https://wikivividly.com/wiki/Schl%C3%A4fli_orthoscheme ; paper #9 in https://books.google.ie/books?isbn=0471010030 ; WFL On 7/4/18, James Propp <jamespropp@gmail.com> wrote:
I didn’t know about Coxeter’s orthoscheme integral. Why 15?
Someone should write an article on the combinatorics and numerology of fractions that keep company with pi and its powers.
Jim Propp
On Wednesday, July 4, 2018, Bill Gosper <billgosper@gmail.com> wrote:
Integrate[((2 + 1/Sqrt[3 + t])*ArcSec[t])/(Sqrt[1 + t]*(2 + t)), {t, 1, 2}] == Pi^2/30 + (1/6)*Pi*ArcSin[(1/16)*(7 - 3*Sqrt[5])]
The integral {t,1,6} = 2 π^2/15 = Coxeter's still-mysterious orthoscheme integral. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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