Spherical Cycloids


Today I don’t have anything big. I just wanted to point people to “Spherical Cycloids”, a post on the WordPress blog The Inner Frame. Cycloids are somewhat familiar, at least to kids who grew up in the United States in my age cohort, because you get them out of spirographs. You make them by taking some point within a rotatable object. Roll that object along the path, normally one that’s defined by another shape. You can get wonderful and strange and exotic-looking curves, many with a hypnotic regularity.

The Inner Frame made a variation of this. It’s got cycloids drawn on the surface of the sphere. This immediately adds a new level of strangeness and wonder to the curves. The pictures are lovely and hypnotic. Folks with 3-D printers can probably also make some grand exotic candleholders from the pattern, too.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

6 thoughts on “Spherical Cycloids”

  1. Thanks for sharing! What an interesting construction.

    I suspect the curves might be too tenuous and become horizontal in too many places to 3D print. But it would be awesome to have physical representations of those space curves.

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    1. Glad you liked. And I defer to expertise in 3-D printing. I haven’t got one or the chance to play with one myself. All I do know is there’s friends who have them and sometimes show off making block of things that are blue plastic.

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    1. Glad that you liked it.

      I wonder if the pure joy of a Lissajous figure is lost a bit to people who first see mathematics stuff rendered on a computer screen instead of by hooking circuits up to an oscilloscope. There’s also a joy in adding together sine and cosine functions you can do by electric circuits that probably doesn’t seem so novel if you’ve seen it without snapping circuit elements into place.

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      1. Yes, I fully agree. I think there is sort of the reverse effect, too: Today you find a beautiful animation for anything (in science) on the internet, so putting hardware together to come up with a less exciting version of that is maybe a let-down.
        I have been asked questions like: Couldn’t you create an animation? – instead of ‘just’ posting data and a series of illustrations that were actually an awful lot of work to create already. If you just see the end result but aren’t into playing / fighting with physical sensors, buggy firmware, and programming your own stuff you see just a static boring scatter plot and images that are not Pixar-Studios-worthy.

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        1. This is true. Although there is a certain fascination that actual raw data, of the kind you see in the laboratory, has. This might reflect some cultural biases on my part, though. I was a kid in the 1970s and American movies in that time were particularly fond of the de-glamorized, rough, barely-visible-pips-on-a-scope sort of display for technical detail. So it reads as authentic and meaningful and even suspenseful to me, even though a later generation might want everything to look like it did on Star Trek: The Next Generation.

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