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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).
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 $0.73908 \ldots$
- 2007: Samuel R. Kaplan: The Dottie Number (Math. Mag. Vol. 80: pp. 73 – 74) www.jstor.org/stable/27642996