[seqfan] How about PI_7 ?
Brad Klee
bradklee at gmail.com
Wed Sep 19 16:10:31 CEST 2018
Hi Seqfans,
>From Elkies "The Klein Quartic in Number Theory" (Cf. [1] Section 2),
we have another lesser known PI constant,
PI_7 = 1/(sqrt(7)*Pi)*Gamma(1/7)*Gamma(2/7)*Gamma(4/7)
PI_7 = A020764*A049541*A220086*A220605*A220609
PI_7 = 3.8666234112336230934661536780596274621 . . .
( Not in OEIS )
This could be a nice addition for expanding geometry at OEIS, including
another link to LMFDB--compare with periods in isogney class 49.a [2].
It's also possible to take a plane slice of the projective Klein Quartic
that preserves D_3 symmetry. Circumscribing this closed plane curve
with the smallest possible equilateral triangle, we quickly calculate
a normalized area integral:
A = A_C / A_T = 0.6913145290746903759426 . . . ( Hmmm ? )
Cheers,
Brad
[1] http://library.msri.org/books/Book35/files/elkies.pdf
[2] http://www.lmfdb.org/EllipticCurve/Q/49/a/
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