The Golden Ratio
An overview of its properties, appearances and applications
Based on the number 1.618, Phi, and also known as
the Divine Proportion, Golden Proportion, Golden Mean and Golden Section
“Geometry has two
The Golden Ratio
An overview of its properties, appearances and applications
Based on the number 1.618, Phi, and also known as
the Divine Proportion, Golden Proportion, Golden Mean and Golden Section
“Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.” Johannes Kepler, 1571-1630 (Other Quotations)
Phi-based grid lines created with PhiMatrix golden ratio software
What makes a single number so interesting that ancient Greeks, Renaissance artists, a 17th century astronomer and a 21st century novelist all would write about it? This “golden” number, 1.61803399, represented by the Greek letter Phi, is known as the Golden Ratio, Golden Proportion, Golden Mean, Golden Section and Divine Proportion. It was written about by Euclid in “Elements” around 300 B.C., by Luca Pacioli, a contemporary of Leonardo Da Vinci, in “De Divina Proportione” in 1509, by Johannes Kepler around 1600 and by Dan Brown in 2003 in his best selling novel, “The Da Vinci Code.” With the movie release of the “The Da Vinci Code”, the quest to know Phi was brought even more into the mainstream of pop culture. The allure of “The Da Vinci Code” was that it creatively integrated fiction with both fact and myth from art, history,theology and mathematics, leaving the reader never really knowing what was truth and what was not. This site studies this golden number Phi, and its mathematical cousin, the Fibonacci series, both of which have roles in the plot of this murder mystery, and distinguishes between the myth and the math.
Mathematics of the Golden Ratio
This Golden Ratio truly is unique in its mathematical properties and pervasive in its appearance throughout nature. The “mathematically challenged” may be more interes