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particular family of parametric curves


rakuenso
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Is there a name for a family of parametric curves [math] x(t) , y(t) [/math]where...

 

[math](\frac{dx}{dt})^2+(\frac{dy}{dt})^2=1[/math]?

 

If possible, generalized to multiple dimensions...

 

[math](\frac{dx_1}{dt})^2+(\frac{dx_1}{dt})^2+...+(\frac{dx_n}{dt})^2=1[/math]

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