Why pi is in Gaussian Distribution area under bell curve
The Gaussian distribution is uniquely determined by satisfying two simultaneous constraints: radial symmetry (dependence only on distance from a central point) and coordinate independence among dimensions. This theoretical necessity forces the probability density function to take the form of an exponential quadratic, $e^{-k r^2}$. The appearance of $\pi$ in the normalization constant arises specifically because these properties imply that the total volume under the associated surface is proportional to the area of a circle relative to its radius squared.
Why pi is in Gaussian Distribution area under bell curve
The Gaussian distribution is uniquely determined by satisfying two simultaneous constraints: radial symmetry (dependence only on distance from a central point) and coordinate independence among dimen…