[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
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
On Thu, Feb 1, 2018 at 6:48 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
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...
Yes indeed. Also, the first approximant swings about. On the 40th point, it gets closest to the final part. So ... 67 gave the game away? Explain 67^4×743^4 vs 6960032968453699315405461491552319616949 in these similar triangle power wheels: http://community.wolfram.com/groups/-/m/t/1278120 --Ed Pegg Jr
participants (2)
-
Adam P. Goucher -
Ed Pegg Jr