Phi

MarxSoccer

BSOD
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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
 

PerfectSK

Daemon Poster
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982
Yeah, didnt they talk about this in the Da Vinci Code? You divide the length between your head and your stomach by the distance between your stomach and your feet. I asked my geom teacher about it and he said that you get a number close to 1.61, but its not always exact.

http://en.wikipedia.org/wiki/Golden_ratio
Look toward the bottom, where they talk about how its used in art. Thats how they talked about it in the Da Vinci Code.
 

MarxSoccer

BSOD
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2,999
Never read or watched the Da Vinci Code, been wanting too. We spent like two weeks on geometry on Phi, doing such things as the body length lab.

We also had to do a project, finding things close to the golden ratio. There were tons, Mona Lisa painting, an iPod, light switch cover..
 

XEN

In Runtime
Messages
457
Isn't that the ratio of females bees to males bees in their hive or somethin?
 

PerfectSK

Daemon Poster
Messages
982
Lol, yeah and the seashell thing. How much did you learn in geom, MarxSoccer? We finished our entire book but its not I can remember that much, :)
 

MarxSoccer

BSOD
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2,999
I'm in an advanced class, have been since 3rd grade so what I learn the same thing that regular Geometry classes learn and more, more stuff, more complicated stuff, etc.. Same with Algebra last year, and will be the same with Advanced algebra next year, then Pre-calc and calc :(

Edit: Oh, and I guess it depends what book you use, some schools use different books. All I remember about our Geometry book is that it's the well known school book company and it was, dark blue I think?
 

kchi55

Fully Optimized
Messages
2,276
yup.. pretty cool. spent a few days on this in geometry too. just one of those things that smack you in the face and you come back saying.. wow..
 

PerfectSK

Daemon Poster
Messages
982
Ah, dunno where you're at, but over in the US we got Houftin-Mifflin or however you spell it. I remember a dark blue book as well. Lol, advanced eh? I took rapid geometry last year, learned the same stuff as the regular class, except our tests were harder and we got more credit. What stuff did you cover? The Triangle stuff was my favorite. Circles are not my friends, lol.
 

MarxSoccer

BSOD
Messages
2,999
PerfectSK said:
Ah, dunno where you're at, but over in the US we got Houftin-Mifflin or however you spell it. I remember a dark blue book as well. Lol, advanced eh? I took rapid geometry last year, learned the same stuff as the regular class, except our tests were harder and we got more credit. What stuff did you cover? The Triangle stuff was my favorite. Circles are not my friends, lol.

The small trigonometry unit within geometry? cos sin tan etc..? That was a breeze
 
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