90,525,801,730 Cannon Balls - Numberphile

Подписаться 4,5 млн

Просмотров 632 тыс.

50% 1

Matt Parker has a new favourite number - again!
More links & stuff in full description below ↓↓↓
Some notes from Matt on how far he has investigated: www.numberphile.com/cannon-ba...
Matt's book "Humble Pi" via Maths Gear (signed and ships almost everywhere): bit.ly/Humble_Pi
More Numberphile videos with Matt: bit.ly/Matt_Videos
James Grime sphere packing: • The Best Way to Pack S...
Lucas Numbers: • Lucas Numbers - Number...
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from Math For America - www.mathforamerica.org/
NUMBERPHILE
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Videos by Brady Haran
Editing and animation on this video by Pete McPartlan
Patreon: / numberphile
Numberphile T-Shirts: teespring.com/stores/numberphile
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9
With special thanks to:
Arjun Chakroborty
Ben Delo
Jeff Straathof
Andy
Yana Chernobilsky
Christian Cooper
Ken Baron
Bill Shillito
Ben
Bernd Sing
Dr Jubal John
Tom Buckingham
Andrei M Burke
Adam Savage
Matthew Schuster
James Bissonette
Robert Donato
john buchan
Joshua Davis
Steve Crutchfield
Jon Padden
Valentin-Eugen Dobrota
Eric Mumford
Charles Southerland
Arnas
Ian George Walker
Jerome Froelich
Tracy Parry
George Greene
Igor Sokolov
Alfred Wallace
Bodhisattva Debnath
Full Patron list at: www.numberphile.com/patrons

Наука

Опубликовано:

12 июн 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 1,2 тыс.

@iabervon 5 лет назад

What's the smallest positive integer that has never been Matt Parker's favorite number?

@numberphile 5 лет назад

Whatever it is will be his new favourite!

@tracyh5751 5 лет назад

No numbers are boring.

@ssdd9911 5 лет назад

@dlevi67 5 лет назад

We can put a higher bound on that at 2, since Matt calls it "a sub-prime", which ain't nice. That doesn't leave many contenders.

@timclark2880 5 лет назад

90,525,801,731

@xaiano794 5 лет назад

"I don't think anyone else has ever bothered doing this" - Mathematicians in a nutshell.

@JosephDalrymple 4 года назад

Hahaha pretty much. The vast majority of a lot of these videos result in two expressions from me, almost simultaneously: (1) that's absolutely fascinating, and (2) why on earth would anybody even think of doing that? [now how, mind you: why] 😂 I ask myself the same questions every time I conclude my work and discover the answer to one of my engineering problems. It starts out the same and ends with the same questions.

@Triantalex 7 месяцев назад

false..

@jekyllgaming99 5 лет назад

The 31,265-sided polygon, also known as the Triamyriahenachiliadihectahexacontakaipentagon.

@Sylocat 4 года назад

Or the Parker Circle.

@hamiltonianpathondodecahed5236 3 года назад

~Felt like the name of some chemical compound~ Sorry

@wizard-pirate Год назад

Thanks for answering the dangling question of "What is the actual name for the 31265-agon?" I like Parker's Polygon, if not just because it's easier to remember.

@user-qu2jr2wt9k 11 месяцев назад

Googolplex, also known as 'Ten Triacontrectricentitriadecatriavecitriacentitriadecitriaxonitriacentitriadecitriayoctatriacentitriadecatriazeptitriacentitriadecatriaattitriacentitriadecatriafemtitriacentitriadecatriapicitriacentitriadecatriananitriacentitriadecatriamicritriacentitriadecitremillinilliduotrigintatrecentillion'. (Note: this might be inaccurate, because it also feels like 9.1×10^(10^99).)

@Proto_Divi 7 месяцев назад

medial omnicircumfacetopental triakishecatonicosachoron mommy

@davidross7467 5 лет назад

Eagerly awaiting the follow up video in which Professor Eisenbud constructs the 31,265-gon with just ruler and compass

@numberphile 5 лет назад

Good Numberphile knowledge.

@AlisterCountel 5 лет назад

David Ross Sadly, the 31,265-gon is not constructible. One may draw one with a relatively high degree of accuracy though, using just a compass, no straightedge needed!

@baijokull 5 лет назад

@@AlisterCountel Sure it is, just bring me 90,525,801,730 cannonballs!

@bledathehun328 4 года назад

And Carlo Séguin to 3D print it.

@orbitalteapot21 4 года назад

@@AlisterCountel I see what you did there.

@jonthecomposer 5 лет назад

The Parker Conjecture: The amount of non-useful numerical discoveries will always be greater than the rate at which Matt Parker can discover them.

@peppybocan 5 лет назад

well, non-useful. What he does is - searching for solutions of non-linear diophantine equations, a tricky task to do!

@Tehcarp 5 лет назад

a modern day Tristram shandy

@Veggie13 5 лет назад

You can't compare a number to a rate, silly.

@jonthecomposer 5 лет назад

@@Veggie13 I do what I want! You don't know me! Wait, wut? lol It's all in fun, man. I say it because it's ridiculous. Nothing more, nothing less. :)

@randomdude9135 5 лет назад

@@Veggie13 I was about to type just that.😂.

@nataliekanakova9496 5 лет назад

You can see it in his eyes how excited he is about his discovery :)

@ericstoverink6579 5 лет назад

Because he thinks this will make us forget about Parker squares.

@richardtickler8555 5 лет назад

@@ericstoverink6579 maybe it turns out to be a parker pyramid

@Nemelis0 5 лет назад

@@ericstoverink6579 No Parker Squares are unforgettable, but this will tell people that there are 31263 more sides to Parker than just the 2 in a square

@macswanton9622 5 лет назад

@The Idiot Reviewer If it was a hat it would barely fit

@janschmeink9296 5 лет назад

it's so cute right

@ramonalainmirandaquintana6515 5 лет назад

"Is not useful, but I love it". Denotes both great appreciation for mathematical beauty, and terrible parenting skills :)

@Erichwanh 5 лет назад

Please pin this comment, hahaha

@maxnullifidian 5 лет назад

It may not be useful yet, but who knows what the future holds? It may someday be found to answer some critical question that hasn't even been asked yet!

@tqnohe 5 лет назад

Describes my son Michael.

@beauwilliamson3628 5 лет назад

@@maxnullifidian Like: What's the coolest way to stack the 90,525,801,730 plasma torpedos I've stockpiled for my invasion of the Galactic Empire?

@maxnullifidian 5 лет назад

@@beauwilliamson3628 See, it's useful already! LOL

@bookslug2919 5 лет назад

I thought this was going to be good but it's just a load of balls

@zippy-zappa-zeppo-zorba-etc 5 лет назад

*Clap* *Clap* *Clap*

@Danilego 5 лет назад

@@zippy-zappa-zeppo-zorba-etc *MEME* *REVIEW*

@Kris.G 5 лет назад

ba dum tssss

@fafnir242 5 лет назад

I applaud you.

@vipcesh 4 года назад

Hey! I thought he was really ballsy!

@codesimpson6010 5 лет назад

"And so that's when 4,900 stopped being my favorite number, and I upgraded to just over Ninety billion!" - Matt Parker, 2019

@j.hawkins8779 3 года назад

LOL😂

@johnchessant3012 5 лет назад

Fun fact: A hyper-pyramid with a cube "base" can always be arranged into a square, no matter the height of the hyper-pyramid. This follows from the amazing fact that 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2.

@NAMEhzj 5 лет назад

Thats very cool!

@TheRealFlenuan 5 лет назад

But then the question is: Which can be arranged into a cube?

@alexanderehrentraut4493 5 лет назад

@@TheRealFlenuan I don't think there are any.

@witherfly5811 5 лет назад

Just as any 3-D Pyramide can be arranged into a Line. So nothing special.

@pleaseenteraname4824 5 лет назад

Withi Nah, this is cooler

@KurtRichterCISSP 5 лет назад

The 31,265-gon is one of my favorite shapes.

@eternalreign2313 5 лет назад

It looks more and more like a circle the further you move away from it. In fact, even if you're right next to it you probably can't tell where one of the corners is.

@KurtRichterCISSP 5 лет назад

@@eternalreign2313 depends how big it is relative to me...

@therabbits69 4 года назад

@@KurtRichterCISSP People should figure out how big it actually would be IRL using the average canon ball.

@markreynolds1436 4 года назад

@@eternalreign2313 I don't believe it's round. It's probably a sphere or something mad.

@bertblankenstein3738 3 года назад

Maybe a 31415-agon could be used in calculating pi. Can a 31265-agon be constructed?

@iggusify 5 лет назад

"Matt, seriously, I'm proud of you!" -- That's beautiful...

@Mr.E-Bachs 3 года назад

I love Matt’s self-aware pause, “with enough... spare time and a laptop.” And that is why we keep coming back for more.

@cooloutcoexist 5 лет назад

Takes a lot of balls to search for this number.

@clayz1 5 лет назад

Thats probably enough cannonballs to do the job. He’s a agon-er.

@unclvinny 5 лет назад

Brady, your animator is so good! They were really working overtime on this one.

@spaceatlantis3504 5 лет назад

Yeah, his name is Pete McPartlan

@spinter1310 5 лет назад

“That’s not useful”, said every mathematician about his discoveries a few decades or centuries before it is integral to revolutionary technology.

@Kylora2112 5 лет назад

Now: Matt: "I found this useless object and it's fun and cute!" 3019: "Matt's discovery lead to the Unified Theory Equation and is the key to intergalactic and interdimensional travel. Human civilization is now based on 90525801730."

@KuraIthys 5 лет назад

Meanwhile, think of all the people that aren't mathematicians that randomly mess around with numbers sometimes (like me say) come up with something weird, look at it, have no idea what it is, and then forget they ever did it... Hopefully I've never 'discovered' anything new or useful, because if I have I've since forgotten again. XD For that matter, I ran into a youtuber recently that claimed to have 'invented' something that I had made a version of more than 15 years ago. They presented it as some great amazing breakthrough, and 90% of their audience agreed, meanwhile I did it randomly, looked at it and decided 'this is so obvious I'm sure there's been thousands of people before me that have come up with the same thing.', and then just ignored it and more or less forgot I did it until I saw someone else do it. So... Did I invent something unique and not realise the significance? Or was my assessment that it was a super-obvious solution that's probably been done a million times before correct and this guy on youtube is just full of himself? Either way, you never know. What seems trivial to you may turn out to have been an amazing discovery and/or invention, which is lost forever because not even it's creator remembers it, simply because it didn't seem particularly important or impressive to them. XD

@wolfson109 5 лет назад

@@KuraIthys now I really want to know what it was.

@Xeridanus 5 лет назад

@@wolfson109 Same

@petros_adamopoulos 5 лет назад

Not this one, trust me.

@asailijhijr 5 лет назад

Something that nobody was looking for but that is genuinely impressive, a Parker Pyramid.

@sophiegrey9576 5 лет назад

Or a Parker Cone.

@SpySappingMyKeyboard 5 лет назад

There's one! Well, I didn't look any further, but there's only one! Parker proof?

@pleaseenteraname4824 5 лет назад

Proof by exhaustion, i.e. I was too tired to look any further

@sb-jo2ch 5 лет назад

Natural number: exists Matt Parker: It's free real estate

@maximiliand2180 4 года назад

Person: "Hey Matt what is your favorite number?" Matt: "Yes"

@unitrader403 4 года назад

Computer: Error, encountered -NaN, expected Number

@imveryangryitsnotbutter 4 года назад

I agree, what is a very cool number.

@BeeCeeJay 4 года назад

I think this is my favorite video on your channel. Matt’s curiosity, skill, and sheer joy are all turned up to 11. Perfection.

@pipolwes000 5 лет назад

"4,900 is the only number which can be both a square and a square base pyramid" Counterexample: 1.

@dcs_0 5 лет назад

Tut tut. You forgot 0

@SpaceboyBilliards 5 лет назад

How is a single sphere a square

@cemerson 5 лет назад

@@SpaceboyBilliards How are any number of spheres a square?

@Tfin 5 лет назад

A sphere is a square because you're only considering the packing of that number of spheres. You have a square tray with sides of length x(n). How many spheres of diameter n fit on it? But 1 is trivial, and works for all numbers.

@SpaceboyBilliards 5 лет назад

@@cemerson 4 spheres is a square because the outline of them is a square shape. 1 sphere has the outline of a circle.

@ZachGatesHere 5 лет назад

My favorite part of this video is actually that I had to do some thinking about how "pentagonal" and "hexagonal" numbers are formed because at first the shapes seem wrong since their visual isn't like "pizza slices" that meet in the shape's center but rather wedges that meet at the top. Had to look that up and saw that any -gon numbers are constructed by making a "1x1" version of the shape and then building new layers around it anchored at one corner, leading to this rather unusual appearance.

@michaelzimmermann3388 5 лет назад

Usefulness lies in the eyes of the spectator. I love your discovery, it is nothing short of amazing

@NUGGet-3562 5 лет назад

I love how proud he is of his numbers. "And I found it first!"

@raghavproach2444 3 года назад

I wish I had such a maths teacher, I have fallen in love with maths all over again. Would love to see more such cool stuff from Matt. Also, someone said this isn't a useful number, I think it is - it is fascinating and exciting, such that it pulls you towards math.

@numberphile 5 лет назад

BTW, there is a new Numberphile podcast out too: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9y1BGvnTyQA.html

@adelarscheidt 5 лет назад

How exactly do you arrange spheres on a pentagon surface?... I mean what rule(s) do you follow?

@gadrill4285 5 лет назад

1 sphere = 1 unit

@Theraot 5 лет назад

You melt them and pour them in a pentagon mold

@theznayx808 5 лет назад

I think the idea is maximum packing. If you check that scene where they showed all the layers of the pentagonal one, you see there's big blank spaces inside.

@debblez 5 лет назад

For height 1: Pentagon size 1 (just one sphere) For height 2: Pentagon sizes 1+2(total 6 spheres) For height 3: Pentagon sizes 1+2+3 (total 16 spheres) And so on

@ig2d 5 лет назад

I am wondering the same thing. Can this problem be clearly defined...

@TeodorMusic 5 лет назад

Did I miss something or why do you ignore triangle base pyramid?

@pedrolmlkzk 5 лет назад

Tetraedron

@philipyao5989 4 года назад

Not sure with squares but the formula is n(n+1)(n+2)/6

@poofishgaming5622 4 года назад

For 3 it’s 10, 120, 1540,

@matthewstuckenbruck5834 3 года назад

He has it in the description

@quarkonium3795 Год назад

@@poofishgaming5622 and 7140

@timsullivan4566 5 лет назад

That's nice - I've always thought 90,525,801,730 deserved some recognition. His factors must be so proud!

@betabenja 5 лет назад

1919: I thought about it and proved it in concept for infinity cases using a clever logical argument 2019: I brute force found one solution, and I didn't even do the calculations. who knows, eh?

@ElektrykFlaaj 5 лет назад

well, we use bruteforce to calculate something 1919 mathematicians couldnt do analytically

@GeodesicBruh 5 лет назад

betabenja oof haha

@gajbooks 5 лет назад

I think it's more of "Is there anything within the realm of sanity that works, and can I find it without huge effort, because it's not exactly a useful answer".

@adamsbja 5 лет назад

@@ElektrykFlaaj If they'd added a 1920th mathematician I bet they could've figured it out.

@ElektrykFlaaj 5 лет назад

@@adamsbja imagine the possibilities with 1921 mathematicians

@ameyaparanjpe6179 5 лет назад

Amazing content as always Numberphile

@levengli 5 лет назад

Discovery for the sake of discovery. The beauty of pure mathematics. Well done, Matt!

@Ken.- 5 лет назад

The computer was probably thinking, "I must be doing something really important!" ....And that's why the AI computers will kill all of the humans.

@bookslug2919 5 лет назад

Nope, they will just make our lifespans more 'efficient'.

@TheRealFlenuan 5 лет назад

Let's hope

@mystifiedoni377 Год назад

These animations are amazing! Really help you understand what's being talked about.

@johnchancey3941 5 лет назад

At 6:42, Brady sounds like a proud father whose child did something somewhat strange but surprisingly creative

@SlyMaelstrom 5 лет назад

"So the people whose names you're seeing on screen at the moment... these are all the people that found the number before Matt Parker."

@numberphile 5 лет назад

Ha ha.

@jonathanwalther 5 лет назад

Damn, these animations! Well done!

@nok400 5 лет назад

I really like how you have uped the production of these videos. Keep it up, I am loving it. - A fellow Tim

@Latchfpv 5 лет назад

And this is now one of my new favourite Matt Parker number videos.

@harrypounds456 5 лет назад

i thought this was a genuinely cool discovery, well done!

@krumuvecis 5 лет назад

Hey, what about a triangle? Seems you missed the simplest polygon

@SSGranor 5 лет назад

10. You can do it with 10.

@krumuvecis 5 лет назад

@@SSGranor Ok, that's one solution. Are there any others?

@PhilBagels 5 лет назад

Yeah. Why did he skip over triangles? One of the ways you can actually stack cannonballs, as opposed to octagons and 31,265-gons. 10 is the first and easiest one to find. I suspect there are others, but I don't remember, and I don't have time to look for them now.

@krumuvecis 5 лет назад

Apparently there are only 5 solutions: 1; 10; 120; 1540; 7140

@ffggddss 5 лет назад

@@krumuvecis And don't forget 0. Fred

@SAAAMTV 5 лет назад

This. is. absurdly. fascinating. I've the same enthusiasm as numbers as Matt, but none of the coding knowledge to realise these sorts of things. Thanks for doing these!

@malcom91 5 лет назад

"And I found it first". With a proud smile on your face. Awesome!!

@tetsuoumezawa5833 5 лет назад

0:37 remember when matt had hair

@andrewkepert923 5 лет назад

h=hair, f=favourite number. d/dt (hf) = 0

@TheRealFlenuan 5 лет назад

“Is this what it took?” 😂😂😂

@sam08g16 5 лет назад

We are all very proud of you Matt!

@todork.3240 5 лет назад

At this point i can say, that this channel cannot get any nerdier, or can it. Thanks for the great video.

@arkantyne7122 5 лет назад

"What's your favourite number Matt?" "Oh, err, somewhere between, err, 90 billion, or was it 80? Maybe 85..."

@AviMehra 5 лет назад

I was expecting a 31,265-gonal Parker square but I got a 31,265-gonal Parker pyramid

@DeNappa 5 лет назад

I love it how enthusiastic Matt gets over stuff like this. :)

@akaelalias1113 5 лет назад

At 0:34 Matt says that his club of favourite numbers is finite, but at 0:27 the graphic shows that all real numbers are a subset of his favourites!

@LukePalmer 5 лет назад

At 4:36 I can hear matt thinking "yep, this is who I have become"

@MrCyanGaming 5 лет назад

Yeah but matt, I think cannon balls can't be stacked in shapes greater than a hexagon right? like, I'm pretty sure you can only have them in triangles squares and hexagons

@julienhau999 5 лет назад

Yeah i dont understand either how they are stacked for higher polygons

@dfhgjhg 5 лет назад

It's the Parker's cannon ball stack

@KurtRichterCISSP 5 лет назад

The foundation level is inside a frame made of adamantium.

@Tahgtahv 5 лет назад

@@julienhau999 They are all stacked in the same way. It's successive layers, with sides of length n-1. That fact that this would be more or less impossible to pull off physically is irrelevant.

@theznayx808 5 лет назад

If you look at the scene with all the individual pentagon layers you see big spaces so it's probably just maximal packing

@Duey8808 5 лет назад

I really like your observation that the number has been waiting since the beginning of time for someone to attach some significance to it. That's a very interesting way of looking at it.

@reidtrevar 5 лет назад

My list of favorite Numberphile videos is large, but finite. This is my current favorite.

@julienhau999 5 лет назад

I cannot imagine how you can stack cannoballs for higher base polygons I thought you could only make triangular base pyramids (tetrahedron) and square base pyramids only PLEASE respond matt

@Ellyerre 5 лет назад

They had a note in the video at 3:35 that said that those pyramids wouldn't necessarily stack in the real world.

@kevinslater4126 5 лет назад

Of course you can! With enough time, expendable labor, and glue

@Anchor9Studios 5 лет назад

7:29 is that Adam Savage of Mythbusters? He watches Numberphile? I feel like I’m in great company with so many superstars :)

@trequor 3 года назад

Props to you for actually reading the patreon credits

@sean..L 5 лет назад

I can’t get enough sphere-packing videos I NEED MORE!

@trahlem 5 лет назад

i smiled so much throughout that video, so wholesome

@only2ndplace 5 лет назад

"It's not useful, but I love it." - every mathematician about every field of math ever

@beeell8017 5 лет назад

Is there a relationship between the 1k and 5k hexagon stacks? That could predict the next size?

@Vaaaaadim 5 лет назад

If so, I think the solutions would be a recurrence relation. In the past before I had looked for where the sum of integers from 1 to n equals a perfect square, for whatever reason. In other words solutions to the equation n*(n+1)/2 = k^2, for integers n and k. I remade a program to look for this after seeing your comment, and found the following solutions 0,1,8,49,288,1681,9800,57121,332928 and I noticed that this sequence of solutions fits the following recurrence relation: F(0) = 0, F(1) = 1, F(n) = 6*F(n-1) - F(n-2) + 2 and it seems this recurrence relation predicates the next value of this sequence being 1940449, and indeed sqrt(1940449*1940450/2) = 1372105 an integer. Seeing that something like this comes up with a recurrence relation like this is what would prompt me to think that the hexagon stacks thing would also do similarly, if such a relationship exists. Though there is a difference between this example and that which comes up in the video, as my thing has a quadratic on both sides, whereas the video has a quadratic on one side, and a cubic on the other.

@blackraven114 5 лет назад

There are more solutions higher up but there doesn't seem to be any sort of relation. I ran things up to 10^22 and you end up with 1045 , 5985 , 123395663059845 , and 774611255177760.

@lvl1969 5 лет назад

Turns out the equation is that of an elliptic curve. Siegel's theorem gives us that there are only a finite number of solutions. The recurrence formula you are looking for is that of point addition/duplication on elliptic curves, but they will eventually start producing rational numbers.

@Rabbit-the-One 4 года назад

Proud of you too Matt.

@izme1000 4 года назад

I love how it looks like a circle and a cone.

@arthurdequeiroz8393 5 лет назад

Greetings from Brazil , absolutely love this channel

@guepardiez 5 лет назад

I don't understand the point of this. Only the outer layer of those polygons is regular. How are the inner layers formed?

@jokusekovaan 5 лет назад

Right, some things weren't explained at all. Is this something like the least surface area where the surface is 'stuck' like oranges in a cardboard box, and each round thing above the previous layer touch at least 3 things below in a stabile way?

@Koisheep 5 лет назад

The video says such forms may not be possible in real life, they are made up

@kevinslater4126 5 лет назад

There’s a previous video about stacking cannonballs

@to2podemosaprender630 5 лет назад

I like this guy... He's always happy to find this numbers, I feel like all these numbers are going to be useful one day... I used to think like that..

@151Phace 5 лет назад

You guys are just awesome!

@joe9832 5 лет назад

3:38 - Damn, I was really looking forward to stacking hundreds of cannonballs - in differently shaped polygons nonetheless - in the comfort of my home, sadly confined within the real world.

@whatno5090 3 года назад

Luckily, by Siegel's theorem, for each number of sides of your polygon there are only finitely many solutions (if any at all).

@muralikonda6233 5 лет назад

“ And I found it first “ 😂😂😂😂

@arw000 5 лет назад

Matt Parker is just a joy.

@havhavproductions8725 5 лет назад

The animations this episode were awsome!

@tyzonemusic 5 лет назад

I don't know if you took this into account, but from the animations in the video it looks like your pentagons, hexagons, etc. always have a cannonball in the center. If you look at flat squares however, 3^2 will have a cannonball in the center while 4^2 will not. Was that taken into account when calculating the different values you could get?

@Casowsky 5 лет назад

"Really! Is this what it took?" Lmao

@MyHouseOnTheMoon 4 года назад

Congratulations, Matt!

@torchwood815 5 лет назад

May be my favorite numberphile video!

@Answerisequal42 5 лет назад

Does this work with tetrahedrons too?

@Monosekist 5 лет назад

I’ve discovered every number... Just not a use for each one.

@gunthertoastbrot3738 5 лет назад

He seems so happy while doing this.

@bradmorris67 5 лет назад

Love the new animation style - still has that brown-paper look we love in numberphile!

@WarpRulez 5 лет назад

How exactly do you arrange spheres into a regular polygon?

@kourii 5 лет назад

Pedant.

@EpicMathTime 5 лет назад

Woah, that's a lot of damage!

@NoriMori1992 5 лет назад

Nice job on the animations, Pete!

@Resomius 5 лет назад

Greetings from Germany, just bought the Book and i´m realy looking forward to read it!

@thomasturner6980 5 лет назад

What would win, nuke or 90 billion cannonballs

@slowsatsuma3214 5 лет назад

90 billion nukes

@rafbammens1032 5 лет назад

He what about triangle based piramides? Just asking? Greeting Raf.

@matthewpeltzer948 5 лет назад

10. 1 + 3 + 6 (levels of a triangular pyramid) = 1 + 2 + 3 + 4 (rows of a flat triangle)

@RichardPenner 5 лет назад

{m -> 1, n -> 1, s -> 3 }, # 1 - trivial {m -> 3, n -> 4, s -> 3 }, # 10 - stack triangles 3 high or make one triangle with a side of 4 {m -> 8, n -> 15, s -> 3 }, # 120 {m -> 20, n -> 55, s -> 3 }, # 1540 {m -> 34, n-> 119, s -> 3}, # 7140 I am told these are all the solutions when the number of sides is 3, but I haven't seen a proof yet.

@GeneralYouri 5 лет назад

@@matthewpeltzer948 Besides the trivial solution and your given solution of 10, there are at least three more: 120, 1540, 7140. There are no more until at least 2^53.

@namewarvergeben 5 лет назад

I started reading "Things to make and do in the fourth dimension" just this morning and came across the Cannonball Numbers. I recognised the thumbnail immediately. What are the odds that Numberphile would upload a video of Matt Parker talking about this topic just now? I mean, coincidences like this happen, and it could have been any of the other topics I've read in the first few chapters so far, but man. Freaky.

@TIO540S1 3 года назад

You just gotta love Matt Parker

@sekundus9274 5 лет назад

Are this Parker-pyramids?

@LaSDetta 5 лет назад

It's definitely a Parker Pyramid!

@Jp4wt 5 лет назад

as long as its not again a parker square xD

@gadrill4285 5 лет назад

@Parody Poops pretty sure it'd be a pyramid. definitely not a cylinder though

@gadrill4285 5 лет назад

@Parody Poops well i wouldn't call it a circle either

@kourii 5 лет назад

I don't know, but that was a spot of Parker grammar there, mate

@partygirl0101 5 лет назад

the biggest meme of numberphile is back at it again

@htmlguy88 5 лет назад

a meme ? ahem.

@partygirl0101 5 лет назад

@@htmlguy88 yes

@QuoteVG 5 лет назад

no the biggest meme is -1/12

@danielbergman1984 5 лет назад

Awesome! 👌💪 I wish I was as persistent as you! Great work!

@danielbergman1984 5 лет назад

I just realized that "persistent" wasn't the word I was looking for, but it seems you got my point... 😅

@nathanderhake839 5 лет назад

0:25 WHAT DO YOU HAVE AGAINST COMPLEX NUMBERS???!!

@hoggyapproved3040 5 лет назад

What about triangles?

@LeoStaley 5 лет назад

Easily the most important comment here, but jokes reign Supreme.

@mattj6604 2 года назад

Anybody else notice that 31265 is also a beautiful euphemism for “There’s 12 months in a year”? (12 inside of 365) Or am I just weird?

@AUDI80ROBLOX 5 лет назад

Matt Parker always a thumbs up!

@SteveHodge 5 лет назад

You can generate some cannon ball numbers with the formula: 1/2 (27x^7 + 189x^6 + 513x^5 + 684x^4 + 474x^3 + 171x^2 + 30x + 2)

@w0ttheh3ll 5 лет назад

most of those pyramids aren't actually proper stacks of spheres, you would need some kind of complex support structure to hold them in shape, defying the point of stacking in the first place

@HanabiraKage 5 лет назад

Would they be called Parker Pyramids, then?

@tomkerruish2982 5 лет назад

What about 0 and 1? Don't they always work for every shape?

@sebastianjost 5 лет назад

They're boring. It's about the non-trivial cases. But you are right :)

@ragnkja 5 лет назад

Tom Kerruish Too trivial.

@tomkerruish2982 5 лет назад

Agreed, they're trivial. But IMO they should have been mentioned. You always need to take care of such cases. E.g., when defining a field, it's always made explicit that 0 and 1 are unequal.