Lune (Plane)
A figure bounded by two circular Arcs of unequal Radii. Hippocrates of ChiosBC. 
Two moreEuler 
in 1771). In the 20th century, N. G. Tschebatorew and A. W. Dorodnow proved that these are the only five squarable lunes(Shenitzer and Steprans 1994). The left lune above is squared as follows,
so the lune and Triangle have the same Area. In the right figure,
.
For the above lune,
See also Annulus, Arc, Circle, Lune (Surface)
References
Dunham, W. ``Hippocrates' Quadrature of the Lune.'' Ch. 1 in Journey Through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 1-20, 1990. Heath, T. L. A History of Greek Mathematics, Vol. 1: From Thales to Euclid. New York: Dover, p. 185, 1981. Pappas, T. ``Lunes.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 72-73, 1989. Shenitzer, A. and Steprans, J. ``The Evolution of Integration.'' Amer. Math. Monthly 101, 66-72, 1994.
- Fano Plane
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- Farey Series
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- Feit-Thompson Conjecture
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- Fejes Tóth's Integral
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