Email Gateway (Jun 16 2026 at 12:23): Email Gateway (Jun 16 2026 at 12:23):From: Manuel Eberl <manuel@pruvisto.org>
The Dottie Number
by Lawrence C. Paulson
The Dottie number is the unique fixed point d of the cosine function:
cos d = d. It is approximately 0.739085133215 and has no known closed form.
This theory establishes the Dottie number's key properties: the fixed
point exists (by the intermediate value theorem) and is unique (because
"cos x - x" has a strictly negative derivative). Next, the value of d to
12 decimal places is shown using the approximation proof method. Two
more properties of d are also shown: first, that it is transcendental
(via the Hermite–Lindemann–Weierstrass theorem); second, that it is a
universal attractor, in the sense that iterating the cosine function
from any real starting point converges to it.
https://isa-afp.org/entries/Dottie_Number.html
Enjoy,
Manuel
Last updated: Jul 02 2026 at 07:34 UTC