#142857

[math1089]

Mathematical Beauties of the Number 142587

There are some mysteries that the human mind will never penetrate. To convince ourselves we have only to cast a glance at tables of primes and we should perceive that there reigns neither order nor rule.Leonhard Euler Welcome to the blog Math1089 – Mathematics for All. I’m glad you came by. I wanted to let you know I appreciate your spending time here on the blog very much. I do appreciate your…

[positivelyprime]

My favourite fucked up math fact™ is the Sharkovskii theorem:

For any continuous function f: [a,b] -> [a,b], if there exists a periodic point of order 3 (i.e. f(f(f(x))) = x for some x in [a,b] and not f(x) = x or f²(x) = x), then there exists a periodic point of ANY order n.¹

Yes you read that right. If you can find a point of order 3 then you can be sure that there is a point of order 4, 5, or even 142857 in your interval. The assumption is so innocent but I cannot understate how ridiculous the result is.²

For a (relatively) self-contained proof, see this document (this downloads a pdf).

(footnotes under read more)

¹ The interval does not have to be closed, but it should be connected. (a,b), (a,b] and [a,b) all work.

² Technically the result is even stronger! The natural numbers admit a certain ordering called the Sharkovskii ordering which starts with the odd primes numbers 3 > 5 > 7 > ... , then doubles of primes odds, then quadruples of primes odds and so forth until you get no more primes odds, left, ending the ordering in 2³ > 2² > 2. Sharkovskii's theorem actually says that if you have a periodic point of order k, then you have periodic points of any order less than k in the Sharkovskii ordering.

Edit: corrected footnote 2

[msexcelfractal]

1/7 = .(142857)r

125/1001 = .(124875)r

Might be potential for a prank there. You mean to tell me you don't recognize this number?

[lvpwwfz10]

. . .

[unusualshrimp]

im sure everyone knows this already but its a bit Neat that when you divide a not-7's-multiple number by 7 you get a 142857 repeating in a circle

for example

22÷7 = 3.142857142857142857...

100÷7 = 14.2857142857142857...

do any other numbers do this or is 7 just a freak

[sunview]

Lil pohpoh

[novossamples]

#NovosSamples: 142,857 by Sacred Geometry: Dagha & Mike P.

[reed-right]

fun math fact since nobody asked: if you have a repeating decimal (for example, 0.1428571428571...), you can take the repeating part (142857) and divide it by the same number of digits but all 9's (142857 / 999999) to get the ratio of that repeating number. In many cases, you can then reduce the fraction (1 / 7).

also, because it's even somewhat relevant (and I'll take any opportunity to share this with people): for any number that is just a series of digits that are all 9 (for example, 999), the (repeating) decimal value of the reciprocal of the square of that number (1 / 999²) will list every single n-digit number (000 001 002 003 004 005...) except for the penultimate one (... 995 996 997 999 000 001...).

and of course, as with anything in math, these aren't coincidences; there's nothing special about the digit '9' here other than being the highest one in our base 10 (decimal) number writing system. this works in any base -- the same occurs in base 8 (octal) with the digit 7, in base 2 (binary) with the digit 1, in base 20 (vigesimal) with the digit 19, etc.

Reddit is such a perfect mixture of hauty arrogance and downright stupidity, sometimes. It's almost beautiful.

[math1089]

40 Quirky and Fascinating Facts about Mathematics

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate. Leonhard Euler Glad you came by. I wanted to let you know I appreciate your spending time here at the blog very much. I do appreciate your taking time out of your busy schedule to check…

[melody-lines]

124875 || 142857 (Lyric video)

[jacksmusesdrv3]

Long numbers games!?

So as this post showed, Tsumugi’s birthmonth divided by birthday brings up this- 0.5333333333. Pretty straightforward association: 53rd game. Rantaro’s comes up with 3.3333333333 (like ‘Don’t forget Oct 3rd’ or something?? haha). Seems there’s something going on with more of them, so

Let’s uh, try the rest of them:

Kaito Momota: 4th month / 12th day = 0.3333333333

Miu Iruma: 11th month / 16th day = 0.6875

Kiibo: 10th month / 29th day = 0.3448275862

Kirumi Tojo: 5th month / 10th day = 0.5

Himiko Yumeno: 12th month / 3rd day = 4 (LMAO, cursed)

Maki Harukawa: 2nd month / 2nd day = 1

Angie Yonaga: 4th month / 18th day = 0.2222222222

Gonta Gokuhara: 1st month / 23rd day = 0.0434782609

Ryoma Hoshi: 7th month / 1st day = 7

Tenko Chabashira: 1st month / 9th day = 0.1111111111

Korekiyo Shinguji: 7th month / 31st day = 0.2258064516

Kaede Akamatsu: 3rd month / 26th day = 0.1153846154

Kokichi Ouma: 6th month / 21st day = 0.2857142857

Shuichi Saihara: 9th month / 7th day = 1.2857142857

They seem to look meaningless much of the time. But. Curiously

0.2857142857 1.2857142857

Ouma's and Saihara's look the exact same, save for the number before decimal

There's something else too (go to this post for context!)

Alright. Ouma's ‘ni shi’, 24 / Saihara's ‘shi ni’, 42 gives us... this: 0.5714285714. It's basically the same as their birthday results after the decimal, except removing the first 2 and 8. A reason for this I’ve found after a little research is that the repeating number chain ‘142857′ is called a ‘cyclical number’, and I’ve found others of this exact type testing out other characters’ birthdays: Chiaki/Chihiro, Gundham, Nagito and Masaru. 

That said, none of those match this pattern so precisely. But if you multiply Ouma’s birthday result by two, you get a perfect match to the 24/42 number even if you use the precision calculator to calculate everything.

I've noticed there are other cyclical numbers too (one other is 692307 shared by Sakura and Sonia, who have the same birth day but a month apart) but still a lot of variation among all the long numbers besides. Having two varied long numbers turn out almost the exact same like Ouma’s and Saihara’s do is so... weird. It’s like the birthdays were engineered to have nigh perfect correlation with each other at the base level or something...

I’m also curious- is there some kind of relevance to the number loop 142857? Or idk, any other numbers that are showing up? Because one other birthday that had my attention was Gundham’s whose is identical to Okabe Rintaro from Steins;Gate (maybe because... chuunis LOL), and had that same number loop. And oh here’s a fun one: Monaca’s result is 4, the same as Himiko’s :’) Both of them are self-prescribed ‘mages’. That had to be done on purpose.

Seriously, what is going on with these numbers!?

[bruxadepano]

1. I have insomnia since I was a small child

2. I can play some instruments, but don't know musical theory

3. I love art, but don't have the ability to make it

@hufflefuckersss, @thegirlnoonetexts, @saturnsbasement, @v-142857, @betwixttwoendlesswinters, @samblerambles, @skellybonesandtrees

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facts about me

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[grennsw]

This is a thing. Specifically a thing that I made. Hi, I am Gren. Just gonna info-dump about myself. An introduction, per se.

I hail from the UK. I play a lot of games, mostly Splatoon, Tetris and Mario. I am a speedrunner. I like lizards, as do 99% of this website. I stream on Twitch here where I play games and chat. I can play Geoguessr pretty well. I'm losing the will to live. I'm queer, whilst also being here. I made this to shitpost, to spread fun facts, and that's it. I have no idea how this site works yet. I like green-blue-purple colour schemes. I'm a big Pokémon fan. My favourite is Trapinch. I enjoy researching things that have very little meaning. And mathematics. My favourite/the best number is 142857. The perfect number is 6. And 28. And 496.

I'm not funny. I try my best. My favorite musician is Stromae. I'm learning to speak French. I'm a science nerd. I'm running out of things to talk about. Take care.

T'inquiète pas, ça va aller. C'est fini.

[thelreads]

142857 x 1 = 142857, 142857 x 2 = 285714, 142857 x 3 = 428571, 142857 x 4 = 571428, 142857 x 5 = 714285, 142857 x 6 = 857142, 142857 x 7 = 999999

[csdragon]

142857

Broke: 142857 is an important number to math, being the best known cyclical number in base 10, representing the cyclical nature of The Reaper’s game.

Woke: It’s prime factorization is 11, 13, 3, 3, 3, 37. LLLEEEEET