Tree-house Numbers - Numberphile

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Matt Parker goes on a mathematician's journey and shows us Heegner Numbers (and the Ramanujan Constant). See part 1 (Caboose Numbers) here: • Caboose Numbers - Numb... --- More links & stuff in full description below ↓↓↓
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Опубликовано:

27 сен 2024

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Комментарии : 771

@matt-parkers-evil-twin 3 месяца назад

11:45 "At least I tried" *brady zooms in on the parker square* that just feels mean...

@unvergebeneid 3 месяца назад

I had to laugh out loud. So savage.

@ChrisBreederveld 3 месяца назад

Yeah, just the sneaky diss of zooming in made me laugh

@JorgeLopez-qj8pu 3 месяца назад

🤣

@WaffleAbuser 3 месяца назад

“I hate to be that on brand” Right in the feels

@niklashagg7112 3 месяца назад

So, is this a Parker discovery or a Parker proof?

@unvergebeneid 3 месяца назад

I like when "soon on Numberphile" means "now on Numberphile but you have to click on a link in the description."

@zzzaphod8507 3 месяца назад

That's pretty soon!

@VestalNumbre 3 месяца назад

Can they doe math on the Bible effects on the mind ?

@SwordQuake2 3 месяца назад

@@VestalNumbre what?

@unvergebeneid 3 месяца назад

@@VestalNumbre given the state of your mind, maybe you need a new Bible?

@zzzaphod8507 3 месяца назад

@@unvergebeneid Was that Vestal comment posted by a deer, perhaps?

@tehbertl7926 3 месяца назад

e^(π√163) is a Parker integer.

@Charliehuangmagic 3 месяца назад

which basically meant it is NOT an integer XD

@blue_tetris 3 месяца назад

That classic Parker enthusiasm when he got to e^(π√19). I expected him to say, "It's not an integer, but it's less than 1 away from an integer!"

@KBRoller 3 месяца назад

@@blue_tetris "But aren't all non-integers less than 1 away from an integer?" "Ignoring that and moving on..."

@russelleverson9915 3 месяца назад

😂

@danielyuan9862 3 месяца назад

@@blue_tetris I can do you one better: it's less than 0.5 away from an integer!

@bernhardkrickl3567 3 месяца назад

When is Matt gonna write a book called "Things to make and do with terrible Python code"?

@KBRoller 3 месяца назад

async def fork(): while True: await fork() await fork()

@TechnoHackerVid 3 месяца назад

@@KBRollersomehow I feel that code would just recurse rather than fork bomb

@KBRoller 3 месяца назад

@@TechnoHackerVid Well, yes and no. It'll be a fork bomb, but only until the stack overflows, and then it'll just crash 😂 The proper fork bomb form would be to spin off a thread or process for each of those forks, but that's more code than I wanted to write in a RU-vid comment 😁 (And actually, it may *only* work with multiprocessing; I'm not sure. But Python threads don't work the way most threading does, because of the GIL, so there's a chance a Python thread-based fork bomb wouldn't even work.)

@pierrecurie 3 месяца назад

@@KBRoller Just spin off additional python processes with multiprocessing.

@KBRoller 3 месяца назад

@@pierrecurie ...that...is what I said.

@hasch5756 3 месяца назад

e^π(√-1) gives -1.0000000000000, which is arguably closer to an integer than e^(π√163)

@softy8088 3 месяца назад

If you follow that through to the corresponding caboose number, n²-n+0 is a prime for all positive integers less than 0. Amazing!

@ianstopher9111 3 месяца назад

e^π(√-1) = -0.999999999999999999999999.... as many 9s as you could possibly want.

@chingpongsiu1508 3 месяца назад

I was going to leave the same comment, but I saw yours~ 👍

@xinpingdonohoe3978 3 месяца назад

@@softy8088 it's weird and wonderful how that statement of yours is true. No counterexamples exist to make it false, so it is not false. So it's true. Or maybe independent. But who's going to make an axiom stating "n²-n+0 is prime for all positive integers less than 0"?

@DeadJDona 3 месяца назад

This is related to Г(n²-n)

@algorithmizer 3 месяца назад

8:29 The true journey of mathematics is the stunning joy of discovering something only to realize someone did it before...

@threadripper979 3 месяца назад

And just like Ramanujan was wrong here, he was wrong about the sum of all integers being equal to -1/12

@Nolord_ 3 месяца назад

@@threadripper979Actually, Ramanujan never knew about e^(π√163) and the sum of all integers does equal -1/12 in some sense, that is not the usual sense.

@threadripper979 3 месяца назад

@@Nolord_ Sure, if you ignore converging series vs. diverging series rules. LOL

@Nolord_ 3 месяца назад

@@threadripper979 Yeah and complex numbers do not exist, LOL.

@threadripper979 3 месяца назад

@@Nolord_ Get real; be rational.

@davecorry7723 3 месяца назад

The Caboose numbers fizzled out: I wasn't impressed. The treehouse numbers give _near_ integers: I wasn't impressed. Matt finds a connection between the two: I WAS SUPER IMPRESSED. Matt reveals he didn't find that connection: I wasn't impressed. Matt gives a little talk on the connection: I was impressed again.

@distinctdipole 3 месяца назад

You missed out "Matt writes terrible Python code: I wasn't surprised". Sorry Matt, I do love you and your terrible Python code.

@Platanov 3 месяца назад

This is the true armchair mathematician's journey.

@newwaveinfantry8362 3 месяца назад

What a rollercoaster!

@larsdebrabander3613 3 месяца назад

that zoom on the end was hilarious

@waffling0 3 месяца назад

"The integers are a field" ah yes, a Parker field

@mattlm64 3 месяца назад

I guess a ring shall be known as a Parker field from now on.

@eliasmochan 3 месяца назад

@@mattlm64 an integral domain. I think calling Z/4Z a Parker field would be like calling the square with all 1s a Parker square.

@05degrees 3 месяца назад

BTW I think he was actually to say “rationals”. I see this state very familiar when he tried to explain what a field is in a simplest way possible off the bat and pausing each word; I find contexts like this blocking my own brain in some way and then I’m derailed and make mistakes; maybe something like that happened. (The joke about a Parker field is still obviously gold unrelated to this attempt at explanation.)

@Anonymous-zp4hb Месяц назад

I looked for this comment lol

@thomasjdurfee 3 месяца назад

Recommendation to the new viewer: They say at the start of the video that you don't *need* to see the first video, and that is true, but the conclusion of this video is deeply pleasing if you watch the other video first.

@Kyle-nm1kh 3 месяца назад

You need the foreplay to appreciate the climax

@Jaeghead 3 месяца назад

Brady seems to have forgotten that he's already made a video about these numbers 12 years ago, it was titled '163 and Ramanujan Constant'.

@EPMTUNES 3 месяца назад

a numberphile classic. back when they used to just do one number and talk about it.

@sadaharu5870 3 месяца назад

Funny cause I just watched that video lol

@ianstopher9111 3 месяца назад

I was convinced this could not be the first time Heegner numbers had been mentioned.

@LeoStaley 3 месяца назад

I knew this sounded familiar!

@syjwg 3 месяца назад

Thanks for mentioning that! I've found the video.

@DjImpossibility 3 месяца назад

"The integers are a field"... Such a Parker thing to say

@seijurouhiko 3 месяца назад

Came here in the comments looking for this comment. Thx!

@guruone 3 месяца назад

But... are integers green?

@RolandHutchinson 3 месяца назад

Well, a ring is sort of a Parker field, wouldn't you say?

@6cef 3 месяца назад

@@RolandHutchinson actually, i think british mathematicians call fields parker rings

@sudhenduahir802 3 месяца назад

Came here to say this..

@DubioserKerl 3 месяца назад

Maths God to Euler and Ramanujan: "Why is it always the two of you if something mathemagically strange happens?"

@unvergebeneid 3 месяца назад

In this case, the answer is: because it's a meme. Ramanujan didn't discover this number and he didn't lie to people about it being an integer. Martin Gardner did as an April Fool's joke and just claimed it was Ramanujan who said it.

@Catman_321 3 месяца назад

Them: "idk why'd you put it there"

@andrasszabo1570 3 месяца назад

Usually it"s Euler and Gauss

@ArawnOfAnnwn 3 месяца назад

Don't forget Gauss!

@AquaWeiner 3 месяца назад

@@ArawnOfAnnwnYeah Gauss is just crazy, the greatest imo

@ShiningRaven 3 месяца назад

I think that Matt might have misspoken at 10:20. The integers do not constitute a field as they aren't closed under taking multiplicative inverses (dividing two integers generally does not result in an integer). Matt was probably thinking of the rationals or the reals

@dojelnotmyrealname4018 3 месяца назад

Wouldn't they be a field if restricted to the addition and subtraction operators?

@ShiningRaven 3 месяца назад

@@dojelnotmyrealname4018 Not as such. Typically in algebra, we don't think of subtraction as a binary operation, but instead as a shorthand for expressions of the form a+(-b). We can instead equip the integers with the operations of addition and multiplication, which turns the integers into what we call a ring. But the integers still only contain inverses with respect to addition. In order to obtain a field, we need to extend to the rational numbers (or something bigger).

@charliesteiner2334 3 месяца назад

Or to something smaller! (Modular arithmetic)

@jonasgajdosikas1125 3 месяца назад

it's a parker field

@JGMeador444 3 месяца назад

I'm almost certain that he meant the integers modulo prime numbers constitute fields. He definitely misspoke, but I think that's what he was going for.

@mikeebrady 3 месяца назад

"At least you tried." Zooms in on the Parker Square. savage.

@LaGuerre19 3 месяца назад

"Suspiciously close to an integer" is my new favorite maths term of all-time 😂 I mean, just the pure, firm rigor of the concept 😂😂

@SteelBlueVision 3 месяца назад

Reminds me of a college student's answer to an indefinite integral he could not solve, so he wrote as the answer: 0 + C. When asked why in the world he provided that answer when he knew that it would obviously be wrong, he stated that this is in fact the correct solution to the problem and any indefinite integral problem. His rationalization of this was that give that the constant is arbitrary by definition, we can make said constant take on whatever value we want to make the solution correct for any integral. This proves once again the old adage that a false hypothesis can always lead to a vacuously true conclusion.

@anosmianAcrimony 3 месяца назад

They definitely fall within the set of interesting numbers

@yonimaor1005 3 месяца назад

They could have just defined "Treehouseness" of a number n as the relative deviation from an integer it gives in that the exp(pi*sqrt(n)).

@Tinker001 2 месяца назад

Pretty much the mantra of failed engineers through history...

@usernamenotfound80 3 месяца назад

"The integers are a field." - Matt Parker, 2024

@ianstopher9111 3 месяца назад

A Parker field.

@benburdick9834 3 месяца назад

Big respect to Matt for sharing all the near misses that happen when doing math.

@SteelBlueVision 3 месяца назад

Like missing the correct definition of a field, by including integers as an example.

@johnchessant3012 3 месяца назад

Interestingly, the numbers that Matt found, 652 and 1,467, are just 2^2 and 3^2 times the Heegner number 163. (noticed this because this is such a fundamental mystery in modern number theory that we would've heard of the numbers 651 and 1,467 if they weren't so directly related to 163)

@yonimaor1005 3 месяца назад

If exp(pi*sqrt(n)) ≈ integer Then exp(pi*sqrt(x^2*n)) = (exp(pi*sqrt(n))^x ≈ integer^x which is integer if x is integer

@animaniacsfan2 3 месяца назад

@@yonimaor1005 I don't think that explains it, though. exp(pi*sqrt(163)) is about 10^17, and is about 10^-12 away from an integer. At that scale, the error is more than enough to change the square by 1, which means if you round exp(pi*sqrt(163)) to an integer and then square it, the answer is more than one away from exp(pi*sqrt(163))^2. So there must be a different reason why exp(pi*sqrt(163))^2 and exp(pi*sqrt(163))^3 are almost integers.

@yonimaor1005 3 месяца назад

@@animaniacsfan2 You are right. I was wrong. This is an example of the symbol ≈ being mal-defined and should not be used.

@whophd 3 месяца назад

“Just off the top of my head” … camera points to the top of Matt’s head

@Tinker001 2 месяца назад

Pretty sure a light check got edited in accidentally. :P

@DavidDyte1969 3 месяца назад

This epiphany happened for me in discovering a recurrence relation for multiplicities of eigenvalues in the stochastic matrices generated by the move-to-front rule for the linear search problem. I still remember the moment and it was over 30 years ago. Mathematics is the best.

@vinicius-alexmr 3 месяца назад

Parker is the best exemple of not being afraid to give It a try. Wish I was like that.

@hedlund 3 месяца назад

It's learnable, to some extent. Start small. Doesn't really matter what, so long as you a) Actually do try, and; b) Remember that failure is a great teacher, and use that to your advantage. Can take years and years, but it's well worth the effort.

@MB256s 3 месяца назад

652 and 1467 after 163 are just 163*4 and 163*9, which means the numbers you obtain afterwards are just the square and the cube of the original Ramanujan's constant. But that makes me think... If we write Ramanujan's constant as (N-eps), then, we get that (N-eps)^2=N^2-2*N*eps+eps^2. Now, eps is small, but 2*N*eps seems to be much larger than 1, which means that, in principle, it (and by extension the final result, eps^2 is clearly negligible) has no reason to be also close to an integer. And yet, (N-eps)^2 is still very close to an integer? Same with -3*N^2*eps for the cube, and also +3*N*eps^2, which is probably less than 1 but still about 100 times the offset of the cube from the integer, which means that that term also plays a role in correcting the number, if I did the computations right. I know that there is a lot of complicated maths behind these numbers, but is there a chance we might hear more about this?

@officialEricBG 3 месяца назад

look up the j-invariant

@zanshibumi 3 месяца назад

"If? we'd like to watch more videos with Matt Parker?" Of course we want to watch more videos with Matt Parker. We've aready watched all those.

@37wheels 3 месяца назад

well, we'd nearly like to watch more videos. We'd almost like to watch more videos. We're suspiciously close to wanting to watch more videos. But sadly, in the end, we're just slightly off wanting to watch more videos.

@pion137 3 месяца назад

Brady is king of naming numbers!

@toolebukk 3 месяца назад

In honour of Brady, I will forever call Heegner numbers Treehouse numbers instead.

@nintendoswitchfan4953 3 месяца назад

underrated

@Slowphoton 3 месяца назад

This side of the pond we spell it “honor” so get on the program soldier.

@willnewman9783 3 месяца назад

Mathematicians already did Heegner dirty, and now you are trying to bring that back. Poor Heegner

@Reydriel 3 месяца назад

@@Slowphoton Neither of the people featured in this video are from your side of the pond bruh

@unvergebeneid 3 месяца назад

Wait, this wasn't found by Ramanujan! Wolfram Mathworld says: Although Ramanujan (1913-1914) gave few rather spectacular examples of almost integers (such e^(pisqrt(58))), he did not actually mention the particular near-identity given above. In fact, Hermite (1859) observed this property of 163 long before Ramanujan's work. The name "Ramanujan's constant" was coined by Simon Plouffe and derives from an April Fool's joke played by Martin Gardner (Apr. 1975) on the readers of Scientific American. In his column, Gardner claimed that e^(pisqrt(163)) was exactly an integer, and that Ramanujan had conjectured this in his 1914 paper. Gardner admitted his hoax a few months later (Gardner, July 1975).

@vsm1456 3 месяца назад

how do people discover things like that before computers. it blows my mind :D

@unvergebeneid 3 месяца назад

@@vsm1456 Apparently by not having computers and therefore nothing but time on their hands to compute stuff like this by hand :D

@JohnDoe-ti2np 3 месяца назад

@@vsm1456 Hermite didn't discover it by computing lots of numbers blindly and hoping to find a pattern. There's a special function in mathematics called the j-invariant. On the one hand, there is some theory that tells us that j((1 + sqrt(-d))/2) is an integer if a certain number system (the "ring of integers of Q(sqrt(-d))") has unique factorization. In particular, the ring of integers of Q(sqrt(-163)) has unique factorization. On the other hand, there is an infinite series expression for j that tells us that j((1 + sqrt(-163))/2) is very close to e^(pi*sqrt(163)). If you know this underlying theory then you can deduce that e^(pi*sqrt(163)) is very close to an integer without having to explicitly calculate e^(pi*sqrt(163)).

@not-on-pizza 3 месяца назад

@@unvergebeneid Funny you say that. The term "computer" was originally used to refer to people who did all of the heavy calculations involved in creating mathematical tables for trigonometric functions, that were widely used until the mid-20th Century in a number of fields (engineering and navigation).

@JohnDoe-ti2np 3 месяца назад

@@vsm1456 Hermite didn't discover it by computing lots of numbers blindly and hoping to find a pattern. There's a special function in mathematics called the j-invariant. On the one hand, there is some theory that tells us that j((1 + sqrt(-d))/2) is an integer if a certain number system (the "ring of integers of Q(sqrt(-d))") has unique factorization. On the other hand, there is an infinite series expression for j that tells us that j((1 + sqrt(-d))/2) is very close to e^(pi*sqrt(163)). If you know this underlying theory then you can deduce that e^(pi*sqrt(163)) is very close to an integer without having to explicitly calculate e^(pi*sqrt(163)).

@ianstopher9111 3 месяца назад

Sadly, Heegner died without his proof of the Stark-Heegner theorem being accepted. Sometimes considered an amateur mathematician, his proof was ignored by many for years. I came across the Stark-Heegner theorem in the context of studying factorisation and I was very taken aback that these 9 numbers are the only ones that provide for quadratic imaginary number fields whose rings are PIDs. The Wikipedia page on Heegner numbers provides a rabbit hole of possibilities.

@punkdigerati 3 месяца назад

That zoom in was iconic, thank you Brady.

@tonybielecki9360 3 месяца назад

A mathematical proof that e^(π√163)=integer was reported in the Mathematical Games column in Scientific American magazine in April 1975. Years later, I realized that it was an April Fools hoax. The same column announced other amazing discoveries, one of which had to do with the Four Color Map Conjecture.

@TranscendentBen 3 месяца назад

11:38 "It's good to publish our null results." This was discussed by Richard Feynman in his "Cargo Cult Science" essay/speech, easily found online.

@Epsilon3141 3 месяца назад

I propose they be called “Parker integers”

@renerpho 3 месяца назад

They form a Parker field.

@SeanKennedy 3 месяца назад

"Try something, and it doesn't always work." That deserves to be a poster or t-shirt with the Parker Square.

@Toon81ehv 3 месяца назад

Here I am writing a Rust program, in like 15 minutes I've checked 8 million numbers for caboose numbers, only to be bested by Matt proving there aren't any!

@unvergebeneid 3 месяца назад

These numbers are also connected to the proof of Fermat's Last Theorem via modular forms. I have no idea in what way but I found that interesting while we're on the topic of unexpected connections between seemingly unrelated mathematical facts or even fields.

@JMUDoc 3 месяца назад

"We need a name for these numbers..." Kurt Heegner: "What am I? Chopped liver?!"

3 месяца назад

glad I watched this one before I started writing a script to enumarate more Caboose numbers :D

@XJScott 3 месяца назад

Alternatively: The Journey is the Reward

@YTEdy 3 месяца назад

What's truly remarkable is that every number is within 0.5 of an integer.

@billberg1264 3 месяца назад

If we're being pedantic, I don't think that necessarily applies to non-real numbers.

@YTEdy 3 месяца назад

@@billberg1264 I stand corrected.

@BenAlternate-zf9nr 3 месяца назад

A process that generates random normal reals should get within 1/10^12 of an integer about 2/10^12 of the time just by chance, so it's not at all obvious that there shouldn't have been an infinite number of these.

@irober02 3 месяца назад

Labrador unimpressed - dreaming of its next meal.

@twrhancock 3 месяца назад

I'm getting major Parker Square vibes about this

@PC_Simo 3 месяца назад

0:41 Transcendental numbers, like e and π are like those MVPs, who know they’re super important: ”We don’t need to behave well, because we know we’re super important, for Mathematics, as a whole. We can’t be replaced. You, folks, need us!”. 😅

@surya912003 2 месяца назад

Mathematical beauty in treehouse architecture

@GenericInternetter 3 месяца назад

Greatest achievement ever. He really did draw directly from one brown paper to ther other.

@PaulPaulPaulson 3 месяца назад

From now on, zeros are known as Parker nines

@aner_bda 3 месяца назад

The zoom in on the Parker Square though, that was perfect. 🤣

@Frahamen 3 месяца назад

Try smaller numbers, like -1

@danielyuan9862 3 месяца назад

Holy frick

@xinpingdonohoe3978 3 месяца назад

I've checked 12 trillion decimal places. All 0s so far. I know there are infinitely many 0s. At least 40% of the decimals are 0s. But I won't stop until I've seen if all of them are 0s.

@dannymac6368 3 месяца назад

The ending was so perfectly done. 🤗

@WAMTAT 3 месяца назад

So this is the Caboose video?

@aceman0000099 3 месяца назад

This is the first class carriage

@williamnathanael412 3 месяца назад

This is the Parker video

@alansmithee419 3 месяца назад

This is post-caboose.

@someoneunknown6553 3 месяца назад

This is the caboose to the caboose video

@Amonimus 3 месяца назад

No, this is Patrick.

@annahanslope7528 3 месяца назад

For 101×4-1 (which is 403). e^(π√403) isn't close to an integer, but what it is close to is an integer+(3/8)

@uesdtosignin1038 3 месяца назад

2:36 In fact, that is the example how you get your name after something while you have nothing to do with it at all. The number was discovered in 1859 (28 years before Ramanujan born) by the mathematician Charles Hermite. And "Mathematical Games" columnist Martin Gardner made the hoax claim that "the number was in fact an integer, and that the Indian mathematical genius Srinivasa Ramanujan had predicted it".

@yanntal954 3 месяца назад

2:49 Parker integer

@convindix9638 3 месяца назад

All numbers below 2,000,000 which give 6 nines: 478233, 881967, 1053883, 1341615 ...which give 6 zeros: 2608, 880111 ...which give 7+ nines: 163, 1467, 1844122 ...which give 7+ zeros: 652

@finefreefine9994 3 месяца назад

Very funny. I wrote code to find all the complex numbers that conjugate to primes and found this same relation. Nice to see it explained so well here.

@U014B 3 месяца назад

While using -1 as a treehouse number does produce a true integer, adding 1 to it and dividing by 4 does not produce a valid caboose number. It seems we've got a Heisenberg situation with this relationship.

@roomfullofpigeons 3 месяца назад

(-1+1)/4 =0, and 0 is vacuosly a carboose number as there are no natural numbers less than zero.

@gtp259 3 месяца назад

the true journey of a mathematician is discovering some pattern , being amazed , and figuring out you have no clue what to do with it 🤣🤣🤣🤣

@liamogrady5868 3 месяца назад

For those interested, if the large integer at the beginning represented the circumference of the earth, then the level of precision given by e^pi*sqrt(163) would give the circumference with an error of about 40 micrometers. That's about as big as one of your skin cells can get. Incidentally it's also the lower limit of human vision, so if those two numbers were wrapped around the entirety of the earth, you would not be able to see the difference.

@henrygreen2096 3 месяца назад

Matt said something that really made me love undergrad physics actually. It's when you can't solve something, or get an experimental conclusion that you expect or looking for BUT YOU KNOW WHY you can't get it. Like being able to explain why to me makes all the difference. having something mess up and you're in the dark about it sucks haha. Great video!

@leonardofontenelle3560 3 месяца назад

Matt already has his square, let Ramanuyan have his integer!

@AlRoderick 3 месяца назад

The thing about searching for things with terrible python code is that eventually you're going to run into floating point rounding errors, so eventually these are going to equal integers to the degree of precision that your CPU is capable of determining. Very very big integers.

@leonolszewski4744 2 месяца назад

When I watched the video, I was thinking about the precision, combined with the fact that these are irrational numbers. Combined, you are always going to have some deviation from the actual result.

@DanatronOne 3 месяца назад

I think you might get quite close to an integer if you use the treehouse number -1 ;)

@toolebukk 3 месяца назад

"Zeroes have same effect as 9s for closeness to an integer" 😂 Yeah thanks mate ❤

@jetison333 3 месяца назад

That's correct though?

@WAMTAT 3 месяца назад

He's not wrong

@litigioussociety4249 3 месяца назад

It's a Parker discovery.

@maximiliandc2 3 месяца назад

I was about to say that there seems to be a theme going on here...

@joedeshon 3 месяца назад

By FAR, the best Numberphile video EVER!!!

@nekogod 3 месяца назад

e^(pi*sqrt(-1)) is an integer.

@minmagletsplay6710 3 месяца назад

❤ What a cool coalation. I love when the same pattern appears in two seemingly unrelated places.

@ElderEagle42 3 месяца назад

I hope the you one day actually can discover something completely new, and if you do, do a poll on you channel so we can name them

@zerosiii 3 месяца назад

Damn, Ramanujan seemed like such a chad, he was hunting for all the bugs in this simulation of a universe we are living in

@Marcel-yu2fw 3 месяца назад

It's a Parker integer!

@Zach010ROBLOX 3 месяца назад

I like to think that many viewers are like the dog on Matt's couch, taking an afternoon or evening nap falling asleep to interesting maths facts

@AttackSpeed407 3 месяца назад

Funnily enough, e^(π√π) gives 261.995675220194595466440575392237995276999642828242... which is close to an integer by the weakest margins. It's not using a square root of a whole number so it doesn't count, but it's something I thought was a neat coincidence.

@levishadow 3 месяца назад

Love how Skylab is relaxing in the background :D

@vicenteroberts3009 3 месяца назад

This was a Parker Maths Journey.

@wobblysauce 3 месяца назад

We almost need a part 3...

@itryen7632 3 месяца назад

THE FAMOUS CONSTANT

@barrysoper9183 3 месяца назад

Wow, a video to replace the “Parker Square”. ❤ You’re the best, Matt.

@arcanics1971 3 месяца назад

I've probably known Matt Parker sans hair as long as I ever knew Matt Parker with hair, but whenever I see a video has Matt Parker in it, I am always mildly surprised that he no longer has hair.

@abdulllllahhh 3 месяца назад

No way we already got Parker caboose and Parker tree house numbers

@guillaumelagueyte1019 3 месяца назад

Oh damn, I suspected when seeing the previous video that there may be a link between Caboose numbers and Heegner numbers, and at the beginning I suspected that the last Caboose number would be 163, but then as I saw that the two lists didn't match I dropped the idea. Seems like there is a link between the two, and I just didn't see the pattern. Nice to know that my intuition was correct though

@mathphysicsnerd 3 месяца назад

Matt: *points at expression* "These are just, growing exponentially..." WHAT? A THING WITH e IS GROWING EXPONENTIALLY!?

@Im_Rainrot 3 месяца назад

A NUMBER WITH AN EXPONENT GROWING IS GROWING EXPONENTIALLY???

@LeeChesnalavage 3 месяца назад

That crash zoom at the end is playing dirty. 😂

@jonathanrichards593 3 месяца назад

Setup... in previous videos, Matt has had the treasure hanging on the wall. As a previous commenter said, I really hope it gets rehung *just* out of perpendicular.

@SatisfyingWhirlpools 3 месяца назад

This is the first Numberphile video in a while that has me completely gobsmacked.

@NomenNescio99 3 месяца назад

Matt's destiny seems to be to try really hard and almost make it. Parker square, caboose numbers and tree house numbers - it's definitely a pattern.

@teeweezeven 3 месяца назад

It makes a lot of sense why 652 and 1467 have so many nines. They're 4×163 and 9×163, so you're basically squaring and cubing the number with a bunch of nines!

@Tfin 3 месяца назад

Me taking a cue from previous video: "But does the pattern hold?" Matt: "The pattern stops right there."

@joequincy5574 3 месяца назад

Love this new "off the top of my head" bit Matt used in these.

@mustafasahinturk9651 3 месяца назад

This guy always do things almost spectacular. Such a parker square...

@quezzert 3 месяца назад

i thought for sure he was gonna write the square root of -1...

@aceman0000099 3 месяца назад

Numberphile rarely goes near the complex zone

@DontMockMySmock 3 месяца назад

absolutely brutal zoom-in on the Parker Square at the end

@dancoroian1 3 месяца назад

Man, it's almost criminal the way Matt pronounces Ram-a-NYOO-jen 🤣

@davidappelgate320 3 месяца назад

I can very easily believe that there are no more caboose numbers after 41, because you keep adding more and more constraints on the number the higher you go up. But there being no more treehouse numbers greatly surprises me, because as square roots of larger and larger numbers give you more and more precision I would expect more near-misses as you go higher.

@convindix9638 3 месяца назад

Since he never put a hard cutoff on whether a number is a treehouse number or not (only "looks close enough to an integer"), there's no theorem that definitively rules out all numbers past 163 from being treehouse numbers. Some other higher numbers like 1844122 get pretty close (seven 9s)

@grumpyparsnip 3 месяца назад

Did Matt Parker say "The integers are a field."? That's, umm, interesting.

@jonaszurba4906 3 месяца назад

The integers - the classic Parker Field

@noel.gonsalves 3 месяца назад

11:05 So the Parker caboose near-misses and Parker treehouse near-misses have a Parker pattern. Got it.

@mal2ksc 3 месяца назад

I think a reasonable cutoff for how close you have to get would be "does it look like an integer in 64-bit floating point?" That means the bigger the number gets, the less close you need to be, but more importantly it indicates where you stand to get _actual real-world errors_ if you ignore these numbers, in circumstances where you wouldn't otherwise think you're anywhere near the limits of 64-bit FP.

@JamesTM 3 месяца назад

The zoom-in on the Parker Square is both savage and hilarious. 😆

@dragonmudd 3 месяца назад

I tried to work out how impressive it is that the Ramanujan Constant is that close to an integer. If you were to draw the number line from 0 up to the Ramanujan Constant, and then stretch that number line to the size of the observable universe, the distance between consecutive integers would be about nine times the distance from the Earth to our moon. Meanwhile the difference between the Ramanujan Constant and the integer that it's closest to would only be about 2.5 millimeters.

@gtziavelis 3 месяца назад

12 years ago there was a Numberphile on the number 163 and this very same topic of Heegner numbers. FYI. Guest Alex Clark looked a little like a Baldwin brother, but I digress.

@jakobthomsen1595 3 месяца назад

Great to learn about the connection between Heegner numbers and Gauss's ("caboose") and Ramanujan's ("treehouse") numbers 🙂 Would be great to see a Numberphile episode explaining Heegner numbers more in-depth!

@PaulHenkiel 3 месяца назад

Wikipedia “This number was discovered in 1859 by the mathematician Charles Hermite.[7] In a 1975 April Fool article in Scientific American magazine,[8] "Mathematical Games" columnist Martin Gardner made the hoax claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa Ramanujan had predicted it-hence its name.” I do not like April fools' hoaxes.