History of $\cos(\pi x)$ for rational $x$

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when	who	what
2026-08-19 05:08	bmatschke	the link to the roots of unity said Roots_or_unity and went nowhere	current
2026-08-14 21:31	bmatschke	how well the digits are known: proven (cos(pi*x) at exact rationals, evaluated into an interval field)
2026-08-13 22:16	bmatschke	how well the digits are known: proven (cos(pi*x) at exact rationals, evaluated into an interval field)
2026-08-13 22:06	bmatschke	how well the digits are known: heuristic (a fixed-precision value wrapped in an interval field)
2026-08-09 09:13	flattening	entries rewritten as records with named parameters
2026-08-09 08:34	data-repository import	the current state of the data repository	reviewed
2021-05-06 12:38	bmatschke	from the data repository, 5211f06b

What changed between 2026-08-14 21:31 and 2026-08-19 05:08

from line 8 (5 lines) @@ -8,5 +8,5 @@

 Comments:   comment-real-parts-of-roots-of-unity: For $x = 2k/n$, $\cos(\pi x)$ equals  the-    real part of the  $n$'th HREF{Roots_or_unity}[root of unity] $\exp(2\pi i k/n)$+    real part of the  $n$'th HREF{Roots_of_unity}[root of unity] $\exp(2\pi i k/n)$     CITE{WikiRootsOf1}.   comment-roots-of-Tn: For $x = (k-1/2)/n$ ($k = 1, \ldots, n$), $\cos(\pi x)$ equals