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The question came from reading the following post: A proof of the Isoperimetric Inequality - how does it work?

I almost can follow the whole proof, but I am stuck at one point. Why does $(x^2 +\bar{y}^{2})⋅({y_s}^2 +{x_s}^2)=x^2+\bar{y}^{2}$?

I actually came across this proof in Do Carmo's "Differential Geometry" and had the same question. I'm still new to this site so if this is the wrong place to post this, please let me know.

Thanks!

Community
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Paul Hlebowitsh
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1 Answers1

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The curve is parametrized by arc length, i.e. the ''speed'', $x_s'^2 + y_s'^2$, equals $1$.

mrf
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