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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 (\(d\)).

A definition of the exponential function that has found application in numerous approximation schemes is \(e^x = \lim_{y\to\infty} \left(1+\frac{x}{y}\right)^y\).

Integrating the Gaussian function from minus to plus infinity yields \(\int_{-\infty}^{\infty} e^{-x^2}dx=\sqrt{\pi}\), which is known as the Gaussian integral.