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Golden Ratio
by Lo Man Wai
# Golden Ratio

## Definition

### Euclid's Elements

### The larger value
1.6180339887498948482…

### irrational

## way to find Phi using calculator

### Calculator Method 1: Invert and Add 1

## History

### First studied by Ancient
Greek mathematicians

### 1875 - first
known use of
this term in
English

## Application

### Aesthetics

### Architecture

### Painting

### Book design

### Perceptual studies

### Music

### Industrial design

### Nature

### Optimization

### Finance

## Other names

### divine proportion

### golden mean

### golden section

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

"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"

Φ = (√5 + 1) / 2

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... .

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

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

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

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

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

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

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

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

Example, shapes of postcards, playing cards

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

key to the golden section search

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