The basics of pi

“Pi (π) is a numerically-rich, universally-engaged, geometric dimensionless constant; it’s never-ending, never-repeating, scale invariant, irrational, and transcendental. Its very essence inculcates continuity (numbers), symmetry (geometry) and harmony (dynamics). It is the face of the finite and the perfection of the infinite. All these qualities are among the most fundamental processes that define our universe.

Pi is most-known as the ratio of the circle’s circumference to its diameter. It’s more.

It is the oldest, most-used, mathematical constant, and the basis for most equations describing a fundamental principle of our universe. That includes automorphic forms, eigenvaluesFourier series of periodic functions, group homomorphisms, asymptotic distribution of the prime numbers; harmonic oscillators; modular forms and theta functions holomorphic functions and Jacobi theta function; Heisenberg’s uncertainty principle, orthopositroniummodulus of elasticityarea moment of inertia,  spherical coordinate systems (pendulum), fractals (Mandelbrot set), linear complex structure, conjugate harmonic functions, Shannon entropy, Cauchy distribution… and more.

People rightly believe that pi touches many facets of our life. Yet, it should be taken further. It touches all facets of our life. The most unexamined role of pi is her active definition of continuity, symmetry, and harmony, and those qualities define the infinite and pre-condition the finite, everything, everywhere for all time. – Bruce E. Camber

This file is referenced from the following pages:
All concepts must include pi somewhere in its history

Also, see: Undeveloped — the horizontal chart where Notations 116-and-117 provide touchpoints to things around the size of a range human beings (1.34 – 2.68 meters).

This working statement above is a description of the essential nature of pi; and pi tells us that it is also a description of the essential nature of the universe. Even at that, this statement is a human construction so it is always subject to change.

There are a total of nine secondary pages (like this one).

An in-depth discussion about pi was written for Pi Day 2021:

However, the very nature of pi (π) and spheres has been a constant discussion since this website began taking shape in December 2011 in a New Orleans high school.

Other key pages about pi (π) include:
10. Same page different URL
associated with, and