Definition:Dottie Number

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The Dottie number $\d$ is defined as the unique fixed point of the cosine function:

$\cos \rd = \d$

Its approximate value is given by:

$\d \approx 0 \cdotp 73908 \, 51332 \, 15160 \, 64165 \, 53120 \, 87673 \ldots$

This sequence is A003957 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

Source of Name

The name Dottie is of no mathematical significance.

It refers to a professor of French who noticed that if she took the cosine of seemingly any number repeatedly, the result would always converge to the value $0.73908 \ldots$