Two Ways of Generalizing π 📐🔢

The constant π is the ratio of a circle’s circumference to its diameter. But we can generalize π by generalizing what a “circle” is. We define a p-circle to be the set of points satisfying

$∣x∣^p+∣y∣^p=1$

για $1≤p≤∞$.

Mathematician John D. Cook explores how the familiar π can be extended beyond the geometry of the Euclidean circle. By redefining what we mean by a circle — using p-norms — and by changing how we measure its perimeter, Cook arrives at two distinct families of π-like constants. Surprisingly, the classical π (from the Euclidean unit circle) turns out to be the minimum value in one of these generalizations.

🔗 Read more: Two ways of generalizing π – John D. Cook