OFFSET
1,2
COMMENTS
This number can be interpreted geometrically as the angle in radians of a fan made of stacked right triangles, with the length to height ratio doubling each successive triangle as seen in the illustration.
Since this angle exceeds Pi/2, the set of rotation angles used in the CORDIC algorithm covers an angle range sufficient to compute sine and cosine for any angle between 0 and Pi/2. This means the algorithm can converge to any angle in that range through appropriate combinations of these basic rotations. - Daniel Hoyt, Oct 25 2024
LINKS
Daniel Hoyt, Illustration of this angle's arctan relationship.
Wikipedia, CORDIC.
FORMULA
Equals Sum_{k>=1} (-1)^(k+1)*2^(2*k-1)/((2^(2*k-1)-1)*(2*k-1)).
EXAMPLE
1.743286620472340003...
MAPLE
Digits:= 140:
evalf(sum(arccot(2^k), k=0..infinity)); # Alois P. Heinz, Jun 02 2021
PROG
(PARI) suminf(k=0, atan(1/2^k))
(PARI) sumalt(k=1, ((-1)^(k+1))*2^(2*k-1)/((2^(2*k-1)-1)*(2*k-1)))
CROSSREFS
KEYWORD
AUTHOR
Daniel Hoyt, Jun 01 2021
STATUS
approved