The number π is then defined as half the magnitude of the derivative of this homomorphism. Ī variation on the same idea, making use of sophisticated mathematical concepts of topology and algebra, is the following theorem: there is a unique ( up to automorphism) continuous isomorphism from the group R/ Z of real numbers under addition modulo integers (the circle group), onto the multiplicative group of complex numbers of absolute value one. Īnd there is a unique positive real number π with this property. The choice of the symbol π is discussed in the section Adoption of the symbol π. In mathematical use, the lowercase letter π is distinguished from its capitalized and enlarged counterpart Π, which denotes a product of a sequence, analogous to how Σ denotes summation. In English, π is pronounced as "pie" ( / p aɪ/ PY). The symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase Greek letter π, sometimes spelled out as pi.
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