Parametrization for the figure '8' curve? [on hold]












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Is there a parametrization for the figure '8' curve, which is self-intersected?






geometry differential-geometry curves parametrization







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put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 20 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel

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  • 3




    $begingroup$
    See mathworld.wolfram.com/Lemniscate.html
    $endgroup$
    – Cheerful Parsnip
    Jan 13 at 6:34
















-1












$begingroup$


Is there a parametrization for the figure '8' curve, which is self-intersected?






geometry differential-geometry curves parametrization







share|cite|improve this question











$endgroup$



put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 20 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.












  • 3




    $begingroup$
    See mathworld.wolfram.com/Lemniscate.html
    $endgroup$
    – Cheerful Parsnip
    Jan 13 at 6:34














-1












-1








-1





$begingroup$


Is there a parametrization for the figure '8' curve, which is self-intersected?






geometry differential-geometry curves parametrization







share|cite|improve this question











$endgroup$




Is there a parametrization for the figure '8' curve, which is self-intersected?






geometry differential-geometry curves parametrization




geometry differential-geometry curves parametrization






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 13 at 6:46









Eric Wofsey

189k14216347




189k14216347










asked Jan 13 at 6:29









winstonwinston

527418




527418




put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 20 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.







put on hold as off-topic by user21820, Xander Henderson, RRL, Saad, Parcly Taxel 20 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, RRL, Saad, Parcly Taxel

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 3




    $begingroup$
    See mathworld.wolfram.com/Lemniscate.html
    $endgroup$
    – Cheerful Parsnip
    Jan 13 at 6:34














  • 3




    $begingroup$
    See mathworld.wolfram.com/Lemniscate.html
    $endgroup$
    – Cheerful Parsnip
    Jan 13 at 6:34








3




3




$begingroup$
See mathworld.wolfram.com/Lemniscate.html
$endgroup$
– Cheerful Parsnip
Jan 13 at 6:34




$begingroup$
See mathworld.wolfram.com/Lemniscate.html
$endgroup$
– Cheerful Parsnip
Jan 13 at 6:34










3 Answers
3






active

oldest

votes


















2












$begingroup$

This is an example of a Lissajous figure. (If you've got an oscilloscope with separate $x$ and $y$ inputs and a couple of signal generators you can have hours of fun generating them by applying sine waves of appropriate frequency ratio to the two inputs.)






share|cite|improve this answer









$endgroup$





















    3












    $begingroup$

    An easier parameterization of an 8-like figure is $(x,y) = (sin 2t, cos t),$
    where $0 leq t leq 2pi.$ It can easily be made more 8-like by scaling.






    share|cite|improve this answer









    $endgroup$





















      1












      $begingroup$


      $x = frac{asqrt{2}cos(t)}{sin^2(t) + 1}; qquad y = frac{asqrt{2}cos(t)sin(t)}{sin^2(t) + 1}$




      Check out this source:




      https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli







      share|cite|improve this answer









      $endgroup$




















        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        2












        $begingroup$

        This is an example of a Lissajous figure. (If you've got an oscilloscope with separate $x$ and $y$ inputs and a couple of signal generators you can have hours of fun generating them by applying sine waves of appropriate frequency ratio to the two inputs.)






        share|cite|improve this answer









        $endgroup$


















          2












          $begingroup$

          This is an example of a Lissajous figure. (If you've got an oscilloscope with separate $x$ and $y$ inputs and a couple of signal generators you can have hours of fun generating them by applying sine waves of appropriate frequency ratio to the two inputs.)






          share|cite|improve this answer









          $endgroup$
















            2












            2








            2





            $begingroup$

            This is an example of a Lissajous figure. (If you've got an oscilloscope with separate $x$ and $y$ inputs and a couple of signal generators you can have hours of fun generating them by applying sine waves of appropriate frequency ratio to the two inputs.)






            share|cite|improve this answer









            $endgroup$



            This is an example of a Lissajous figure. (If you've got an oscilloscope with separate $x$ and $y$ inputs and a couple of signal generators you can have hours of fun generating them by applying sine waves of appropriate frequency ratio to the two inputs.)







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Jan 13 at 19:13









            timtfjtimtfj

            2,468420




            2,468420























                3












                $begingroup$

                An easier parameterization of an 8-like figure is $(x,y) = (sin 2t, cos t),$
                where $0 leq t leq 2pi.$ It can easily be made more 8-like by scaling.






                share|cite|improve this answer









                $endgroup$


















                  3












                  $begingroup$

                  An easier parameterization of an 8-like figure is $(x,y) = (sin 2t, cos t),$
                  where $0 leq t leq 2pi.$ It can easily be made more 8-like by scaling.






                  share|cite|improve this answer









                  $endgroup$
















                    3












                    3








                    3





                    $begingroup$

                    An easier parameterization of an 8-like figure is $(x,y) = (sin 2t, cos t),$
                    where $0 leq t leq 2pi.$ It can easily be made more 8-like by scaling.






                    share|cite|improve this answer









                    $endgroup$



                    An easier parameterization of an 8-like figure is $(x,y) = (sin 2t, cos t),$
                    where $0 leq t leq 2pi.$ It can easily be made more 8-like by scaling.







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered Jan 13 at 8:57









                    md2perpemd2perpe

                    8,21111028




                    8,21111028























                        1












                        $begingroup$


                        $x = frac{asqrt{2}cos(t)}{sin^2(t) + 1}; qquad y = frac{asqrt{2}cos(t)sin(t)}{sin^2(t) + 1}$




                        Check out this source:




                        https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli







                        share|cite|improve this answer









                        $endgroup$


















                          1












                          $begingroup$


                          $x = frac{asqrt{2}cos(t)}{sin^2(t) + 1}; qquad y = frac{asqrt{2}cos(t)sin(t)}{sin^2(t) + 1}$




                          Check out this source:




                          https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli







                          share|cite|improve this answer









                          $endgroup$
















                            1












                            1








                            1





                            $begingroup$


                            $x = frac{asqrt{2}cos(t)}{sin^2(t) + 1}; qquad y = frac{asqrt{2}cos(t)sin(t)}{sin^2(t) + 1}$




                            Check out this source:




                            https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli







                            share|cite|improve this answer









                            $endgroup$




                            $x = frac{asqrt{2}cos(t)}{sin^2(t) + 1}; qquad y = frac{asqrt{2}cos(t)sin(t)}{sin^2(t) + 1}$




                            Check out this source:




                            https://en.wikipedia.org/wiki/Lemniscate_of_Bernoulli








                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered Jan 13 at 7:28









                            BadAtGeometryBadAtGeometry

                            188215




                            188215















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