MathDB

Let

D_{x,y}

denote the half-disk of radius

1

with its curved boundary externally tangent to the unit circle at the point

(x, y)

, such that the straight boundary of the disk is parallel to the tangent line (so the point of tangency is the middle of the curved boundary). Find the area of the union of the

D_{x,y}

over all

(x, y)

with

x^2 + y^2 = 1

(that is,

(x,y)

is on the unit circle).

Problem Statement