There are three approximations at play here: -- the ratio between two large terms is approximately given by alpha (a particular cubic irrational); -- alpha^24 + 720 is approximately equal to the negative of the j-invariant j((1 + sqrt(-67))/2) = -5280^3; -- the j-invariant j((1 + sqrt(-67))/2) is approximately equal to 744 - e^(pi sqrt(67)). The Heegner number 67 gave the game away...
Sent: Thursday, February 01, 2018 at 10:51 PM From: "Ed Pegg Jr" <ed@mathpuzzle.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] The basketball scoring approximation.
https://oeis.org/A077835 is the basketball scoring sequence.
Something special happens between the combined scores equaling 39 and 40. It's often said that by then, you can be 67% sure of who will win the game.
Using math explored at http://community.wolfram.com/groups/-/m/t/1277291 , I show this value is actually
*66.99999999999999999997299*
--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun