[seqfan] How about PI_7 ?

[Brad Klee]

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/