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Meta
Category Archives: sciences
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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what the cat did in the night-time
Whenever I get settled in my big chair, Pillow (the junior cat) is all over me; but when I’m in bed he almost never comes within reach. So I was surprised when, on waking in the night, I found him … Continue reading
Posted in medicine, pets
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to balance a calendar
A Martian year is 668.6 Martian days; that’s 3.4 less than 24×28. I asked myself, how should the short months be arranged for best ‘balance’? I ran all combinations and this is it: The three big dots represent the missing … Continue reading
symmetries made simple
This may be of interest to only a few: Simplest Canonical Polyhedra of Each Symmetry Type (rotable in Java); in other words, canonical forms of the simplest topologies that allow the specified symmetries and none higher. Any convex polyhedron can … Continue reading
Posted in mathematics
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how much is in there?
I reloaded MacOS, restored my home directory from backup, and was surprised to learn that I have 3e5 files. Most of the bulk is music, but that’s only 7e3 files. Is there a tool analogous to du that gives the … Continue reading
happy leap day
If I were Pope Gregory’s advisor, I’d urge this: all months to have 30 days until the first (or last) of some month falls on a solstice or equinox; thereafter, alternate 30, 31, 30, 31, 30, 31, 30, 31, 30, … Continue reading
negative curves
For years I’ve wished to learn enough hyperbolic geometry to write a simple ray-tracer. Recently a post on comp.graphics.algorithms advised me to look up Euclidean and Non-Euclidean Geometry by Patrick J. Ryan; I was pleased to find that its subtitle … Continue reading
Posted in mathematics
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