Number theory - geometrical connection (part 1)

[KanyeTroll]

i was gonna write a troll comment, but i cant think of anything bad to say.

this is too awesome

[thekkl]

That's neat, you wrote a visualization of how a basic is/isn't a prime number program works.

+10 points.

[thekkl]

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[thekkl]

@thekkl Dammit.

[soulessnessD]

this is amazing. you have powerful intuition.

[asker2610]

adaycalledzero

Your triangle is very closely connected to pascal triangle in mod N.

see upside down link (google upside down text converter):

ɾoɯʞı/ɯoɔ˙ןɹnʇןɐ//:dʇʇɥ

[LanceCampeau]

What is the name of the song in this video?!

[adaycalledzero]

@LanceCampeau I don't know. I had to change the original audio for this one, because of copyright infringement. Youtube has an application for changing the audio with hundreds of free audio clips. This is one of them. And when I go to the video details, I can't see anywhere this audio info again. Sorry.

[OtagoMark]

What5s so wonderful about this triangle?? its just a sieve of eratosthenes

And on line 6 he has 4 marked??..I must have missed something...

[dopeanimal]

nice video, i'd like to say that this reminds me of Pascal's triangle, where if you leave only the prime numbers, the create a line and some triangles, uhmm maybe that's an other union i'm not sure..anyway really nice idea.

[genobahamut1337]

I like this video. It makes finding prime numbers cool somehow.

[lordlugworm]

Great Video. Hello. Equasions are already there?=YES= We only discover them?

We do not make the Maths?

But

Maths is Behind Every last thing?=YES

So. How does the big Bang Make the maths?=It does not.

How does the big Bang Make a Uniform universe?=It does?

The Maths are in the Big Bang Or Bangs ,how can this be? = If we are discovering them. Who left them for us to Discover?

Nope. i Cannot work this one out? mathematicians can you work that one out for me Please???

[adaycalledzero]

@lordlugworm Hi, well, I'm not a mathematician. I like the metaphor of Big Bang that you can find on this process on the video: It's something that starts apparently as a mistake (starts on 2, not on 1) and spreads far away, unstoppable. That's not the answer you required, but I had to comment it. :)

[imranbug81]

@lordlugworm Simple Answer Existence of God .....

[cybermunkey13]

@lordlugworm Whoa dude, you need grammar practice.

[gongargongar]

@lordlugworm We invent mathematics, not discover. Mathematics are a construct of man, in an attempt to understand and describe the existence we are experiencing.

[lordlugworm]

@gongargongar

how do you exlains time, gravity, all the laws of Pysics...

are you also trying to say that no apple fell untill sir Isacc newton said there was gravity.. he worked out the formula that already existed silly.

[gongargongar]

@lordlugworm Time is something we made up. It is based on perspective. These laws of physics you hold on to so dearly state this in clear terms. Gravity is an attractive force, what more do you want me to explain? Just because you do not know how something works, does not mean that the mathematics we have used to describe it are predetermined. Objects attracting one another is not evidence of a fatalistic universe. I'm not saying your initial theory is wrong, but your reasoning is not very sound

[lordlugworm]

@gongargongar I cannot belive you think we invent the maths? Have had same argument before, it became a long one.

But if your thinking maths.You personally get taught them from another human yes?So they exsisted before you knew about them?= yes. So before any human being described any formula to any maths to himself,

then to another, eventually to you?then surly the maths aready existed but had not been discovered= yes.

So if humans invent them. apple falls before gravity gravity explained

[lordlugworm]

@gongargongar

We also rely to much on Mathemantics in our lives for them to be mans invetion... we realsied they were there and by working them out realised how they could help us maybe.

depend heavily on mathematics that we only discover but are infact there already as i said you learn and work up formulas, that aready exist and did, well before any man discovered them. we do not understand nature but what little we do know is undeniably mathematical. Ie Gravity. Physics. motion . time ???

[gongargongar]

@lordlugworm sigh. Do me a favour, read some books on the subject. Start with Mathematics: The Grand Tour

[huckleberrykid]

so i herd you liek triforce



[shitzoalc6v]

i know a lot about math and this really surprises me, i have never seen that before. how did you proove this numbertheoretically?

[adaycalledzero]

@shitzoalc6v I don't know much about math, so I just played with factors, grids, etc, and I noticed those reflections, that's why, Then in a math forum, someone saw this video and prooved this is true, and that is just a new way of represent the Sieve of Eratosthenes, but with the "autopilot" on. Check the info of the video. Thanks for comment

[blackmassus]

Math is bad for you brain.

[CLSkill]

@blackmassus What?!?! Good god, who told you that??? Math is amazing for the brain, it can work wonders man!

[Spaga92]

it's nothing special when you know some basic math... if you expand (a+b)^n .. you can't get a prime number next to a^n-k * b^k .. where k E [0,n]...and thats used to draw this, it's very similar to Pascals triangle :)

[TheAntiFascist2010]

more people need to take time and understand that a prime number represents a top down pyramid that cannot be broken by even numbers. Or by the central integer one.

[TheAntiFascist2010]

the interesting thing to me about prime is that prime means dominance. When you get to three, from a whole number perspective everything breaks down upon itself. Like a fractal tree. A good study here would be infinite number domain because the paradox really begins with the number three and will always exist within any triangle. there is no simple mechanical equation for this phenomenon either though it exists everywhere. Dominance changes everything.

[FaaarLeft]

Number theory puts me in a tizzy. Thinking of arrangements of this sort as the natural echos of universal causality creates profound feelings.

[returnoftheramble3]

not that i had a good brain, but i had some reasoning ability, like you, but they can't handle it because they're trying to place us all. all they're doing is making demons under themselves.

[returnoftheramble3]

and they came for my brain, same fucking reason as why everyone tries to make me homeless. I'm appealing.

[returnoftheramble3]

I explained with my triangle why that is.

[Nyquirk]

Looks a lot like the designs on native quilts and sweaters.

[Rat656]

Sierpisnki triangle

[returnoftheramble3]

My triangle is better.

[TheAntiFascist2010]

This is simply the study of prime numbers and the Pythagorean theorem which is compromised due solely upon the reality that one is not prime. One will never be prime. All methods and attempts to prove that Pythagorean doctrine is true and that one is prime will always end with an infinite set that doesn't exist.

[fknkewl]

TRIFORCE!

[willrandship]

@fknkewl you're looking for the sierpinski triangle

[scamoosh]

I'd like to know how you are constructing these reflections. i spent a few minutes trying to figure it out and they seem almost random to me

[adaycalledzero]

@scamoosh I think the clip is showing these "reflections". It starts on the upper floor, and keeps going down step by step, but, the previous reflections are designing the future reflections, cause they added new red triangles.

[scamoosh]

@adaycalledzero

yeah, i got that, on watching it again i can see that each point between the outer triangles of each line is used to map another smaller point below in order to create a smaller triangle. If the process was started on the first or second rows the process would give a solid block of triangles. have you tried starting the process on lines 4, 5 etc. might get some interesting results?

[adaycalledzero]

@scamoosh Yes, if you start on the first row (the high top we can callt it zero floor, one triangle) you get a solid block of triangles, so it's interesting that this pattern comes from a 'mistake', not taking that first row in account.

I didnt try to start from any other row, I guess you'll get a very empty pattern, as it would happen in Eratostenes' Sieve.

[KiteFlyingGuy]

@adaycalledzero well is the first row is 1 well 1 isnt a prime or composite so i geuss that why he didnt start there some 1 correct me if im wrong though

[willrandship]

@adaycalledzero sounds like factoring tests to me. Since the first row = 1, all numbers highlighted makes sense.

If triangles = prime, then perhaps the first row means 0? not really sure, just hypothesizing

[marango4576]

I just may have made a huge advancemeng in the twin prime conjectury , anyone got any info on how to publish?

[robertlewisvazquez]

@marango4576 google math clay institute.

[Narend1987]

goo

[arphamdb]

Great studies of the prime numbers.

[albi7]

Is it your own idea?

[elmer1410]

I have no idea how u create those triangles, sorry. you should explain it better. :/

[ProiektKarton]

What is the big O of that way ?

Is it comparable to sieve of Atkin or Eratosthenes?

[adaycalledzero]

@ProiektKarton

Check the link posted on the video info. It's the sieve of Eratosthenes indeed, but more "automatic"

[telesniper2]

Your calculations are incorrect - calculate the elements in row n=15 and you will see that when k=3,4,5,6,7 are all have 5 as a prime factor, which you DO NOT show as a result in your picture. Likewise, k=3,4,5 all have prime factors of 3. Maybe you should check your calculations

[albi7]

@telesniper2 What's k? And what are you talking about? :P

[telesniper2]

@albi7 Hi, k is a variable representing the row. In pascal's triangle, the value of each cell is represented as (n,k)= (n choose k) =n!/(k!(n-k)!) where n is the row and k is the column (there is a zero column and a zero row)

[albi7]

@telesniper2 It is about the second part, right? I didn't see it.

[deadlybug]

why did you start multiplying from the third row?

[adaycalledzero]

@deadlybug

Because if you start from the second row following the same process, you will obtain just 100% red triangles. The triangle I am showing in the video is a consequence of the "reflection" or "multicopy" of that empty space of the third row, that, as you noticed, should have been red, not empty. That "mistake" is like a big-bang, and creates all the numbers (at least in my poetic view)

[amh1230]

good work, sierpinski.

[jebovasgugl]

I CAN'T BELIEVE!! GREAT!

[ananiasacts]

What does "in a triangle symmetry way" mean? What's the algorithm for generating the interior triangles?

[adaycalledzero]

As english is not my natural language, maybe I just confused you. But I think it is quite simple what I was trying to express by that, once you see the video. I guess.

At (part 2) you can see some kind of formula.

[dkim87]

@ananiasacts Each row determines the diagonals in a recursive fashion. That is, when a row is highlighted in red, these determine the red diagonals. These then become blue and are later used for the following rows in descending order.

[sergiorgio2000]

numbering the row, start from 0, 1, ..

then strart from the 2 row (first two in blue), then rotate this row by 60° clowkwise by the left extreme fixed, and 60° unterclowkwise by the right end fixed. Then go to the next row and so on..

[coreytk]

that is weird but it works

[hamoan66boi]

good work!

[AkiraBergman]

Dude, you are gonna be famous for this.

[elliottfour]

Native American Patterns:}

[hfluismhf]

Hola: Esta interesante tu simulacion, sin embargo mi pegunta es la siguiente::: podria ayudarnos tu calculo geometrico en algo para demostrar la Hipotesis de rieman que tiene estrecha relacion con la distribucion de los numeros primos

Atte luis

saludos desde mexico

[classicmusic05]

when do people learn this? like what year in school?

[gremlinextreme101]

you don't it's a strange way of looking at prime factors, a topic you probably learned age 8, even if it wasn't that by name. It gets revisited in Fundamentals of Math which is a freshman or sophomore class at college

[Reglay]

In the IB math higher level course you can choose it as an option

[luksenborg]

aaarh. great !!! xD

[leneymusic]

Very nice, great representation.

[WildStar2002]

That is fantastic!

[JT78]

O-M-F-G

[J2daSC]

By which artist is the music made????

[adaycalledzero]

The song is a b-side by Björk, called Batabid.

[NeedsEvidence]

I still don't understand the construction recipe. Can you be more specific? Can you generate all prime numbers by the triangle method? :-)

[adaycalledzero]

I am doing this triangular reflection (2 symmetrical reflections 60º) and I get a big mix of factors, revealing the empty lines as prime numbers. You may find interesting the link provided on the "more info" text.

[scepticalchymist]

Can you use this to factorize large numbers into their prime factors? :-) Is there a theory behind it, why and how it works from an algebraic viewpoint?

[adaycalledzero]

I guess not, not really large numbers, there is always this recurrence needed. You can see the explanation of how it works in the link provided on "more information". Thanks for comment

[4198241982]

what a fascinating video. As someone new to number theory this was quite interesting to see. thanks!

[noobyfromhell]

That was pretty obvious, but still interesting. Is there any more abstract variant of this structure that can be studied?

[adaycalledzero]

Thanks. Maybe you would be interested in the second part of this video, related to Pascal's Triangle.

[bingvc]

Awesome!

[forgotmypassword3]

thank you so much. I couldn't see this.

[wayzey]

Whoa I can't believe that's correct.

Stuff like this makes you think man, it's amazing you came up with this, great video congrats.

[adaycalledzero]

Thanks so much, now you can check the second part of the video. I hope it's clear, as I am not used to math's language

[hujispyro]

very Good work!

[KillerDrummer88]

awesome work mate ;)

[eligao]

convolution again

[2high4pie]

I have a question ... it just took me 10 minutes of repeating it and thinking about it but i finally understand it... but how did you think to do this?... how did you come up with it...?

very awesome vid

[adaycalledzero]

thanks, mmm I wanted to see patterns in natural numbers, just as a challenge, so i tried many ways in my free time, and still doing it.

[r2itos]

@2high4pie Javier Torres Ruiz bases his theory on the logic of the Tiwanaku's Tetralectics.

[Muvlonion]

in the nth line, there are n-phi(n)+1 triangles right?

[adaycalledzero]

Yes, because these triangles are the coprimes of n. And that's what phi(n) is about. Thanks for comment.

[adaycalledzero]

Sorry, my mistake, the void triangles are the coprimes. You mentioned one of the properties of the Phi(n) function. Nice observation

[mynameinc]

it appears to be a fractal

[Abe27342]

but it would have to be one hard fractal to find formulas for area, etc. since it contains all the primes.

[osmanli911]

go buy a handmade Turkish carpet to see this on your carpet : )

[osmanli911]

bizim evdeki halının deseni la bu :P

[rockyreggaeclark]

how to "triangular symmetry" way? thanks

[ispollock]

When does this method of generating primes break down?

Cool video!

[Muvlonion]

it goes on forever

[simplic10]

But presumably it only generates some (infinite) subset of the primes, not all of them, right? That's what I mean.

[Ogilvy12]

if you could find a pattern in prime numbers, you'd be a freaking genius. after that you'd be loaded

[stshrive]

Reminds me of Sierpenski's Triangle

[rialtominx]

this is a relaxing video

[ratskan]

you know what's sad... some people can just understand math like a sensible conversation. Those people I give enormous credit to. Because, to me... it's a pyramid with pretty colors... LOL. Good on you if you can understand this stuff.  I really wish I could.

[RatchetHacker]

lulz funny

wahahahaha!!^^

[geoffreyefloyd]

Very cool work sir. Actually i would like to know who did the music on this its very nice :D

[adaycalledzero]

Thanks a lot. And the music is a b-side by Björk, a song called "Batabid". It appears on the single of Pagan Poetry.

[geoffreyefloyd]

Thanks, been a while since i looked at this page haha nice to know who does the music on it :)

[Argonaut22j]

This reminds of me of the story of how Mandelbrot took the French math exams as a youth and even though he was never taught formally to do a lot of the problems, he visualized many of them to find the answers.

[niunanfen]

00!

[jemsut]

From the looks of it, what's happening is an analogue of the Sieve of Eratosthenes, i.e. to have the smaller triangle units appear on a line, the line number needs to be a multiple of a previous line, and the pattern that appears on that line is determined by its prime factors.

[adaycalledzero]

Yes, I didn't know that when I did the video, but then, some person contacted me and told me. You can check it in the INFO of this video (More info)

[glasscricket]

That's excellent. Thank you for sharing!

[SandroAerogen]

MAN MY BRAIN IS STARTING TO OVERHEAT

[FMMAROTO]

this is gorgeous

[alltherestaretaken]

The number of elements in a row are related to n + 1 - phi(n). See A062830 in the OEIS.

[foxabilo]

hmmm, what is new here?, does this give a way of calculating primes wthout n(p) calculations? It looks to me like it would be alot of calculations for any prime. If your video got deleted by the goverment, then .. I kinda think this stuff would stay, its hardy SSL busting knowlage, tell me the 2 prime factors of 172638628763827631897632198761­653265817438920010730870387098­709871098736760168790362976196­519786163987632978604387323

[adaycalledzero]

hehe

i recommend you to look the web I mention in the info of this video (click on "more"). Real mathematician concluded that this is the Sieve of Erastones, in a brand new way. Just that. Maybe there is still some clue unsolved, who knows? Thanks for comment.

[apf77]

Thanks! Its something more. I found something neat with the center parts, down the middle and see each downward facing triangle, just three #s. What I did was single digit pascal which saves lots of room [horizontal math]. Every three of these are 3 3, 6 6, or 9 9 6 3 9 They repeat pretty coherently, only catch is, after three sets of 27 [81], it isn't done, so I think the pattern may be 81*2=162. I have to keep drawing and see what I get.

[apf77]

my #s looked funny. its triangular:

3 3 6 6 9 9 6 3 9

two threes with a six below, two sixes with a 3 below, two nines with a nine below. maybe i should upload a pic of the drawing i did at some point so its more readable.

[adaycalledzero]

I don't understand you at all, but maybe you can write your comments and pictures on the forum i talk in the video information. Thanks for your interest

[pgeeme]

2x3=6 (6) --two threes with a six below

2x6=12 (1+2=3)--two sixes with a 3 below

2x9=18 (1+8=9)--two nines with a nine below

[triplesquarednine]

if you want to undrestand why your numbers add up that way, either look at vedic numerology charts or simply take our mathematics times table and sum each number to 1 digit IE: 5x5=25 2+5=7.... then it should be pretty obvious or you tube rodin mathemeatics...which is another way to look at the same thing. or study music theory and convert your theory lessons into math...

[trukkstop1]

While I understand the basic construction process (not why it works), I don't understand which triangles correspond to the prime factors of a given integer. Could you explain how that works?

[adaycalledzero]

When I say: "for example, number 30", as you know it's composed by 2, 3 and 5. And you can see in the 30th line, that this little triangle icons can be perfectly separated ONLY in spaces of 2 , 3 and 5. This happens for every number.

[trukkstop1]

This is beautiful! I am still trying to figure out why it works. It is possibly related to Pascal's Triangle or the Sieve of Erastothenes. It also reminds me of the book "A New Kind of Science" by Stephen Wolfram, in which he shows how a cellular automata can generate the prime integers. Have you published this work anywhere?

[adaycalledzero]

I dont know why it works, but I showed to a mathematician, who could demonstrate why a value is reflecting in that triangle way. But i think there is still something magical that it has not answer, like a "Story of the Creation of numbers". I don't know...