Parameterization of Sum of Squares

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1. Jun 4, 2015

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!

2. Jun 5, 2015

Orodruin

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

3. Jun 5, 2015

patrickbotros

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

4. Jun 5, 2015

Orodruin

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

5. Jun 5, 2015

patrickbotros

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

6. Jun 5, 2015

Orodruin

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

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