Geeeeometry (Help!)

[Monk]

Most of you are probably familiar with the Pythagorean Theorem. In a right triangle, a² + b² = c²

I need the most simple way to prove it. Does anybody know?

[Eli]

I know but i'm too lazy to write it in English.

[Eli]

But...

http://www.usna.edu/MathDept/mdm/pyth.html
http://www.emsl.pnl.gov:2080/docs/mathexpl/ptprove.html

[Monk]

Thanks Eli, I think the second link will be most helpful, I'll go have a look at it.

I just have to figure out what "perpendicular" means.

[Skanky Burns]

At right-angle to.

[Urban Ranger]

I think you can start bt the Cosine Rule and work it as a special case.

Cosine Rule: a² = b² + c² - 2bc*cos A

A = 90°
cos(A) = 0

Q.E.D.

[Monk]

Thanks guys. Learning, learning.

[reds4ever]

if you can get your hands on the book 'Fermats Last Theorem' theres a (proper) proof in the appendics of that (my copy is at work)

[Angelo Scotto]

I remember that once an Applet proving the Pythagorean Theorem won a Sun Contest, i was unable to find it, anyway the following seems to me well done too.

http://www.utc.edu/~cpmawata/geom/geom7.htm

Obviously you need a Java-enabled browser, just try the link, if it starts you have it

P.S. No, i found it, it's here:

http://www.math.ubc.ca/~morey/java/pyth/

[Immortal Wombat]

Originally posted by Urban Ranger
I think you can start bt the Cosine Rule and work it as a special case.

Yeah, but then you have to prove the Cosine Rule.

Although there is a trigonometrical proof somewhere...

I like Angelo's first one the best. I think that is the one Pythag himself used.

[Japher]

Stephen Hawkings did a good proof of it in the Brief History of Time.

[Urban Ranger]

Originally posted by Immortal Wombat
Yeah, but then you have to prove the Cosine Rule.

Well, you could, but you're not asked to do it.

[reds4ever]

The area of the large square can be found in two ways:

1) Area of large square = (x+y)^2


2) Measure each element in the large square. The area of each triangle is 0.5xy. The area of the tilted square is z^2

Area of large square = 4*(area of each triangle)+ area of tilted square

= 4 (0.5xy)+z^2

1) and 2) give different expressions but must be equivilent because the represent the same area

so (x+y)^2 = 4(0.5xy)+z^2

= x^2+y^2+2xy = 2xy+z^2

= x^2+y^2+z^2 which is the theorem.

[orange]

or you could just make a right triangle that's 3x4x5

[Az]

something a humanities major would say.

Thats called an example orange, not a proof.
With that triangle, you could claim all right triangle have sides a,b,c such that a+b=c+2... which of course is not true