей і методів точних наук висунули біологію в середині 20 століття на передові рубежі природознавства.
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Кількість сучасних видів організмів сягає близько 2 млн, серед яких понад 1,5 млн тварин. Приблизно стільки ж відомо викопних видів. Біологи досліджують будову рослин і тварин, їхні життєві функції, спосіб життя та поширення на Землі, їхній історичний розвиток і значимість, шляхи використання тощо. Ці дослідження дають можливість щонайбільше й раціональніше використовувати в інтересах людини корисні форми й усе успішніше знищувати шкідливі.
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Основоположником наукової систематики був К. Лінней.
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", 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Крім того, розрізняють ще гідробіологію — науку, що вивчає життя організмів у водному середовищі, паразитологію — науку про паразитичні організми та боротьбу з ними.
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Для вивчення внутрішньої будови організмів морфологія користується методом розтинів та зрізів, тому цей її розділ відомий ще під назвою анатомії. Застосування порівняльного аналізу внутрішніх структур уможливило здійснити низку важливих узагальнень. Без порівняльної анатомії неможливе розв'язання такої важливої проблеми, як еволюція органічного світу.
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З фізіологією споріднена біохімія, або фізіологічна хімія, яка досліджує хімічні процеси, що лежать в основі обміну речовин, провадить хімічний аналіз тканин та різних виділень організму.
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З даних екології і ценології виходить у своїх висновках біогеографія, яку поділяють на фітогеографію (географія рослин) і зоогеографію (географія тварин). Індивідуальний розвиток організмів (онтогенез) поділяють на два етапи — ембріональний (зародковий) і постембріональний (післязародковий). Закономірності ембріонального розвитку вивчає ембріологія, яку, природно, поділяють на ембріологію рослин та ембріологію тварин і людини. Питання спадковості й мінливості організмів досліджує генетика.
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Вельми важливе значення для виявляння спорідненості організмів має палеонтологія, яка досліджує викопних рослин (палеоботаніка) і викопних тварин (палеозоологія) та їхній розвиток протягом усіх геологічних часів. Саме вона дозволяє на підставі документальних даних — скам'янілих залишків викопних організмів — відтворити реальну картину еволюції органічного світу, послідовні етапи розвитку життя на Землі.
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Біологічні дисципліни Акарологія — наука про кліщів, розділ зоології. Альгологія — наука про водорості, розділ ботаніки. Анатомія — збірна група розділів біології, які вивчають структуру організмів або їхніх частин на рівні вище клітинного. Антропологія — біологічна наука, що вивчає тілесну природу людини, її походження і подальший розвиток.
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Біогеологія — науковий напрям, який досліджує роль організмів в утворенні та розвитку земної кори. Біогеофізика — галузь геофізики, яка досліджує фізичні процеси, пов'язані з життям, зокрема — вивчення закономірностей міграції радіоактивних ізотопів в природних біоценозах.
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Біоінженерія — галузь біології та медицини, що займається свідомим внесенням змін до живих організмів для керування їхніми властивостями. Біоінформатика — область обчислювальної біології, що застосовує машинні алгоритми і статистичні методи для аналізу великих наборів біологічних даних.
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Біомеханіка — наука, котра вивчає на основі ідей та методів механіки властивості біологічних об'єктів. Біоніка — використання біологічних методів та структур для розробки інженерних рішень та технологічних методів. Біосеміотика — наука, що досліджує властивості знаків та знакових систем (знакові процеси) в живих системах.
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Ботаніка — розділ біології, що вивчає рослини, гриби і водорості.
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Гельмінтологія — наука, яка вивчає гельмінтів (паразитуючих червів), хвороби, які вони викликають та міри боротьби з ними, розділ зоології. Генетика — це наука про гени, спадковість та варіативність організмів. Геронтологія — наука, що вивчає закономірності старіння живих істот.
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Дендрологія — розділ ботаніки, що вивчає деревні рослини (дерева, чагарники). Еволюційна біологія — галузь біології, що вивчає походження видів, їхні зміни, розділення і виникнення біорізноманіття. Екологія — один з розділів біології, який досліджує взаємовідносини між біотичними та соціальними цілісностями та їхнім середовищем.
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Ентомологія — наукова дисципліна, що вивчає комах. Інколи це означення набуває ширшого змісту і охоплює також вивчення інших наземних членистоногих, як-то павуків, скорпіонів та кліщів. Етологія — польова дисципліна зоології, що вивчає поведінку тварин. Зоологія — це біологічна дисципліна, що вивчає тварин та їхні взаємозв'язки з довкіллям.
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Клітинна біологія — розділ біології, що вивчає структурно-функціональну організацію прокаріотичних та еукаріотичних клітин. Космічна біологія — біологічна наука, або розділ біології, що вивчає можливість існування живих організмів у космосі та на інших планетах крім Землі. Ксенобіологія — наука про форми життя позаземного походження. Ліхенологія — наука, яка досліджує лишайники як особливу групу комплексних організмів, тіла яких складаються з гриба та водорості, але мають свої тільки для них характерні структурні та функціональні властивості.
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Мікробіологія — розділ біології, що займається вивченням мікроорганізмів, головним чином вірусів, бактерій, грибків, одноклітинних водоростей і найпростіших. Молекулярна біологія — галузь науки, яка вивчає біологічні процеси на рівні біополімерів — нуклеїнових кислот і білків та їхніх надмолекулярних структур. Морфологія — розділ біології, що займається вивченням форми та будови організмів та їх специфічних структурних особливостей.
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Протозоологія — наука, що вивчає одноклітинних, розділ зоології. Птеридологія — наука про папоротеподібні.
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Теріологія — наука про ссавців, один з розділів зоології. Токсикологія — наука, що вивчає отруйні, токсичні та шкідливі речовини, потенційну небезпеку від їхнього впливу на організми та екосистеми.
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Фізіологія тварин і людини — галузь науки, яка вивчає механізми і закономірності всіх проявів життєдіяльності організму, його органів, тканин, клітин та субклітинних утворень, використовуючи для вивчення й пояснення цих проявів методи й поняття фізики, хімії, математики й кібернетики. Філогенетика — область біологічної систематики, що займається ідентифікацією і проясненням еволюційних взаємин серед різних видів життя на Землі, як сучасних, так і вимерлих.
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Цитологія — розділ біології, що вивчає живі клітини, їхні органоїди, будову, функціонування, процеси клітинного розмноження, старіння та смерті. Дослідження біології Методи дослідження До біологічних методів дослідження відносять: Метод спостереження — є основою морфологічних наук, використовується, як на мікроскопічному, так і макроскопічному рівнях. Сутність методу полягає у встановленні індивідуальності об'єкта, що досліджується, без штучного втручання до його процесів життєдіяльності. Зібрана інформація використовується для подальшого дослідження.
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На відміну від методу спостереження, експериментальний метод передбачає навмисне втручання експериментатора у природу, що дозволяє встановити наслідки від впливу тих, чи інших факторів на об'єкт дослідження. Метод може застосовуватись як у природних умовах, так і лабораторних.
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Цитологія
371
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Залежно від використовуваних методів — наука про генетику, екологічну генетику та інші. Ідеї та методи генетики грають важливу роль в медицині, сільському господарстві, мікробіологічної промисловості і, а також в генетичній інженерії.
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Екологія як наука стала дуже популярна в наш час, у зв'язку з погіршенням довкілля.
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Історичний метод допомагає на основі даних про сучасний органічний світ та його минуле, пізнати процеси розвитку живої природи.
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Біологічна безпека
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Див. також Біологічна класифікація Біотехнологія Червона книга Царства Примітки Література Гродзинський Д. М. Біологія // Біологічний словник : 2-е вид. / за редакцією академіка АН УРСР К. М. Ситника, члена-кореспондента АН УРСР В. О. Топачевського. — К.: Головна редакція УРЕ, 1986. — 680 стор., іл. — 27 000 пр. Біологія: навчальний посібник / З. Д. Воробець, О. Я. Чупашко, Л. М. Сергієнко, О. С. Корчинська. — Київ: Знання, 2010 . — 436 с. — ISBN 978-966-346-721-4
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Mazzarello, P (1999). «A unifying concept: the history of cell theory». Nature Cell Biology 1: E13-E15. doi:10.1038/8964 Посилання
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Ліцензія Creative Commons Attribution (CC-BY). Current Biology — науковий журнал з проблем біологічних досліджень. Природничі науки Надпопулярні статті
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Інструментом для побудови кола є циркуль. Визначення Евкліда Термінологія
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"path": null }
Діаметр кола дорівнює двом радіусам. Пряма може не мати з колом спільних точок, мати з колом одну спільну точку (така пряма називається дотичною до кола) або мати з ним дві спільні точки (така пряма називається січною до кола). Дотична до кола завжди перпендикулярна до його діаметра, один з кінців якого є точкою дотику.
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У математиці вивчення кола допомогло розвитку геометрії, астрономії і числення.
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Деякі важливі та цікаві моменти з історії кола: 1700 до н. е. — Папірус Рінда описує метод знаходження площі круглого поля. Результат відповідає такому значенню (3.16049…), що дає наближене значення числа . 300 до н. е. — Книга 3 із Начал Евкліда (Елементи) присвячена властивостям кола. У Платона подано детальне визначення і пояснення кола. Платон пояснює, що таке ідеальне коло і чим воно відрізняється від будь-якого малюнка, слів, визначень або пояснень.
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Рівняння кола з радіусом та центром в початку координат має вигляд: Загальне рівняння кола: Якщо відомі координати трьох точок на площині і , то рівняння кола, яке проходить через ці точки, можна записати через визначник: Параметричне означення
241
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Якщо записати та через параметр , що пробігає множину всіх дійсних чисел, отримаємо: Полярні координати Рівняння кола в полярних координатах: де — радіус кола, — відстань від початку координат до центру кола та — кут відкладений проти годинникової стрілки від додатної осі до лінії, що з'єднує початок координат з центром кола. Для кола, центр якого знаходиться в початку координат , це рівняння спрощується до вигляду . Якщо або якщо початок координат лежить на колі, тоді отримуємо рівняння: . В загальному випадку, рівняння можна розв'язати для r: ,
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Ізопериметрична нерівність: З усіх замкнутих кривих певної довжини коло обмежує область максимальної площі.
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Кут між дотичною та хордою дорівнює половині градусної міри дуги, що стягується хордою. Відрізки дотичних до кола, проведених з однієї точки, рівні й утворюють рівні кути з прямою, що проходить через цю точку і центр кола.
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Квадрат довжини відрізка дотичної дорівнює добутку довжин відрізків січної і дорівнює абсолютній величині міри точки відносно кола. Довжина кола і площа круга Довжину дуги кола з радіусом , утвореного центральним кутом , виміряним у радіанах, можна обчислити за формулою . Довжину кола з радіусом можна обчислити за формулою , де — число пі, яке визначається як відношення довжини кола до його діаметра.
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У вужчому сенсі коло — окремий випадком еліпса, тобто еліпс з однаковими півосями, або іншими словами, коло є еліпсом з нульовим ексцентриситетом. Дотичні і нормалі Рівняння дотичної до кола в точці визначається рівнянням , де A, B і С — коефіцієнти в загальному рівнянні кола.
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Коло на сайті cut-the-knot FIZMA.neT — Математика онлайн (Коло та його елементи) Планіметрія Конічні перетини Алгебричні криві Стереометрія Надпопулярні статті Криві Кола
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Лінійні розміри тіла
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"path": null }
Річки мають довжину русла, ширину і глибину. Одиниці довжини
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1 миля = 1609,344 м 1 миля = 1760 ярдів 1 миля = 5280 футів 1 морська миля = 1852 м Пункт Пункт — британська та американсьма міра довжини.
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Це явище називається лоренцовим скороченням довжини. Див. також Довжина (фонетика) Довжина хвилі Довжина Планка Довжина кривої Відносне видовження Стрибки в довжину Віддаль між двома точками Порядки величин (довжина) Примітки Посилання
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Поняття точки використовується в геометрії, математиці, фізиці та багатьох інших галузях. У функціональному аналізі під точкою розуміють елемент будь-якого топологічного (зокрема, метричного) простору; тому в цьому розумінні точкою може бути, наприклад, функція. Пояснення
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Точка — це пряма в поперечному розрізі. В геометрії точки зазвичай позначаються великими літерами. В евклідовому просторі положення точки можна задати за допомогою координат.
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Розмірність точки В залежності від контексту в математиці існує декілька еквівалентних визначень вимірності. Спільним для всіх цих визначень є те, що точка 0-вимірна. Розмірність векторного простору
193
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Топологічна розмірність Топологічна розмірність топологічного простору X визначається як мінімальне значення n, таке що кожне скінченне відкрите покриття для X допускає скінченне відкрите покриття для X, яке є подрібненням в якому немає точок, які б включали більше ніж n+1 елементів. Якщо таке мінімальне n не існує, кажуть що простір має нескінченну розмірність покриття.
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Геометрія без точок Хоча поняття точка як правило вважається фундаментальним у звичайній відомій всім геометрії і топології, але існують деякі системи в яких відмовилися від нього, наприклад, та . "Вільний від точок" простір визначають не як множину, а через деяку структуру (алгебраїчну або ), яка виглядає як добре відомий функціональний простір над множиною: через алгебру неперервних функцій або алгебру множин відповідно. Більш точно, такі структури узагальнюють добре відомі простори функцій у таких спосіб, що операція "отримання значення у заданій точці" може бути невизначеною.
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Маса точок і дельта-функція Дірака
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В контексті теорії обробки сигналів її часто називають символом або функцією одиничного імпульсу. Її дискретний аналог — дельта-функція Кронекера, як правило визначена у скінченній області і приймає значення 0 або 1.
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Див. також Точка Джерела Український правопис 2015 Пунктуація Розділові знаки
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Структура речення, його члени
174
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"path": null }
На вираз синтаксичних і значеннєвих стосунків слова речення перебувають поміж собою у зовнішньо-формальних зв'язках підрядності (за традицією шкільної граматики, так звані погодження, — узгодження, керування, прилягання й тяжіння) або сурядності (поміж однорідними членами речення: Учні й студенти читають і вчаться).
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