Skip to main content
V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
October 21, 2020
Question

What name has this closed curve?

  • October 21, 2020
  • 3 replies
  • 10890 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

W
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 22, 2020

      Names of curves often are chosen after the way the are created.  These "rolling curves" (German. Rollkurven) often also are created by so called planetary motion (German: Planetenbewegung).

      Epizykloids are also called Hypercycloids or (German: Aufradlinien) and Hypocycloid are (German: Inradlinien).

       

      Most Authors distinguish between cycloids and trochoids, but some call them both cycloids. The latter is wrong in my opinion as a cycloid is a special trochoide, but not the other way round.

       

      So, as usual names are not standardized and always matter of confusion.

       

      Every trochoide (no matter if epi.. or hypo... and no matter if cycloide or not) can be created in two ways by rolling two circles.

      In the case of the epicycloide, the second way to generate it usually is also called an epicycloid, but sometimes its called a pericycloid 

      I think it makes sense to use a third name (pericycloide) as the motion for the pericycloide has more in common with that of a hypocycloide than with that of an epicycloide IMHO.

      If the moving point is not on the circumference of the rolling circle, the curve is of course called a peritrochoide. An example for a peritrochoide is the hull of a Wankel-motor -> http://www.animatedengines.com/wankel.html

      BTW, in the link above you also see a refernce to "507 Mechanical Movements". A lot of them are not (yet) animated (some quite simple, some more complex). Maybe a stimulus for you and/or your students.

       

       

        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

          Terms & ConditionsCookie settingsAccessibility statement