Sorry. What n maximizes n is as clear as infinity can be. I meant what n maximizes A(n)? Steve, stevebg wrote:
Being guilty of the eighth deadly sin, the compulsion to correct, I must point out that number (3) should be "a circle three times as large [in diameter]." Of course if there really are eight deadly sins, that makes (7) wrong too. But the newness (presumably to most of us) of the others more than makes up for it. If A(n) is the number of "amazing" (defined to taste, within limits) facts about the integer n, what n maximizes n? nA(n)? n+A(n)? Etc. Which choice would be best to make n "the most amazing number?"
Steve Gray
James Buddenhagen wrote:
I'm not sure these are 'amazing', but maybe worth a look.
(1) there are 7 topologically distinct hexahedra (2) exotic spheres of dimension 7 exist, but not of smaller dimension, except maybe 4?? (3) 7 equal non-overlapping circles fit into a circle twice as large (4) 7 colors are needed to color maps on a torus (5) there is a torus consisting of 7 planar hexagons that requires 7 colors (the Szilassi polyhedron) (6) The minimal finite projective plane has 7 points and 7 lines (the Fano plane) (7) There are 7 deadly sins: pride, envy, gluttony, lust, anger, avarice and sloth.
Jim Buddenhagen http://www.buddenbooks.com/jb
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