Square cardioid

Forum|Forum|5 years ago
October 13, 2020
1 reply
6543 views

Can you create this "square cardioid" in Mathcad.

With animation!

Algebra_Geometry

Best answer by Werner_E

@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 😉

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

W

Werner_E

25-Diamond I

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?