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ValeryOchkov24-Ruby IV
24-Ruby IV
October 13, 2020
Solved

Square cardioid

Can you create this "square cardioid" in Mathcad.

With animation!

New-Cardioid.png 

Werner_E
Werner_EAnswer
25-Diamond I
October 15, 2020
@ValeryOchkov wrote:

I am waiting too! It is one task for my students!

Lazy guy!! 🙂

But that sure shouldn't take that long, should it?

Waiting for students is easy, but you can only do a thing if you do it yourself.

Couldn't wait any longer 😉

Werner_E_0-1602786066136.gif

Now its your turn! How about a triangle "rolling" on a square or a circle, or, again, the other way round.

 

 

 

 

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10 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
October 13, 2020

I wouldn't call it a square cardiod (even though it would look similar).

The path of the point is relatively unspectacular and consists of three different curves:
1) four quarter circles
2) two parts of an involute of a circle, such as those used in the construction of a particular type of gear
3) two parts of a parallel curve to an involute of a circle

 

You can also do it the other way around and unroll the circle on the square. The point path then consists of alternating circular and cycloid pieces. That doesn't look particularly exciting either.

 

Apropos Cardioid - you sure remember the bicycle with the square wheels

https://thumbs.dreamstime.com/z/driewieler-voor-jonge-geitjes-met-vierkante-wielen-110677055.jpg

https://bike-blog.info/wp-content/uploads/2020/04/fahrrad-mit-eckigen-raedern-800.jpg

 

But did you know that there also are vehicles with wheels in the shape of cardioids?

See https://mathematikalpha.de/zykloide where you also can download software to play around with some kind of animations 🙂

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    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    October 13, 2020

    Thanks, Werner!

    But it will be good to see animtion!

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    October 13, 2020
    @ValeryOchkov wrote:

    Thanks, Werner!

    But it will be good to see animtion!

    Sure! Feel free to create and show your animation 🙂

     

    EDIT: @ValeryOchkov  I'm still waiting to see your animation!

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