|
| |
|
|
A258403
|
|
Decimal expansion of the area of the regular 10-gon (decagon) of circumradius = 1.
|
|
2
|
|
|
|
2, 9, 3, 8, 9, 2, 6, 2, 6, 1, 4, 6, 2, 3, 6, 5, 6, 4, 5, 8, 4, 3, 5, 2, 9, 7, 7, 3, 1, 9, 5, 3, 6, 3, 8, 4, 2, 9, 8, 8, 2, 6, 2, 1, 8, 8, 2, 1, 5, 7, 2, 9, 9, 5, 5, 3, 6, 1, 3, 6, 2, 4, 0, 3, 7, 8, 6, 3, 9, 2, 3, 7, 0, 8, 1, 1, 7, 5, 9, 7, 8, 7, 5, 4, 2, 5, 2, 0, 2, 4, 9, 3, 1, 3, 7, 0, 6, 6, 7, 9, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Quartic number of degree 4 and denominator 2; minimal polynomial 16x^4 - 500x^2 + 3125. - Charles R Greathouse IV, Apr 20 2016
|
|
|
LINKS
|
Eric Weisstein's MathWorld, Decagon
|
|
|
FORMULA
|
Equals (5/2)*sqrt((5-sqrt(5))/2).
Area formulas from triangle to dodecagon, with circumradius 1:
n-gon area(n) = (1/2)*n*sin(2*Pi/n)
3-gon (3*sqrt(3))/4
4-gon 2
5-gon (5/4)*sqrt((5+sqrt(5))/2)
6-gon (3*sqrt(3))/2
7-gon (7/2)*cos((3*Pi)/14)
8-gon 2*sqrt(2)
9-gon (9/2)*sin((2*Pi)/9)
10-gon (5/2)*sqrt((5-sqrt(5))/2)
11-gon (11/2)*sin((2*Pi)/11)
12-gon 3
|
|
|
EXAMPLE
|
2.9389262614623656458435297731953638429882621882157299553613624...
|
|
|
MATHEMATICA
|
RealDigits[(5/2)*Sqrt[(5 - Sqrt[5])/2], 10, 101] // First
|
|
|
PROG
|
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
