Spirolaterals are an idea that I don't remember where I read about them, but the idea is relatively simple. You take the the decimal expansion of some fraction and using the digits create segments of those lengths then rotate some fixed number of degrees. I have an Excel spreadsheet that creates these pictures. If I figure out a way to post the file I will. Let me know if you know of a way to do that.
Here is 8/147 with a 90 degree turn at each step.
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I can host it on my web server if you want, so then you can just post a link to it.
how can i get the file?
Do they always end up forming a loop like this? I like how it has rotational symmetry - is that always the case?
No they don't always form a loop. They if the don't form a loop then the go off in a particular direction. They don't have to have symmetry, but they generally do.
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