# 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 $\theta$?