Parameterization of Sum of Squares

[patrickbotros]

I've seen the parameterization of a^2+b^2=c^2 and also a^2+b^2=c^2+d^2, but I don't know how they arrived at those parameterizations. Would it be possible to parameterize something with two equalities like a^2+b^2=c^2+d^2=e^2+f^2? Any help is appreciated!

 

[Orodruin]

Yes, the idea is the same as for the others. Just add another angle.

 

[patrickbotros]

Yes, the idea is the same as for the others. Just add another angle.

How? Specifically how to do the a^2+b^2=c^2+d^2=e^2+f^2

 

[Orodruin]

Start by parametrising the first equality, then the second. How do you parametrise the first?

 

[patrickbotros]

Start by parametrising the first equality, then the second. How do you parametrise the first?

I don't know. That's what I'm asking. I just know what the answer ends up benign. Not the steps.

 

[Orodruin]

Do you understand why $a^2 + b^2 = c^2$ is parametrised by an angle $\theta$?