This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370393 #9 Feb 27 2024 06:51:51 %S A370393 2,2,7,3,5,4,9,1,8,9,8,4,1,6,5,5,1,4,8,2,4,2,3,7,2,3,8,7,3,9,3,7,6,3, %T A370393 5,7,6,1,0,6,4,1,9,9,1,4,6,9,3,3,0,9,8,8,6,0,3,5,6,5,9,4,4,0,3,9,7,2, %U A370393 3,2,5,1,4,8,7,9,6,7,7,7,5,7,4,7,6,4,6 %N A370393 Decimal expansion of the area of a unit heptadecagon (17-gon). %C A370393 This constant multiplied by the square of the side length of a regular heptadecagon equals the area of that heptadecagon. %C A370393 17^2 divided by this constant equals 68 * tan(Pi/17) = 12.71140300... which is the perimeter and the area of an equable heptadecagon with its side length 4 * tan(Pi/17) = 0.74772958... . %C A370393 An equable rectangle with its perimeter and area = 17 has side lengths: %C A370393 a = s^2/8 = (17 - sqrt(17)) / 4 = (17 - A010473) / 4 = 3.21922359... %C A370393 b = 136/s^2 = (17 + sqrt(17)) / 4 = (17 + A010473) / 4 = 5.28077640... %C A370393 where s is the parameter from the formula mentioned below. %H A370393 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Heptadecagon.html">Heptadecagon</a>. %H A370393 Wikipedia, <a href="https://en.wikipedia.org/wiki/Heptadecagon">Heptadecagon</a>. %F A370393 Equals 17 / (4 * tan(Pi/17)) = 17 / (4 * A343061). %F A370393 Equals 1 / (4 * A007450 * A343061). %F A370393 Equals 17 * cos(Pi/17) / (4 * sin(Pi/17)). %F A370393 Equals 17 * A210649 / (4 * A241243). %F A370393 Equals 17 * A210649 / (2 * A228787). %F A370393 Equals 17 * cot(Pi/17) / 4. %F A370393 Equals 17 * sqrt(4 / (s^2 - 2 * s - 4 * sqrt(17 + 3 * sqrt(17) - s - sqrt(17) * 16/s)) - 1/16) where s = sqrt(34 - 2 * sqrt(17)) = 4 * A329592. %F A370393 The minimal polynomial is 4294967296*x^16 - 3103113871360*x^14 + 510054948143104*x^12 - 28954726431195136*x^10 + 653743432704327680*x^8 - 6011468019822067712*x^6 + 20881180982314634240*x^4 - 21552361799603318912*x^2 + 2862423051509815793. %e A370393 22.7354918984165514... %p A370393 evalf(17 / (4 * tan(Pi/17)), 100); %t A370393 RealDigits[17 / (4 * Tan[Pi/17]), 10, 100][[1]] %o A370393 (PARI) 17 / (4 * tan(Pi/17)) %Y A370393 Cf. A007450, A010473, A019684 (Pi/17), A210644 (cos(2*Pi/17)), A210649, A228787, A241243, A329592, A343061. %K A370393 nonn,cons %O A370393 2,1 %A A370393 _Michal Paulovic_, Feb 17 2024