The Corner

At Sixes and Sevens

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.

Most Popular


Stick a Fork in O’Rourke

If, as I wrote last week here, Joe Biden may save the Democratic party from a horrible debacle at the polls next year, Beto O’Rourke may be doing the whole process a good turn now. Biden, despite his efforts to masquerade as the vanguard of what is now called progressivism, is politically sane and, if ... Read More

In Defense of the Electoral College

Senator Elizabeth Warren has joined a growing chorus within the Democratic party in calling for the abolition of the Electoral College. Speaking at a forum in Mississippi on Monday night, Warren said that she hoped to ensure that “every vote matters” and proposed that “the way we can make that happen is ... Read More
National Security & Defense

In Defense of the Iraq War

Today is the 16th anniversary of the invasion of Iraq, and Twitter is alive with condemnations of the conflict -- countered by precious few defenses. Yet I believed the Iraq War was just and proper in 2003, and I still believe that today. When Donald Trump condemned the war during the 2015 primary campaign and ... Read More

Ivy-League Schools Wither

A  number of liberal bastions are daily being hammered — especially the elite university and Silicon Valley. A Yale and a Stanford, or Facebook and Google, assume — for the most part rightly — that each is so loudly progressive that the public, federal and state regulators, and politicians would of ... Read More