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24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
October 21, 2020
Question

What name has this closed curve?

  • October 21, 2020
  • 3 replies
  • 10895 views

It is a deltoid (one hypecycloid)

Hypocycloid-Deltoid.gif

It is a cardioid (one epicycloid) - one alternative method of plotting

HypoCardioud.gif

What is it?

NewHypocycloid.gif

3 replies

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Werner_E25-Diamond I
25-Diamond I
October 21, 2020

Not every curve has a unique own name - there are too many of them 😉

    D
    DJF16-Pearl
    16-Pearl
    October 21, 2020

    Well, they can be made with the child's toy known as the Spirograph.  And the wikipedia entry for that calls them roulette curves.

     

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

      V
      24-Ruby IV
      ValeryOchkov24-Ruby IVAuthor
      24-Ruby IV
      October 22, 2020

      I think the cardioid is not one epicycloid but one hypocycloid too!

      Or we have not two but three kindd of of curves - epicycloids, hypocycloids and ??? (see above)

      Cardioid-Epicycloid-Hypocicloid.gif

      W
      Werner_E25-Diamond I
      25-Diamond I
      October 24, 2020

      But why do you think that this orientation is "correct" ???

       

      EDIT: Ah, I think I know - it's because of the supposedly heart-shaped appearance of the curve, right?
      I've actually never found the curve to be reminiscent of a heart. Anyway, there are better ways to generate a heart-shaped curve.

      Here are some examples I collected a while ago:

      Werner_E_0-1603586990871.png

      Or even in 3D (thanks to Viacheslav N. Mezentsev's "implicitplot3D()"):

       
       

      Werner_E_0-1603587253986.png

       

      M
      MaxNori10-Marble
      10-Marble
      November 14, 2020

      About the name of trigonometric function, why sin(x) is called sinus?

      According to the Italian Wiki this is due to an “error of translation" by Gherardo da Cremona (1114-1187, https://en.wikipedia.org/wiki/Gerard_of_Cremona) while translating from arabic to Latin the Algebra of al-Khwārizmī, The arabic word "jiba"  was originally referring to the sanskrit word for chord not bay (sinus in lat.).

      According the English Wiki the same error was made by Robert of Chester https://en.wikipedia.org/wiki/Robert_of_Chester

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