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Mathematics
Euler's Formula for polyhedra
Euler's formula for convex polyhedra is a function of their number of faces (\(F\)), edges (\(E\)), and vertices (\(V\)), stating that \(F-E+V=2\).
Mathematics
The Gaussian integral
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.
Mathematics
The limit definition of the exponential function
A definition of the exponential function that has found application in numerous approximation schemes is \(e^x = \lim_{y\to\infty} \left(1+\frac{x}{y}\right)^y\).