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        riddles >> easy >> Pythagorean Proof
        
(Message started by: Benoit_Mandelbrot on Mar 12^th, 2004, 9:23am)

Title: Pythagorean Proof
Post by Benoit_Mandelbrot on Mar 12^th, 2004, 9:23am

This is another easy one, but here it is:

Prove the pythagorean theorem. There can be more than one way to prove it.

Title: Re: Pythagorean Proof
Post by Sir Col on Mar 12^th, 2004, 9:40am

How about forty-three different ways? ::)

http://www.cut-the-knot.org/pythagoras/index.shtml

Title: Re: Pythagorean Proof
Post by Benoit_Mandelbrot on Mar 12^th, 2004, 10:04am

Pretty much the only way I prove it is by similiar triangles, by having a line from the right angle of the big triangle perpindicular to the hypotenuse. The hypotenuse becomes c=x+y. We have a/c=x/a, and b/c=y/a. We solve both for x and y, and add x+y. We set this as c, and we come up with a²+b²=c².

Title: Re: Pythagorean Proof
Post by Sameer on Mar 12^th, 2004, 11:14am

I will add some more ...

1) Right angled triangle ABC with AB=a,BC=b and AC=c

sinC=a/c and cosC=b/c
sin²C+cos²C=1
a²+b²=c²

2) Consider a point (x,y) on the plane. If you drop a perpendicular on X axis then height = y and horizontal distance from Y axis = x
By distance formula distance of that point from origin is
sqrt(a²+b²) = c(lets say)
Hence the Pythagoras identity follows

Title: Re: Pythagorean Proof
Post by Sir Col on Mar 12^th, 2004, 12:35pm

*ahem* And where does the identity sin²C+cos²C=1 and the distance formula come from?

B_M, I think you meant b/c=y/b.

Title: Re: Pythagorean Proof
Post by rmsgrey on Mar 12^th, 2004, 12:39pm

My personal favourite is #9 (http://www.cut-the-knot.org/pythagoras/index.shtml#9) on Sir Col's link.

Title: Re: Pythagorean Proof
Post by Sameer on Mar 12^th, 2004, 1:06pm

on 03/12/04 at 12:35:31, Sir Col wrote:

*ahem* And where does the identity sin²C+cos²C=1 and the distance formula come from?

LOL but the world is round ;D ;)