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Vector Sum of Pythagorean Triples

The graph of real-valued Pythagorean triples $x^2+y^2=z^2$ forms an infinite cone if we restrict to $z>0$: A sum of $n$ independent vectors on this cone is $n$ times their average, which lies ...
xnor's user avatar
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5 votes

Vector Sum of Pythagorean Triples

By definition of (Euclidean) length, 2-dimensional vector $v_j:=(a_j,b_j)$ has length $|v_j|=c_j$ if and only if $a_j^2+b_j^2=c_j^2$ ($c_j\ge 0$). By repeated application of the we have for any ...
loopy walt's user avatar
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