Hippocrates and Squaring the Circle

Problem 1335. The Lune of Hippocrates has the same area of a Kite.

Lunes of Hippocrates 4

Lunes of Hippocrates 3

Lunes of Hippocrates 2

Lunes of Hippocrates 1, Lunes of Alhazen.

Geometric Art of Lunes of Hippocrates 1, Lunes of Alhazen.

Pythagoras and Circle Area

Proposed Problem 76: Area of a Circle. Square, Circle, Circular Sector.

Problem 99: Circle Area, General Extension to Pythagoras' Theorem.

Geometry Problem 708. Circle, Tangent, Intersecting, Lune, Area, Diameter.