The Fibonacci Sequence - A Base-12 Perspective. A new discovery within a familiar geometric pattern
Вставка
- Опубліковано 7 лют 2025
- Here is the link to buy my book:
www.amazon.com...
I also have a website (for what used to be my other life as an artist) where I am now selling base-12 and dozenal merchandise. Here is the link:
ericlarsenart.com
You can also check out my other website for other base-12 news:
www.dozenalmat...
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!
Interesting. I have heard that many natural patterns are based on the Fibonacci sequence, such as how the seeds in sunflowers and 'scales' on pineapples are arranged. The base 12 system may be more natural in nature than base 10?
Yes, I think so, and I think it will travel down all the way to the quantum scale. Actually, it would be the other way around, in that these structures are already existing at that scale and then keep building on themselves as they grow and "emerge" into our more familiar environment, and we see sunflowers and rainbows.
Is there a base# where pi is rational?
There is a geometry that is built in units of √2, so it is irrational, and yet, within that framework, there are patterns, and there is a structure for dividing the circle perfectly into 360 degrees. I have written a book about it, and made many videos. It is actually very simple, but it has to be approached from a base-12 perspective. It has to do with dispersing the "empty space" around the circumference of the circle as opposed to having an "infinitely" diminishing gap at the end of a solid line.
@ - if the empty spaces were evenly divided wouldn’t that make it a rational number? Or an infinite number of irrational numbers?
@@michaelgarrow3239 I think we need to occasionally ask ourselves: Are the "rules" we are applying to the math actually laws, or are they assumptions we are making about how it is supposed to be because that was the answer we got when we did the math a certain way, in a certain base? If I divide one by three and get a remainder, is it therefore impossible to have a third without a remainder? Of course not. We can't get too hung up on base-10 definitions because we actually live in a base-12 universe. 1/3 =.4 in base-12. Working in units of √2 isn't against any rules, it's just different, and actually solves a lot of problems.
@ - Yes.
The rules we apply are a byproduct of base 10- imo.
Oddly enough; 414 was a number given to me as a child. A spirit number. I know now is part of the root of 2.
Remember- people who use metric- count on their fingers.
Thank you.
Also can you put the Amazon link to your book in the description? It would make it easier to find.
Yes, done. Thanks for the reminder.
i made up a shorthand for saying the dozenal numbers, up to a gros.
un, du, di, va, vi, sec, sep, ock, non, dec, untz, doz... gro
un doz va : 14
du doz sec : 26
I did this when my dog was still a puppy, i'd throw the ball for her for over an hour and stop when we hit "un gro"
Interesting. Sounds sort of like a cross between Italian and German and French. I think Base-12 was used by all those cultures in the distant past.
Seems to be caused by the six factor of twelve. See a similar pattern in base six.
Are you also exploring different bases in math?
@@dozenalmath Sometimes! I like playing with Binary, Quaternary, and others. There are interesting practical trade offs and patterns.
As a humerus addendum does this mean that get and inches are a more natural system than metres😊
yes.
What about Pascal's triangle? The 1001, 2002, 3003 and 3003, 5005 and 8008 pattern is nice for memorization of this most practically useful little pattern. Each row is a power of 11, you know, so it has to be this way. But in base twelve, hmm.
Sounds like an interesting project: explore Pascals triangle from a dozenal perspective!
But wouldn't it be a docimal instead of a decimal?
could be. I think it's good to use words that are different in order to really differentiate between the bases.
I've never met an intelligent mathematician.
Are you a mathematician?
@@dozenalmath Very funny!
@ sounded like you've been to a lot of math conventions or something.
@@dozenalmath Look at the problems mathematicians are eager to solve. I've found the human pheromone cures for 100 incurable diseases. Which would you rather I work on? Codes for dummies at NSA or real clinical medical problems?
Great channel..
I am an Italian in Italy..
I think I have a idea and a project that can change the vision of the DOZENAL NOTATION.
I am not a mathematician.
I just love mathemathic, aritmethic and geometry.
I live in Bari, not far from Pitagora area.
can we have a talk, better a videocall to explanin my theory.
I think that if You will like it, you can explain it much better than me.
I hope it will be revolutionar.
1st role: also a duodecimal math is a decimal math, even if 20 has 24 unities of the used one, and hundered has 144 unities.
For me (to explain in few words) the position of A and B is wrong.
Waiting for your apreciated contact.
regards
Francesco
Hello Francesco,
Thank you for your support.
I am interested in hearing what you have to say about the dozenal notation,
and I am open to having a video call.
We will need to arrange the timing.
Let's keep in touch.
How does base 12 math impact the matrix math done in AI models? I read a suggestion that it would greatly improve their power. Can you explain why it would?
My journey into the world of math started in 2017, which was when I began exploring base-12 geometry. My main focus was exploring the geometry of the circle, with the intent of discovering the true value of pi. Having now accomplished this, I am beginning to explore "all the rest" of mathematics from a base-12 standpoint. Thats the preamble of my answer to your question, which is: I don't know much about the matrix math done in AI models. so... I'm not sure how to articulate how it would improve their power. That being said, I believe that all math is better in base-12. Therefore, if someone more knowledgeable than me suggests that a particular branch of mathematics would be better in base-12, I believe them. At it's most fundamental, it's the perfect divisibility of 1 by 3, 4, and 6 that leads to results which are difficult to predict. No one is exploring base-12 because no knows for sure what the advantages are. That's why exploring is necessary! My intent is to get more people exploring diverse branches of mathematics from a dozenal perspective. Are you involved in AI programming? I 100% agree we need to be programming AI in base-12 and giving it computational capability in dozenal mathematics and geometry.
@ Since AI is the most powerful technology showing it’s better in base 12 would bring enormous attention to base 12. I use AI every day in my job as a computer programmer. I was thinking that if there were libraries that you could use for doing base 12 math and graphing the results it would be easier to learn and explore.
@ How easy do you think it would it be for someone to program a base-12 calculator that just did the basic +, -, x, etc., in base-12, but allowed for many decimal places...like 108, or even a few more? It would be great for the "dozenal movement" if someone could design a calculator like that. I have one, but it has been discontinued, and I don't know much about programming. (I can't do everything). The base-12 calculators currently available are not very good.
If you were inspired and bought my book, you would learn at the end that there is another Cartesian plane that needs to be built. It would be a boon for humanity if someone could build a geometry program that accommodated the pattern presented at the end of my book. Something like geogebra, but different, and in base-12, obviously.
@@dozenalmathI can take a look at it and see how much work it would take to create. What’s the name of the base12 calculator you used? I ordered your book and will check out that Cartesian plane info.
@@nitroflight I'm really glad you decided to buy the book, and that you are interested. The name of the calculator app is: Any Base Calculator, but as I mentioned, it's not available anymore anywhere that I can find. Their symbol was a brown square with a white + sign in the center. It can actually be adjusted to be a calculator for any base up to 36, but that is not necessary. That's why I think it can't be that difficult to just do base-12, and just the basics! What is important is the ability to process large numbers. If you were really interested in pursuing this I would do a video just for you to show you how it is set up. I was very disappointed when I found it had been discontinued.
Learn Python. Let it do the work for you on stuff like this.
Yes, another thing to learn, but sounds like a good idea. I wonder if it has a built in base-10 bias. A lot of geometry programs do.
@@dozenalmath Well the base 10 bias is unavoidable lol, it is pretty deeply intrenched. But python is a programming language and does what you tell it to. You can't program python in base-12 you have to use base 10 or 16 in most programming languages. But you can use it to convert massive amounts of data to any base very quickly, like base 12 for example.
You can find this modular analysis described under the title Pisano Period, en.m.wikipedia.org/wiki/Pisano_period
You might want to brush up on your understanding of the Pisano Period. It's not the same thing at all.
@dozenalmath For all I know, looking at the last two digits of numbers in the Fibonacci sequence in base 12, corresponds to looking at these numbers modulo 144. Why do you think there is a big difference ?
@@mrstephanwehner Theres a few reasons. Simply naming the pattern modulo 144 brings nothing new to the discussion. When the first twelve iterations of the pattern are plotted on the base twelve Cartesian plane, the lengths of the lines are different than in base-10 in relation to the length of one, AND the length of one appears as the twelfth number. This position then becomes pivotal, and when we then begin squaring the numbers, we see a growth pattern going in separate directions from this point in the pattern.
In future videos I will be going deeper into what is revealed once the numbers are squared - another version of the Fibonacci pattern emerges at right angles to this "flat" version, and the pattern becomes three dimensional. There is a linking of these numbers and other patterns emerge and weave together in a very clear and obvious way, all in base-12, which is not so clear in base-10. I would use the comparison of a b&w t.v. versus colour - we know this pattern of numbers is relevant and important, but it really becomes clear and obvious when viewed from the dozenal perspective.