Definition:Dottie Number

Definition

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

• Existence and Uniqueness of Dottie Number

• Dottie Number is Universally Attractive

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 $0.73908 \ldots$

Sources

• 2007: Samuel R. Kaplan: The Dottie Number (Math. Mag. Vol. 80: pp. 73 – 74)  www.jstor.org/stable/27642996