Dottie number

has infinitely many roots, but unlike the Dottie number, they are not attracting fixed points.

[2] Norair Arakelian used lowercase ayb (ա) from the Armenian alphabet to denote the constant.

[2] The constant name was coined by Samuel R. Kaplan in 2007.

It originates from a professor of French named Dottie who observed the number by repeatedly pressing the cosine button on her calculator.

[3][nb 1] The Dottie number, for which an exact series expansion can be obtained using the Faà di Bruno formula, has interesting connections with the Kepler and Bertrand's circle problems.

[5] The Dottie number appears in the closed form expression of some integrals:[6][7] Using the Taylor series of the inverse of

(or equivalently, the Lagrange inversion theorem), the Dottie number can be expressed as the infinite series: where each

This value can be obtained using Kepler's equation, along with other equivalent closed forms.

[5] In Microsoft Excel and LibreOffice Calc spreadsheets, the Dottie number can be expressed in closed form as SQRT(1-(2*BETA.INV(1/2,1/2,3/2)-1)^2).

In the Mathematica computer algebra system, the Dottie number is Sqrt[1 - (2 InverseBetaRegularized[1/2, 1/2, 3/2] - 1)^2].

The Dottie number is the unique real fixed point of the cosine function.
The solution of quadrisection of circle into four parts of the same area with chords coming from the same point can be expressed via Dottie number.