OFFSET
0,1
COMMENTS
In a letter to Christian Goldbach dated December 9, 1741, Leonhard Euler gave 10/13 as a rational approximation of this number.
Also, real part of 2^i. - Bruno Berselli, Dec 31 2012
The imaginary part of 2^i is A220085. - Robert G. Wilson v, Feb 04 2013
REFERENCES
W. Michael Kelley, The Humongous Book of Calculus Problems. New York: Alpha Books (Penguin Group) p. 233, Problem 15.22.
LINKS
Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1), Princeton, New Jersey: Princeton University Press (1988), 143 - 144.
Elizabeth Volz, An English translation of portions of seven correspondences between Euler and Goldbach on Euler’s complex exponential paradox and special values of cosine, 2008
Elizabeth Volz and Hieu D. Nguyen, Euler, Goldbach and exact values of trigonometric functions, 2008 preprint
FORMULA
cos(log(2)) = (2^i + 2^(-i))/2.
EXAMPLE
0.76923890136...
MATHEMATICA
RealDigits[Cos[Log[2]], 10, 105][[1]]
PROG
(PARI) cos(log(2)) \\ Charles R Greathouse IV, Nov 25 2012
(Maxima) fpprec:110; ev(bfloat(cos(log(2)))); /* Bruno Berselli, Dec 31 2012 */
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Alonso del Arte, Nov 25 2012
EXTENSIONS
a(43) ff. corrected by Georg Fischer, Apr 03 2020
STATUS
approved