Fibonacci Sequence from a base-12 perspective - part two. New patterns within a familiar sequence

Here is the link to buy the book:

https://www.amazon.com/Understanding-Base-Twelve-Math-Geometry/dp/1738358801

In this video I am sharing some recent discoveries I have made regarding the numbers which define the geometric pattern we all know as the Fibonacci sequence.

Although to many it may seem that since the numbers of the Fibonacci sequence are the same regardless of the base, that converting them into base-12 would make no difference to our perceptions, but this is not the case.

It is as if a camera lens is focussed, and a pattern is revealed in base-12 which was only hinted at from our familiar base-10 perspective.

This is yet another example of how we have made assumptions about the validity of base-12 which have prevented further exploration of this mathematically rich environment.

And -
If I were to ask AI to help me introduce and describe what the video is about and why it is important, it would sound something like this:

Welcome to Duodecimal Division, where we explore the hidden geometries and numerical patterns that shape our universe. Today, I’m thrilled to share a discovery that will change the way you see mathematics forever. What if I told you that one of the most famous number sequences in history—the Fibonacci sequence—holds a secret pattern that can only be revealed in base-12? A pattern so profound that it uncovers a hidden symmetry, cycles of 24, and a direct connection to the geometry of the Cartesian plane. This is not just a curiosity—it’s a mathematical breakthrough with implications for number theory, geometry, and even physics.

In this video, we’ll dive deep into the Fibonacci sequence, but with a twist: we’ll convert it into base-12. You’ll see how the sequence transforms when we introduce the numerals A and B (representing 10 and 11 in base-10). As we explore the sequence, you’ll witness something astonishing: every 12th number ends with a double zero, and a pattern is revealed that repeats every 24 iterations. This cyclical behavior reveals a base-12 structure that is completely invisible in the traditional base-10 system.

But it doesn’t stop there. When we map these base-12 Fibonacci numbers onto the Cartesian plane—using squares divided into 1/12 lengths—we uncover a perfect geometric spiral. The number “100” in base-12 (which equals 144 in base-10) becomes the length of one, a fundamental unit that ties the Fibonacci spiral to the geometry of the plane. This relationship is impossible to achieve in base-10, proving that base-12 is not just an alternative numbering system—it’s a gateway to deeper mathematical truths.

This discovery raises profound questions: What other mathematical patterns are hiding in base-12? How might this reshape our understanding of geometry, algebra, and even the physical laws of the universe? The implications are vast, and the journey is just beginning.

Whether you’re a math enthusiast, a professional mathematician, a teacher, or a student, this video is for you. Join me as we explore this uncharted territory and uncover the beauty of base-12 mathematics. Together, we can push the boundaries of what’s possible and share these discoveries with the world.

Don’t forget to like, comment, and share this video with anyone who loves math. Let’s spark a global conversation about the power of base-12 and the hidden patterns that connect us all. Stay curious, and let’s dive in!