Parameterization of Sum of Squares

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The discussion focuses on the parameterization of equations involving sums of squares, specifically a^2 + b^2 = c^2 and a^2 + b^2 = c^2 + d^2. Participants suggest that the approach for parameterizing multiple equalities, such as a^2 + b^2 = c^2 = d^2 + e^2 + f^2, follows a similar method by introducing angles. The conversation emphasizes the need to first parameterize one equality before moving to the next. There is a request for clarification on how to begin this process, particularly for the first equality. Understanding the use of an angle, like θ, for parameterization is also questioned.
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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!
 
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Yes, the idea is the same as for the others. Just add another angle.
 
Orodruin said:
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
 
Start by parametrising the first equality, then the second. How do you parametrise the first?
 
Orodruin said:
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.
 
Do you understand why ##a^2 + b^2 = c^2## is parametrised by an angle ##\theta##?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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