A280207 - OEIS

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A280207

Decimal expansion of x such that tan(Pi/x) + sin(Pi/x)*cos(Pi/x) = 2*Pi/x.

3, 1, 8, 1, 7, 6, 0, 1, 2, 9, 2, 7, 0, 1, 7, 1, 3, 8, 7, 6, 2, 0, 4, 6, 8, 0, 4, 9, 5, 1, 3, 0, 3, 1, 9, 6, 4, 2, 1, 7, 2, 1, 2, 4, 6, 3, 4, 9, 3, 5, 1, 4, 2, 1, 2, 4, 5, 9, 9, 4, 9, 2, 3, 1, 4, 9, 5, 7, 6, 8, 6, 6, 1, 8, 4, 0, 7, 0, 3, 1, 6, 5, 9, 8, 3, 7, 6

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OFFSET

1,1

COMMENTS

This is the hypothetical number of sides an equilateral polygon would have to have in order to create the same area between it and a circle in both its inscribed and circumscribed forms.

It is probably transcendental, though that has not been proved.

LINKS

Table of n, a(n) for n=1..87.

Ondrej Hrdina, First 50000 digits.

Ondrej Hrdina, In-depth description. [Broken link]

FORMULA

Solution of tan(Pi/x) + sin(Pi/x)*cos(Pi/x) = 2*Pi/x. (No closed-form expression for x exists.)

EXAMPLE

x = 3.18176012927017138762046804951303196421721246349351...

MATHEMATICA

RealDigits[x /. FindRoot[Tan[Pi/x] + Sin[Pi/x] * Cos[Pi/x] == 2*Pi/x, {x, 3}, WorkingPrecision->120]][[1]] (* Amiram Eldar, Jun 26 2023 *)

CROSSREFS