MathDB

Let

F_n

be the nth Fibonacci number, defined by

F_1 = F_2 = 1

and

F_n = F_{n-1} + F_{n-2}

for

n > 2

. Let

A_0, A_1, A_2,\cdots

be a sequence of points on a circle of radius

1

such that the minor arc from

A_{k-1}

A_k

runs clockwise and such that

\mu(A_{k-1}A_k)=\frac{4F_{2k+1}}{F_{2k+1}^2+1}

for

k \geq 1

, where

\mu(XY )

denotes the radian measure of the arc

XY

in the clockwise direction. What is the limit of the radian measure of arc

A_0A_n

n

approaches infinity?

Problem Statement