Create your own awesome maps

Even on the go

with our free apps for iPhone, iPad and Android

Get Started

Already have an account?
Log In

Golden Ratio by Mind Map: Golden Ratio
0.0 stars - 0 reviews range from 0 to 5

Golden Ratio

This is just a demo map that you can delete right away, if you feel like it...

Definition

Euclid's Elements

"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.", "extreme and mean ratios"

The larger value 1.6180339887498948482…

irrational

Φ = (√5 + 1) / 2

way to find Phi using calculator

Calculator Method 1: Invert and Add 1

Enter 1 to start the process. Take its reciprocal (the 1/x button or else x^y and power y:-1). Add 1. Take its reciprocal. Add 1. Take its reciprocal. Add 1. Keep repeating these two operations take the reciprocal, add 1) and you will find that soon the display does not alter and settles down ("converging" as mathematicians call it) to a particular value, namely 1.61803... .

History

First studied by Ancient Greek mathematicians

Phildas(490-430BC) made the Pathenon statues that seems to embody Golden ratio

Euclid (c. 325–c. 265 BC), in his Elements, gave the first recorded definition of the golden ratio

1875 - first known use of this term in English

James Sulley's article on aesthetics in the 9th edition of the Encyclopedia Britannica

Application

Aesthetics

1509, Luca Pacioli, De Divina Proportione, explored the mathematics of the golden ratio, advocated the golden ratio's application to yield pleasing, harmonious proportions

Architecture

Parthenon

the Egyptian Pyramids, length of a face of the Great Pyramid : the distance from the same point : the exact centre of the pyramid's base square = 1·6

Painting

Heinrich Agrippa(16th-century philosopher ), a man over a pentagram inside a circle

Leonardo da Vinci, De Divina Proportione (On the Divine Proportion), some bodily proportions exhibit the golden ratio

Book design

truly beautiful page proportions 2:3, 1:√3

Perceptual studies

Fechner, test the idea that the golden ratio plays a role in human perception of beauty

Music

James Tenney, For Ann (rising), upwardly glissandoing tones

Industrial design

Example, shapes of postcards, playing cards

Nature

Adolf Zeising, Animals, the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, Plants, branches along the stems of plants and of veins in leaves

Optimization

key to the golden section search

Finance

used in trading algorithms, applications and strategies, typical forms: the Fibonacci fan, the Fibonacci arc, Fibonacci retracement and the Fibonacci time extension

Other names

divine proportion

golden mean

golden section