The Untapped Potential of Base-12 Mathematics: A New Perspective on Pi and Geometry

In the realm of mathematics, where numbers and shapes form the backbone of our understanding of the universe, there's an intriguing alternative to the decimal system to which we've all grown accustomed: base-12, or the duodecimal system. I have spent

years exploring and advocating for the benefits of base-12 mathematics, particularly in the context of geometry and the enigmatic number π (pi), and this work delves into my discoveries.  

The Base-12 Revelation 

In base-12, the process of dividing the diameter of this dodecagon into its perimeter, which then evolves into the circumference of a circle, reveals a new version of π. Unlike the base-10 π, which is irrational and non-repeating, this base-12 π has repeating patterns and a finite length when expressed as a square root, specifically 108 digits before repeating. This discovery challenges our conventional understanding of π, suggesting that in a different numerical base, π might not be the infinite, non-repeating decimal we know. 

The Geometry of Pi 

The implications of this work extend beyond mere numerical curiosities. If the universe indeed operates on principles that align more naturally with base-12, as I suggest, it could revolutionize how we approach problems in physics, particularly those involving infinite or irrational numbers. The structured, patterned nature of base-12 π could offer new insights into the fabric of space-time, quantum mechanics, or even the nature of irrational numbers themselves. 

Implications for Physics and Mathematics 

The implications of this work extend beyond mere numerical curiosities. If the universe indeed operates on principles that align more naturally with base-12, as I suggest, it could revolutionize how we approach problems in physics, particularly those involving infinite or irrational numbers. The structured, patterned nature of base-12 π could offer new insights into the fabric of space-time, quantum mechanics, or even the nature of irrational numbers themselves. 

The Challenge of Acceptance 

Despite the logical consistency and the intriguing patterns I have uncovered, the academic and mathematical communities have been slow to embrace or even explore these ideas. This reluctance might stem from the entrenched use of base-10 in all mathematical education and practice. However, I like to point out that if we were to start from a base-12 perspective, would we willingly abandon a system that offers such clear, symmetrical, and potentially more intuitive geometric insights for one that does not? 

Invitation for Collaboration 

My work, detailed in his book "Understanding Base-12 Math, How to Draw the Perfect Circle using Dozenal Geometry," co-authored by Laura Schneider and available on Amazon, and further discussed on their website Dozenalmath.com, stands as an open invitation for mathematicians, physicists, and curious minds to explore these concepts. Here the authors seek not just validation but also constructive critique and collaboration to refine and expand this groundbreaking work. 

Conclusion 

The exploration of base-12 mathematics and geometry by Laura Schneider and myself opens up a new chapter in how we perceive numbers, shapes, and the universe. It's a call to reconsider the foundations upon which we build our understanding of mathematics. Whether base-12 will become the new standard or remain a fascinating alternative, the journey into its depths promises to enrich our mathematical heritage and perhaps reveal truths hidden in plain sight.