nephroids, deltoids, astroids, and lemniscates of Bernoulli.
I love the names of these things. Kampyle of Eudoxus! Witch of Agnesi! I keep expecting someone to write an RPG where they’re all fierce creatures or summoning spells or something.
See also:
But I had an actual mechanical version that could do all these things 40 years ago.
The ones with strings are the best.
I still have mine, plus the Super Spirograph.
Right next to my ~50 year old Etch-a-Sketch.
If you like these, you’ll probably like this book as well. It has many interesting mechanical means for drawing straight likes, or almost straight lines. A combination of mathematics, engineering, art and philosophy.
Great book. The author has a video on line of actual physical constructions of some of the concepts:
How Round Is Your Circle?
These are a lot of fun. I especially like the complex circle machine that draws a straight line.
I have built clocks using the Lissajous method of drawing circles on an oscilloscope. There’s analog electronics that makes the sine and cosine waves that comprise the circles; the microcomputer just positions them and controls the enabling of each octant. Lines are made of cosine waves.
I’m working now on getting it back into production.
According to the book that @Jim_Kirk mentioned, it’s a serious problem-- mostly because straight edges aren’t
Thanks for posting this, these videos will be useful in the classes I teach. I cover many of these curves but only from the equations, there are only a few where I can do a convincing job demonstrating the motivation for them using the tools at hand (chalk, string, waving hands).
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