ISOPERIMETRY, a word originally used in geometry to refer to figures of equal perimeter ; e.g., a circle and an ellipse may have equal perimeters (circumferences) although not equal areas. One of the simplest of the problems arising in the study is to determine, from all plane figures having the same perimeter, the one that shall have the greatest area. This figure is the circle. Considered more generally, given any number of geometric figures, all defined in the same way, determine the form of the one possessing a maximum (or minimum) amount of a certain prop erty; e.g., of all the triangles having a given area (figures defined
as plane, three-sided, and of a given area), the one having the least perimeter is equilateral. For the general definition and treatment consult works on the calculus of variations (q.v.), where the theory is extended to include solid as well as plane figures.