pythagoras pentagram and the golden ratio

Pythagoras was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that the human body is built with each part in a definite golden proportion to all the other parts.

Pythagoras' discoveries of the proportions of the human figure had a tremendous effect on Greek art. Every part of their major buildings, down to the smallest detail of decoration, was constructed upon this proportion.

http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm

The Golden Ratio is 1.618033988749895... and referred to as Phi (ϕ)

Phi is the ratio of the line segments that result when a line is divided in one very special and unique way.

The ratio of the length of the entire line (A)to the length of larger line segment (B) is the same as

The ratio of the length of the larger line segment (B)to the length of the smaller line segment (C).

In other words, C:B = B:A

http://www.goldennumber.net/neophite.htm

Please watch the first half of the following video.

This is Disney’s take on the Golden Ratio and Pythagoras’ pentagram.

Video courtesy of YouTube.

Photo Courtesy of: http://www.bbc.co.uk

Photo Courtesy of: http://milan.milanovic.org/math/english/golden/Golden_files/parthenonPhi.gif

Photo Courtesy of: http://library.thinkquest.org/trio/TTQ05063/un.gif

1. Find more examples of the Golden Ratio in art and architecture. Post these to the “Golden Ratio” discussion board.

2. A golden rectangle has a short side of length 100. What is the length of the longer side? Show your work in the “Golden Ratio” discussion board.

100