Making Pretty Pictures, Again

rolling parabola

prolate trochoid

I got interested in making nice pictures in Mathematica again, after a hiatus of ~5 years. I suppose I should be writing up on how I generated these samples, but I’ll try to formalize the mathematics behind these first. For now, enjoy these short movies!


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10 Responses to Making Pretty Pictures, Again

  1. Simon says:

    Very pretty! A quick search ( shows that there is no demonstration of a rolling hyperbola, maybe you should make one?

    • tpfto says:

      Hi Simon! It’s actually a rolling parabola. The focus of a rolling parabola traces out a catenary, the curve a chain or string hanging from two points makes. I have working code, but explaining how to do it is a bit difficult. I suppose I should write about it in a future entry.

  2. Chandrasekhar says:

    Respected J.M,

    I am Chandru1 from stackexchange. I see that you have drawn wonderful diagrams. I would like to have this diagram worked out for me. I don’t know how to draw pics.

    Could you please draw the graph of the curve x^{n}+y^{n}=1 when n is even and tell me what happens when n \to infty.

  3. Lovely graphics. I particularly liked the first one. Seems that the red trajectory is a parabola as well as the blue one.

  4. Jonas says:

    Neat! There was an article this year in the College Mathematics Journal called “The locus of the focus of a rolling parabola” that you might find interesting.

  5. I have a similar post and I have included code that works for the prolate and curtate cycloids.

    here is the link

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