Yeah, yeah, *five* Platonic solids. They’re right there in the link I provided. I think the four-ness of the tetrahedron had taken control of my brain; rather as eleven-ness took control in the classic Martin Gardner essay about the first Moon landing. Gardner claimed that the famous garbling of Neil Armstrong’s words “That’s one small step for a man, one giant leap for mankind” resulted from there being twelve of them. That first “a” had to be dropped in transmission to preserve the eleven-ness of the whole enterprise (officially known, of course, as “Apollo 11″). The number five is critical in an oddly large number of math situations. Not only are there five Platonic solids, five is also the largest number of sides the face of a Platonic solid can have. If you go up a dimension, there are six Platonic “solids” in ordinary 4-dimensional space; but in five and every higher dimension, there are only three (the analogs of the tetrahedron, cube, and octahedron). Also, if you compute the 2-dimensionsal “volume” of a circle (i.e., its area), the 3-dimensional volume of a sphere, the 4-dimensional “volume” of a 4-dimensional sphere-analog, and keep going up through the dimensions, the volume peaks at dimension 5 and then declines for ever. Five is also the 5th Fibonacci number (1-1-2-3-5-…), the hypoteneuse of the smallest Pythagorean triangle (3-4-5), the number of Fermat primes known to exist, etc. Algebraic equations of degree five and up have no general algerbraic solution, and so on.
One of the most comforting talking points in politics is to claim that your political opponents are irrationally obsessed. I’m sure this is as old as time, but I first noticed it in the late 1990s. Many of Bill Clinton’s most ardent supporters responded to every new criticism by claiming the president’s ... Read More
With every twist of the news cycle, reports from London on the evolution of the Brexit negotiations between Theresa May’s government and the European Union get odder and odder. Consider, first, the essential choice on Brexit facing the Brits and how it’s being presented to them. Britain voted two years ago ... Read More
The president wants them away from the border. Read More
An Irish lecturer was stabbed to death by a student outside the Paris university where he taught on Wednesday for allegedly insulting the prophet Mohammed by displaying a drawing of him during class. John Dowling, 66, was speaking with a student, identified by authorities only as Ali R., following a lecture ... Read More
M aybe ballot security isn’t such a bad thing after all. Democrats, who the day before yesterday were insisting that voter fraud didn’t exist, now believe that it was used to steal a North Carolina congressional seat from them — and they may well be right. Republican Mark Harris has a 905-vote lead ... Read More