Unrolling the arc defining angles along the x axis.
Author: Susan Addington

<a href="UnrollArc.ggb">Download</a> complete GeoGebra file

Drag point P  counterclockwise
to unroll the arc along the x axis.

(This only goes from 0 to 2π.)

A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
P = Point(c)
C = (1, 0)
f = CircleArc(A, C, P)
E: (f, 0)
a = Segment(A, E)
α = Angle(C, A, P)
b = Segment(A, P)
v: (f, 1)
c' = Translate(c, v)
A' = Translate(A, v)
E' = Rotate(E, -α, A')
d = CircleArc(A', E', E)
e = Segment(E, A')
g = Segment(E', A')
β = Angle(E', A', E)