Download presentation

Presentation is loading. Please wait.

Published byMarquis Gaines Modified over 2 years ago

1
By Christophe Dufour & Ming Au

2
Finding φ. The property that defines the golden ratio is: L = L+1 1 L a. Cross multiplying and rearranging the equation we obtain the following quadratic equation : L^2 - L -1 = 0 b. Using the quadratic formula to solve the quadratic equation in (a). The “positive” root is called the Golden Ratio: 1 +√[( 1 – 4(1)(-1)] = 1 +√(1 + 4) = 1 + √5 2 2 2

3
φ 2 = 1 + √5 x 1 + √5 ~ 2.618 = φ + 1 2 2 1/φ = 2___ ~ 00.618 = φ - 1 1+ √5

4
Formation of the Golden Rectangle A Golden Rectangle is formed by a regular rectangle that is cut into half's. One of the half is then cut into another half. One of the quarter equals 1 by ½. The rest of the figure equals √5/2. The Length of the figure then equals φ. 1 + √5 ~ 1.618 x 1 = 1.618 = φ 2

5
The Golden Ratio in Art The Golden Ratio can be seen in the physical structure of the human face in great paintings such as the Mona Lisa or The sacrament of the Last Supper; the artist needed a constant which applied to the Golden Ratio to the drawing. A Logarithmic Spiral A special curve that appears in nature in the formation of shells. It is formed by connecting the corners of the squares of a golden rectangle with a smooth curve.

6
The Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, … A number in the sequence is obtained by adding the two previous numbers before it: For example, 1+1=2, 1+2=3, 2+3=5, 3+5=8, …. What is the connection between the Fibonacci Sequence and the Golden Ratio? The ratios of the numbers in the Fibonacci sequence tend toward the Golden Ratio φ. F2/F11/1 =1 F3/F22/1 =2 F4/F33/2 =1.5 F5/F45/3 =1.667 F6/F58/5 =1.6 F7/F613/8 =1.62

Similar presentations

Presentation is loading. Please wait....

OK

The Golden Mean The Mathematical Formula of Life Life.

The Golden Mean The Mathematical Formula of Life Life.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on social networking sites Ppt on digital marketing Ppt on mars one way Ppt on five monuments of india Ppt on networking related topics of psychology Ppt on inside our earth Ppt on cse related topics in biology Ppt on human nutrition and digestion worksheet Ppt on any one mathematician john Ppt on nuclear family and joint family