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things seemed to be going along just fine and then a friend sent me
http://arxiv.org/astro-ph/0310253
this is a preprint of an article appearing in the current (9 October 2003) issue of Nature, which is also their cover article---a picture of a dodecahedron or something on the cover
the gist is like this: you can't tile the plane with regular pentagons because the inner angle is 108 degrees
but you can tile an ordinary 2-sphere with spherical regular pents that have the inner angle 120 degrees, because 3 angles of 120 degrees each will fit together
Also JR Weeks is a freelance geometer Macartherfellow who does educational geometrical computer graphics----works at home (he is not institutionalized) and probably has more fun than a lot of other Math PhDs from Princeton
And JR Weeks (never believe what geniuses tell you) says that since you can tile a 3-sphere with solid regular dodecahedra, well, obviously that must be what the universe is made of
and he got this French Astronomer (Jean-Pierre Luminet) to believe him and they are fitting the bumps in the cosmic background (WMAP data) to this model.
Luminet is at the "Observatoire de Paris" where, in 1675, a young Dane named Olaus Roemer first determined the speed of light---and got within roughly 10 percent of the right answer, which makes it holy ground, and JR Weeks is just running around loose in the town of Canton, NY.
maybe this is all familiar to other people here but it took me by surprise this morning
http://arxiv.org/astro-ph/0310253
this is a preprint of an article appearing in the current (9 October 2003) issue of Nature, which is also their cover article---a picture of a dodecahedron or something on the cover
the gist is like this: you can't tile the plane with regular pentagons because the inner angle is 108 degrees
but you can tile an ordinary 2-sphere with spherical regular pents that have the inner angle 120 degrees, because 3 angles of 120 degrees each will fit together
Also JR Weeks is a freelance geometer Macartherfellow who does educational geometrical computer graphics----works at home (he is not institutionalized) and probably has more fun than a lot of other Math PhDs from Princeton
And JR Weeks (never believe what geniuses tell you) says that since you can tile a 3-sphere with solid regular dodecahedra, well, obviously that must be what the universe is made of
and he got this French Astronomer (Jean-Pierre Luminet) to believe him and they are fitting the bumps in the cosmic background (WMAP data) to this model.
Luminet is at the "Observatoire de Paris" where, in 1675, a young Dane named Olaus Roemer first determined the speed of light---and got within roughly 10 percent of the right answer, which makes it holy ground, and JR Weeks is just running around loose in the town of Canton, NY.
maybe this is all familiar to other people here but it took me by surprise this morning
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