Dividing the circle into 360 degrees can be done on the base-12 Cartesian plane. My book will show you how. Math emerges from the universe and it is dozenal.
I've been exploring base-12 math, and the Fibonacci sequence changes when viewed from this perspective. The decimals are the difference when you switch the base. If you start this sequence with .01, then the 144 becomes the length of one, and the numbers on either side are .75, then 1, then 1.75 (where 89 = 75 in base-10/base-12), but 1.75 does not equal 1.89.
My hypothesis is that the patterns within mathematics like the one you are exploring come into sharper focus when approached in base-12.
There is more to approaching this sequence in base-12 that also relates to the golden ratio, and primes, and also pythagorean triplets when viewed as decimals.
I'm just sharing because I thought you might be interested.
I've also discovered a way to approach the geometry of the circle that brings into question our current geometric model for pi. Actually, there isn't really a geometric model for pi in base-10, but there is one in base-12. A different number with patterns is what emerges from that geometry.
Again, with a handle like mathmaticulous, I thought you might find that interesting.
@EricRWeinstein
I’ve discovered a base-12 Cartesian geometry that produces exact divisions of the circle (including a clean 360° construction) using lattice points and the Flower of Life. It generates precise 7.5° angles geometrically without relying on the usual trigonometric approximations.
Curious if this might interest you given your work on Geometric Unity.
@ericweinstein is anyone asking what makes the waves? is it supposed to be strings? is that the bottom where all the theories start? I agree that calculus introduced a problem while trying to solve another, and I think there is a solution that lies in the realm of dozenal geometry.
The discrete math that everyone is looking for exists on the base-12, or dozenal, Cartesian plane. This is because the ratio between these two fundamental aspects of space (the object and the space around it) is base-12 in nature. There is an entire geometry that exists on the dozenal plane that clarifies our understanding of what an irrational number actually represents. Our current model of a solid line with an infinitely small gap at the end is a flawed model - the gap needs to be dispersed throughout the line, just as "empty" space is dispersed throughout an atom.
Pi, 360 Degrees and √2 - how dozenal geometry surprisingly links dispara... https://t.co/HszoWx1Fxt via @YouTube In this video I am sharing new math discoveries and revealing geometric structures which can only be accessed on the base-12 Cartesian plane. If you are unaware of there being any difference between base-10 and base-12 math, then this video will open your eyes to things new and unexpected.
Because we are studying only one universe, and it has one base, and it is dozenal. You seem to be of the school that we (mathematicians and physicists) are building the mathematical structure. It already exists, and again, it is dozenal. That's what we don't see clearly. There are geometric structures that we are missing. We avoid dealing with paradoxes by ignoring them. Where does the remainder go when we calculate the length of√2 on the x axis? Or any irrational number for that matter. It has been ignored. Why is there no diagram, or geometric structure, for plotting 360 points on the circumference of a circle? Well, such a diagram does exist, but it must be approached in base twelve. The diagram exists on the dozenal Cartesian plane, where the length of one is divided into twelfths instead of tenths. That's the starting point. Switching bases mid equation would only make things more confusing and isn't necessary.
I would ask if they have ever considered that the mathematics of the universe are in a specific base. The follow up question would be: have you ever considered we are approaching that math in the wrong base? The answer to these questions for the outsider is that the Geometry of the universe is in base twelve, and any other approach is flawed, incomplete, and leading to some fundamental misunderstandings.
Well then, people need to understand that the base in math makes a difference. The current model of an irrational number as a solid line with an infinitely small gap at the end is not understood as a flawed model by anyone. That gap needs to be dispersed throughout the line, just as space is dispersed throughout all matter, and the ratio between all matter and space is a dozenal ratio.
In dozenal geometry the length .5√2 is foundational, and is comprised of two aspects, where: .49√2 + .03√2 = .5√2
There is a Geometry of the circle, where the the solid line of the diameter is divided into the circumference, and for each iteration of this equation, a .03√2 gap is dispersed between each each unit of diameter as it is placed precisely on the circumference.
It is simple geometry, and I share the prices of his to do this in my book called: Understanding Base-12 Math, How to Draw the Perfect Circle using Dozenal Geometry. It's available through Amazon.
This geometry enables the construction of a diagram that precisely defines 360 points on the circumference of the circle. Again, in a fairly straightforward manner. This is something that doesn't exist in base-10, and once the initial division of the circle is complete, it becomes clear it can continue in a perfectly symmetrical and balanced manner.
The reason there is controversy around this diagram is that it brings into question our model for pi, which we need to understand makes no sense with regard to physics. The quantum universe is built in units represented by irrational numbers. That little gap in the number is representative of that little electromagnetic gap that surrounds all material things.
It's really not that complicated.
AI is still programmed by people using base-10 math, and so it is very hard to get AI to "think" in base-12. (Just as it's hard to get regular people to think in base-12). Yet base-12 is where all the new math and physics discoveries will be made. This will soon be obvious to everyone.
@TOEwithCurt Is there a significant difference between base-10 and base-12 math? Actually, this is resolved, and the answer is yes. What is yet to happen is for this information to reach the mainstream math and physics communities, and for the implications to be explored.
@Ganeshuor Absolutely. And does the mathematics of nature have a specific base? Well, because we are already in the wrong base, we think the answer is no. Adopting dozenal math will be the game changer in the months and years to come for both the physics and math communities.