General triangle rules and formulas?

1. Aug 10, 2004

Euphoriet

Hi guys I'm looking for a website where I can review basic triangle rules such as the formulas for right triangles... I would look at a geometry book but I dont have one. Its been a long time and I need some reviewing to do.

I also wanted to ask if anyone knew about the group of triangles such as one with sides measuring 4,5,3.... , 24,25, 7 etc? This are the typical SAT triangles.. and I know there is a patter but I dont know what it is.

Thanks.

2. Aug 10, 2004

robert Ihnot

Given integers, a and b, the entire pattern is generated by

$$X=a^2-b^2, Y=2ab, Z=a^2+b^2, where X^2 +Y^2 = Z^2.$$

You can check this by multiplication and by reading Modern Algebra by Birkhoff and MacLane.

Last edited: Aug 10, 2004
3. Aug 10, 2004

Math Is Hard

Staff Emeritus
4. Aug 10, 2004

Gokul43201

Staff Emeritus
Also, given any odd interger 'n', $$\frac {n^2 + 1}{2}, ~\frac {n^2 - 1}{2}$$ complete a triple.

Thus, for 3, you have 4=(9-1)/2 and 5 =(9+1)/2
for 5, you have 12 = (25-1)/2, 13 = (25+1)/2
then there's 7, 24, 25 and 9, 40, 41 and so on..

5. Aug 10, 2004

Math Is Hard

Staff Emeritus
but what's going on at n = 1?
a zero length side on a triangle can't be possible.

or maybe we're not talking strictly about triangles?

Last edited: Aug 10, 2004
6. Aug 11, 2004

Euphoriet

So what statement is true?.. i'm lost now

7. Aug 11, 2004

arildno

You've got a "degenarate" case here:
Two "sides" of length 1, one "side" with length 0; that is a straight line segment of length 1 traversed in opposite directions when going around your "triangle" (ending up on your starting point)

8. Aug 11, 2004

Euphoriet

this is getting confusing now =-/

9. Aug 11, 2004

Math Is Hard

Staff Emeritus
I think our triangle just collapses to line segment when n = 1, that's all.
But correct me if I am wrong, arildno.

10. Aug 11, 2004

arildno

That's what I meant, Math is hard ("degeneracy" is a word often used in similar cases).

11. Aug 11, 2004

NSX

Negative numbers anyone?

hehe