General triangle rules and formulas?

[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 don't 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 don't know what it is.

Thanks.

 

[robert Ihnot]

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

[tex] X=a^2-b^2, Y=2ab, Z=a^2+b^2, where X^2 +Y^2 = Z^2. [/tex]

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

 

[Math Is Hard]

Here's some good info about about Pythagorean Triples:
http://mathworld.wolfram.com/PythagoreanTriple.html

 

[Gokul43201]

Also, given any odd interger 'n', [tex]\frac {n^2 + 1}{2}, ~\frac {n^2 - 1}{2} [/tex] 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..

 

[Math Is Hard]

Also, given any odd interger 'n'...

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?

 

[Euphoriet]

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

 

[arildno]

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?

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)

 

[Euphoriet]

this is getting confusing now =-/

 

[Math Is Hard]

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

 

[arildno]

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

 

[NSX]

Negative numbers anyone?

hehe