MarxSoccer
BSOD
- Messages
- 2,999
Have you guys ever learned about it? I've always been amazed by it. It and pi.
Known as the golden ratio.
To explain the picture:
Since BDC and FBC are 30/60/90 triangles,
BD = CD√3; also FC = 2BC = 4CD
Since they are both radii, FC = AC = 4CD;
By Pythagoras' Theorem, AD^2 + CD^2 = AC^2;
AD = √(AC^2 - CD^2)
= √((4CD)^2 - CD^2) = CD√15
BE/AB = 2BD/AB = (2CD√3) /AB
= (2CD√3) / (AD - CD√3)
= (2CD√3) / (CD√15 - CD√3)
= (2CD√3) / ((√5)CD√3 - CD√3)
= 2/ (√5 - 1)
= 2(√5 + 1) / (√5 - 1) (√5 + 1)
= 2(√5 + 1) / (5 - 1)
= (1 + √5) /2
= Ø = Golden Ratio Proportion
Known as the golden ratio.
To explain the picture:
Since BDC and FBC are 30/60/90 triangles,
BD = CD√3; also FC = 2BC = 4CD
Since they are both radii, FC = AC = 4CD;
By Pythagoras' Theorem, AD^2 + CD^2 = AC^2;
AD = √(AC^2 - CD^2)
= √((4CD)^2 - CD^2) = CD√15
BE/AB = 2BD/AB = (2CD√3) /AB
= (2CD√3) / (AD - CD√3)
= (2CD√3) / (CD√15 - CD√3)
= (2CD√3) / ((√5)CD√3 - CD√3)
= 2/ (√5 - 1)
= 2(√5 + 1) / (√5 - 1) (√5 + 1)
= 2(√5 + 1) / (5 - 1)
= (1 + √5) /2
= Ø = Golden Ratio Proportion