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Is there any way to generate a function whose graph would give a line of finite length?

We know that we can generate functions which give combined graphs of functions by taking $(g (x)-y)(f (x)-y)=0$. Can we get a function which gives a graph of finite lengh?

mvw
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Brilli
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    Of finite length... over all the reals? – Parcly Taxel Jul 17 '18 at 14:50
  • If you allow yourself parametric equations $(x,y)=(\sin t, \sin t)$ will do it. – Mark Bennet Jul 17 '18 at 15:04
  • If picewise functions count it would be trivial – Davide Morgante Jul 17 '18 at 15:28
  • Nope not piecewise function. Infact my question is if we can define piecewise functions with some real mathematical expression. Like we represent some functions with taylor series. Like that can we get some way to draw a given finite shape with a mathematical expression? – Brilli Jul 17 '18 at 15:42
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    @Brilli just speculating here, but what about taking the Fourier series of said picewise function? I know for sure that you can draw pretty much any shape you want what a Fourier series – Davide Morgante Jul 17 '18 at 18:05

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As your example involves an implicitly defined function, how about the implicit function $$x^2+y^2=1,$$ whose graph is the unit circle?

Servaes
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