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A famous irrational number, \(\pi = \frac{C}{d}\) is defined by the ratio of a circle's circumference (\(C\)) to its diameter (\(d\)).

The fundamental theorem of calculus, \(f(x) = \frac{d}{dx}\int_{a}^{x}f(s)ds\), expresses the essential inverse relationship between the derivative and integral operators.

Factorials apply only to nonnegative integers but can be extended to complex numbers with positive real parts using the Gamma function, \(\Gamma(n) = \int_0^\infty e^{-x}x^{n-1}dx\).