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History: The first Pi Day celebration in 1988 at the San Francisco science museum Exploratorium was initiated by their resident scientist, Larry Shaw. They ate a lot of pie and had fun with mathematical trivia. Notwithstanding, by 2009, Pi Day was recognized as a national holiday (USA). By November 2019, UNESCO adopted Pi Day as the International Day of Mathematics.
Pi Day celebrations often begin with pie-eating contests and evolve into a recitation of some part of 100-trillion known digits of pi, yet the perfections of pi (π) reveal its deeper essence and purpose.
Pi is the continuity, symmetry, and harmony from which circles and spheres evolve. That opens at least ten key points to explore pi more rigorously.
#1 Take those three perfect functions as a whole. Continuity is the never-ending, never-repeating numbers of pi. Symmetry is the deeper nature within those numbers that become relations which become circles and spheres. And, harmony is an even deeper dynamic of the sphere, first opened in 1820 by Joseph Fourier, that is a simple harmony that defines every sphere.
#2As a function, continuity-symmetry-harmony are both finite and infinite.
#3 Our scholars continue to build on Fourier’s insights. Many others have uncovered even more exacting relations with pi. At its core, continuity renders time; symmetry renders space, and harmony renders the dynamics of space-time.
#4 Perfected states within space-time. The Planck base units defined by Max Planck in 1899 use dimensionless constants which become natural units and definitions of the smallest possible units of space and time. The smallest are logically the first, the starting points of our universe.Planck Time and Planck Length are where the first infinitesimal-and-perfect sphere emerge. Using Planck’s numbers, one sphere per unit of Planck Time and Planck Length redefines emergence.
#5 At that rate, 539 tredecillion spheres per second are generated. To grasp some order, we apply base-2 notation. The result is 202 notations (or doublings) to explore that encapsulate the known universe. There are numbers to keep the score.
#6 Those numbers are timestamped with sphere-stacking.
#7 Then the numbers are geometrized with cubic-close packing of equal spheres. In the first notations, there is an absence of gaps. The basic geometries all fit perfectly. It is hypothesized that quantum fluctuations can not manifest until at least Notation-50.
#8 Langlands programs and string theory are further defined with pi.
#9Then the known equations that define our foundations emerge. By the 202nd notation, we have our universe, everything, everywhere for all time, all intimately connected by infinitesimal spheres.
#10 All 202 notations are always active and “all time is now.” Each notation adds definition. As we go down the scale, there is increased particularity and coherence. There is no singularity. In the very beginning, within the convergence of equations, there are exacting definitions.
#11 Logically there is a domain with no gaps. Perfectly fitting geometries exists prior to the emergence of quantum fluctuations.
#12 Values. Perfectly-fitting geometries account for earliest notations where there are no gaps; it becomes the basis for value.
With this platform, Pi Day becomes a study of infinitesimal spheres to define the Planck to Electroweak Scale and our Standard Models (Particle Physics and Cosmology).
It is not beyond our imaginations and capabilities.