OFFSET
0,1
COMMENTS
15-gon is the first m-gon with odd composite m which is constructible (see A003401) in virtue of the fact that 15 is the product of two distinct Fermat primes (A019434). The next such case is 51-gon (m=3*17), followed by 85-gon (m=5*17), 771-gon (m=3*257), etc.
From Wolfdieter Lang, Apr 29 2018: (Start)
This constant appears in a historic problem posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593, solved by Viète. See the Havil reference, problem 4, pp. 69-74. See also the comments in A302711 with a link to Romanus' book, Exemplum quaesitum.
REFERENCES
Julian Havil, The Irrationals, A Story of the Numbers You Can't Count On, Princeton University Press, Princeton and Oxford, 2012, pp. 69-74.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
Mauro Fiorentini, Construibili (numeri)
Eric Weisstein's World of Mathematics, Constructible Number
Wikipedia, Constructible number
Wikipedia, Regular polygon
FORMULA
Equals 2*sin(Pi/m) for m=15.
Also equals (sqrt(3) - sqrt(15) + sqrt(10 + 2*sqrt(5)))/4.
Also equals sqrt(7 - sqrt(5) - sqrt(30 - 6*sqrt(5)))/2. This is the rewritten expression of the Havil reference on top of p. 70. - Wolfdieter Lang, Apr 29 2018
EXAMPLE
0.415823381635518674203484568810250332433169521255447672814363947...
MATHEMATICA
RealDigits[N[2Sin[Pi/15], 100]][[1]] (* Robert Price, May 02 2016*)
PROG
(PARI) 2*sin(Pi/15)
CROSSREFS
KEYWORD
AUTHOR
Stanislav Sykora, May 02 2016
STATUS
approved