Why π is in the normal distribution (beyond integral tricks)

Summary by Krater

This video explores why the constant pi appears in the normal distribution, reviewing the classic proof by Poisson and then connecting it to multivariate Gaussians through radial symmetry and coordinate independence.

From the video

Answers: Why does pi show up in the normal distribution formula?

• Gaussian distribution
• Normal distribution
• Area under the bell curve
• Poisson integral proof
• Herschel-Maxwell derivation
• Central Limit Theorem

What it concludes

• The area under the standard normal curve e^(-x^2) is the square root of pi.
• A Gaussian distribution in multiple dimensions can be derived from the assumptions of radial symmetry and coordinate independence.