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It is an algebraic variable.
Actually, the number was discovered and then a symbol had to be assigned to it. Letters of the Greek alphabet are traditionally used for mathematical things, to the symbol for pi was naturally chosen from the Greek alphabet.
A symbol usually only has one or two letters in it and a formula usually has a group/combination of symbols
Mathematician Rudolph Swetchefriz{Added} The symbol is not "for" pi but is pi - one of the letters of the Greek alphabet.