

A019827


Decimal expansion of sin(Pi/10) (angle of 18 degrees).


22



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

0,1


COMMENTS

Decimal expansion of cos(2*Pi/5) (angle of 72 degrees).
One of the two roots of 4x^2 + 2x  1 (the other is the sine of 54 degrees times 1).  Alonso del Arte, Apr 25 2015
This is the height h of the isosceles triangle in a regular pentagon inscribed in a unit circle, formed by a diagonal as base and two adjacent radii. h = cos(2*Pi/5) = sin(Pi/10).  Wolfdieter Lang, Jan 08 2018


LINKS

Hideyuki Ohtsuka, Problem B1237, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 56, No. 4 (2018), p. 366; A Telescoping Product, Solution to Problem B1237 by Steve Edwards, ibid., Vol. 57, No. 4 (2019), pp. 369370.


FORMULA

Equals (sqrt(5)  1)/4 = (phi  1)/2 = 1/(2*phi), with phi from A001622.
Equals Product_{k>=1} 1  1/(phi + phi^k), where phi is the golden ratio (A001622) (Ohtsuka, 2018).  Amiram Eldar, Dec 02 2021


EXAMPLE

0.30901699437494742410229341718281905886015458990288143106772431135263...


MATHEMATICA

RealDigits[Sin[18 Degree], 10, 108][[1]] (* Alonso del Arte, Apr 20 2015 *)


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AUTHOR



STATUS

approved



