The names of these shapes are based on the following:
Arbelos — a shoemaker's knife,
Salinon — a salt cellar, and
Lune — the moon.
Notice that when we make a lune from two circles, we in fact make 2 lunes
— one on each side. The shape formed in the middle,
from the intersection of the two circles, is called a Lens.
The arbelos and salinon were first introduced in Aristotle's Book of Lemmas —
we've already seen Aristotle here: Aristotle's Wheels
The problem of Squaring the Circle
is one of the most famous problems from antiquity, and was only proved impossible
when π was proven transcendental by Lindemann in 1882.
Hippocrates of Chios (not to be confused with Hippocrates of Kos — famous
for the Hippocratic Oath in medicine) showed
a lune of the particular type in the activity above is equal in area to an
This was the first exact calculation of the area of a circular shape!
Try and visualise similar shapes made from the intersections of
spheres in 3D.