#### MarxSoccer

##### BSOD

- Messages
- 2,999

Known as the golden ratio.

To explain the picture:

Since BDC and FBC are 30/60/90 triangles,

BD = CDâˆš3; also FC = 2BC = 4CD

Since they are both radii, FC = AC = 4CD;

By Pythagoras' Theorem, AD^2 + CD^2 = AC^2;

AD = âˆš(AC^2 - CD^2)

= âˆš((4CD)^2 - CD^2) = CDâˆš15

BE/AB = 2BD/AB = (2CDâˆš3) /AB

= (2CDâˆš3) / (AD - CDâˆš3)

= (2CDâˆš3) / (CDâˆš15 - CDâˆš3)

= (2CDâˆš3) / ((âˆš5)CDâˆš3 - CDâˆš3)

= 2/ (âˆš5 - 1)

= 2(âˆš5 + 1) / (âˆš5 - 1) (âˆš5 + 1)

= 2(âˆš5 + 1) / (5 - 1)

= (1 + âˆš5) /2

= Ã˜ = Golden Ratio Proportion