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Meta
Category Archives: mathematics
it’s in the literature
On a truncated icosahedron / buckyball / Telstar-style soccer ball, consider two adjacent hexagons and the two pentagons that are adjacent to both. These four faces can be removed, rotated by a right angle, and reattached, causing only a small … Continue reading
Posted in mathematics
1 Comment
another problem with my clothoids
I wrote: each curve hits alternate dots: first exactly, then with offsets pushing it toward the other curve. I don’t think I’ve mentioned here how the offsets work.
Posted in curve-fitting
3 Comments
clothoid weekend update
For context, see past posts in the curve-fitting category that I just created. To recap: The curves I’ve been drawing are the paths made by a point moving at constant speed at an angle which is a piecewise quadratic function … Continue reading
Posted in curve-fitting
2 Comments
un-meander
Here, each curve hits alternate dots: first exactly (above), then with offsets pushing it toward the other curve. Below is the result of eight iterations. With enough iterations, the top of ‘s’ eventually gets a more symmetrical arch, as the … Continue reading
Posted in curve-fitting
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meander
(Previously: 2014, 2011, 2010; also, less closely related, 2015) I tried to smoothen a stroke by shifting each dot toward the Euler spiral (aka clothoid, aka Cornu spiral) determined by its four nearest neighbors. That didn’t work so well: small … Continue reading
Posted in curve-fitting
2 Comments
mutant dragons
In 2007 I thought of a pretty way to paint a square so that all pixels are different, but similar colors are clustered. For each pixel, set x,y to its coordinates; if their sum is odd, set the low bit … Continue reading
Posted in eye-candy, mathematics
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points problems pointers problems
Two-fifths of the links in my sphere arrangements page were broken. Ouch! I found new addresses for a few of them, and used the Wayback Machine for the rest.
Posted in mathematics
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