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The tetrahedron is the only uniform polyhedron that allows sets of parallel geodesics covering its surface. You can't do it with the sphere for example. Lines of constant longitude (meridians) intersect at the poles, lines of constant latitude are not geodesics.
I had a go at making a tetrahedron by triaxially weaving strips. The strips form parallel geodesics on the tetrahedron. It works, but I m
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Quite a big Tetrahedron.
Near Essen, Germany.
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Archimedes proved the are of a sphere is the same as an open cylinder with the same radius, 4π 𝑟² .
Using an icosahedron, you can make a "discrete" sphere and a "discrete" cylinder that also have the same radius and surface. (20 times the triangle area)
In principle, you could do the same for finer discretization, figure out a way to tile both the sphere and the cylinder with the same triangles.
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This thing is strangely satisfying. I call it a "Yin Yang cylinder". I was not planning to make it, but it arose as a side track of another project.
I looked a bit on the internet, but I did not see any similar things. The closest thing so far it the "Steinmetz bi-cylinder", a kind of intersection of 2 cylinders.
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The tetrahedron is the only uniform polyhedron that allows sets of parallel geodesics covering its surface. You can't do it with the sphere for example. Lines of constant longitude (meridians) intersect at the poles, lines of constant latitude are not geodesics.
I had a go at ma…
Last time I wrote I wasn't going to make a better version of the triaxially woven tetrahedron because it would be too much work. Another part of my brain decided to do it anyway. Indeed it was a lot of work, and I made many mistakes on the…
This gras seems to be unusually hydrophobic. I wonder if there is some evolutionary advantage for this. Other plants in my garden do not have these drops. They shine in the sun.
This thing is strangely satisfying. I call it a "Yin Yang cylinder". I was not planning to make it, but it arose as a side track of another project.
I looked a bit on the internet, but I did not see any similar things. The closest thing s…
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New version of my previous animation. Better forget the old version.
I should also mention that while making the animation, I got useful information from this nice web page by Tadeusz E. Doroziński:
https://geometryka.wordpress.com/2016/06…
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Animation of a tennisbal-style dissection of the sphere.
The seam is composed of circle segments. The projection looks like a Yi-Yang symbol. I am wonder if I can make something like the recent "generalized" Yin-Yang posts on the tennisbal…
Quite a big Tetrahedron.
Near Essen, Germany.
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I was intrigued by a website on the space of triangles and elliptic curves:
https://dmuw.zum.de/wiki/Heron_Triangles_and_Elliptic_Curves
I made an animation, showing how triangles can be warped by a 1 parameter transformation, that keeps b…
There is an interesting and concise 1942 lecture text (the lecture was cancelled because of the war) on "Newton the Man" by John Maynard Keynes. Newton was probably the most important physicist in history, but he spent a lot more time on…
Archimedes proved the are of a sphere is the same as an open cylinder with the same radius, 4π 𝑟² .
Using an icosahedron, you can make a "discrete" sphere and a "discrete" cylinder that also have the same radius and surface. (20 times th…
This Youtube channel featuring Leonard Susskind sometimes has click-bate like titles.
https://www.youtube.com/watch?v=SZWb0tUVeho
But it is actually the kind of excellent stuff you would expect from Susskind.
I "find" this a bit strange.
The letter combination "fi" is somehow displayed in a funny way
in my feed (been like that for a long time)
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