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Meta
Category Archives: mathematics
in memory
Dan Alderson once made a map of nearby stars by mounting little colored spheres on threads strung between holes in two sheets of heavy clear plastic. It occurs to me that, taking the stars in pairs, he could use half … Continue reading
Posted in astronomy, fandom, mathematics
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polytopes
Dr. Richard Klitzing lost his webhost, so I took custody of his polytope pages.
Posted in mathematics
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circles in ellipses
Many people have worked on the problem of packing equal circles efficiently in various regular shapes. David Cantrell asks, what is the ellipse of least area that can enclose n unit circles? Sometimes it’s a circle (n=1,7,19), sometimes it’s highly … Continue reading
Posted in mathematics
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Hilbert’s palette
A space-filling path through this square is matched to an analogous path through the color-cube. I had this idea in mind for years but the algorithm for Hilbert’s curve defeated me; then I stumbled on Steve Witham’s Python code, and … Continue reading
Posted in eye-candy, mathematics
4 Comments
Takana go goth
See Takana. The 306 figures shown there can be reduced to 45 by rotation and reflection. I fitted a polynomial curve to each partial path, and superimposed them.
Posted in curve-fitting
2 Comments
the greatest thing ever!
Forgive my waxing hyperbolic . . . This is a tiling of the hyperbolic plane by triangles whose angles are π/2, π/3, π/7 – the smallest possible tile. I present it in a conformal mapping analogous to the Mercator projection, which I’ve … Continue reading
Posted in eye-candy, mathematics
1 Comment
looking for sanity checks in an insane world
Some years ago, using basic theorems of hyperbolic trigonometry, I worked out a conformal representation of the hyperbolic plane which preserves one line – analogous to the Mercator projection of the sphere, a conformal map which preserves one great circle. … Continue reading
Posted in mathematics
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