5-Sided Square - Numberphile

[@numberphile]

Check our sponsor The Great Courses Plus (free trial): ow.ly/j5cB30hIvm2 More Cliff Stoll videos: bit.ly/Cliff_Videos

[@unusualfabrication9937]

he has done it, he has broke the universe

[@skviper45]

Next Video Idea.........Rayo's Number ....please make it

[@wobblysauce]

But how is the scholar's cradle? on the Dog training.

[@Mnemonic-X]

Numberphile Is he crazy? It is not a square at all.

[@andersseruppoulsen7010]

Why can't I look at it from my PC? It only allows me to access the page from my phone which is very annoying...

[@Mutantcy1992]

Find someone who loves you the way Cliff loves math.

[@DrazkurHW]

watching youtube videos

[@Mutantcy1992]

glitch can't you let me have anything?

[@mike_slav0477]

@@erikpowa Geometry is a part of math.

[@TheRockindio]

Become math and know cliff loves you.

[@TheRockindio]

@@mike_slav0477 false geometry is expressed through mathematics. Math is not an expression of geometry.

[@BangMaster96]

Never seen a person so happy about squares. But, i'm glad people like him exist, who love what they do, and aren't afraid to show it.

[@stevethea5250]

🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴🥴

[@andrewandrei3062]

@@stevethea5250 OMG SQUARESSSS

[@ginge641]

Those people tend to get that trait bullied out of them after a few years in school.

[@TheLinposterIsSus]

Sunny shah Dude, minecraft and tetris sold 180,000,000 and 170,000,000 copies. Also the rubix cube is one of the most popular toys sold, so yah, people really like squares

[@augustdruzgal475]

Yeah this guy loves his life and I love that

[@DanMan5000]

I really love how he loves what hes talking about

[@lee6283]

I really love how you love how he loves what he's talking about.

[@poppy3879]

I really love how you love how he love how he loves what he's talking about

[@finnfinity9711]

My current math teacher is like this and it motivates you so much more

[@howardbaxter2514]

That’s what we should expect out of teachers. Sadly, there is a lack of teachers in this day and age.

[@1.4142]

I really love how he loves your comments saying You really love how he loves what he's talking about.

[@ronswanson1704]

I love how much enthusiasm he has over everything he does. Just makes me happy too.

[@Matt-sc6gg]

Happiness is contagious, I love him, I would love to call him grandpa!! ❤️❤️❤️❤️❤️ What passion for math! WOW! He can teach me anything and I would love ♥️❤️ to listen!

[@cat_atouille]

i love listening to people talk about everything they're passionate about

[@anticlimbmax]

This man must be protected at all costs

[@TheLegendaryPug]

@@BOOG-2 sounds familiar

[@vncntmusic]

Lmgdao

[@thesovietkevin7275]

@pratik mohite ur wrong. he has far less use

[@nadian848]

Yes. Please.

[@thesovietkevin7275]

@@nadian848 no

[@Thee_Sinner]

I hope I can find something in life that makes me as happy as math makes this man.

[@prestigexv2151]

maths

[@xCorvus7x]

Best of luck.

[@kekero540]

Arithmetic

[@livedandletdie]

Math is fun, Cliff has had a long life, and as such has learned a lot of interesting math.

[@SEGLOK12]

...it's you again

[@alexmolina8039]

His enthusiasm makes my heart smile. He's just so happy about squares. ITS SO HEART WARMING

[@cheetahda1o763]

Hahaha yes when you take the furthest step back he's happy about squares :)

[@george5924]

He married a square

[@teamexpt273]

I didn’t like this comment because I didn’t want it to have 333 sorry

[@Jazz-nr7nk]

"It has the _delicious_ property"

[@anarchocommunist3888]

😋

[@walkerhenry2045]

The *Scrumptious* property

[@jn0757]

The *Succulent* property

[@ivanlukas2475]

The *tangy* property

[@why3994]

The *delectable* property

[@ecchou3217]

Math teacher : A square has always 4 sides Numberphile : I’m about to end this man’s whole carrier

[@connorconnor2421]

Spelling teacher: I'm about to educate this man -'s whole career-

[@JonCombo]

There's always inside and outside too.

[@thomasfa18]

*sigh* a square is a two dimensional object. These figures shown have more dimensions

[@mestevesx]

@@thomasfa18 They are 2-dimensional, which means you can map them using only 2 coordinates (x,y) But they aren't a euclidian plane, which is what give them these properties.

[@anissakawther4986]

Actually it depends on what plane the shape is in . So the square does always have 4 sides but that is in euclidian (classical ) plane/space . For example depending on the curvature of the space the sum of the angles can be more (or less) than 180 degrees unlike a triangle in the euclidian space (the sum of it's angles is always 180 degrees).

[@theGouramistOnline]

this is literaly what i imagine of when i think of mad scientists.

[@omniviber2891]

He's a happy scientist

[@alwinwinter1645]

Mad with love for science!

[@ffuukkyootoobffuukkyootoob1411]

Yeah, He's mad. Met him at an SF convention back in the 90s, not all that long after The Cuckoo's Egg came out. Seemed like a nice guy. Seemed very monomaniacal (which fits in with the way the Cuckoo's Egg worked out) -- he got into a subject he'd get INTO that subject, and everything else fell away.

[@lionheart5068]

Crazy..of course with bending, curvature, angulation you can make unexpected shapes and figures. ..So what is new and funny here?..what did you discover? I don't get it.!

[@TheBengineer3712]

He knows that

[@olger05]

This gentleman looks like he's probably making a flux capacitor in his garage. Can't wait doc! :)

[@jakemiller9461]

Olger nah, he has hundreds of Klein bottles

[@flossenking]

Under his house

[@skylark.kraken]

With a robot which collects the bottles

[@blasttrash]

Whoa, this is heavy.

[@mr.cooldude6846]

I was gonna say that

[@markgearing]

Cliff must have been so easy to buy presents for as a kid. Mum: Merry Christmas darling. Cliff: A cube. Wheee. This is the happiest day of my life. Mum: It’s a box, honey. There’s something inside. Cliff: My cube is also a container! Wheeeeee. [Opens box. Sees soccer ball. Faints.]

[@Myrskylintu]

This made me laugh out loud

[@nuzayerov]

A sphere and a cube!! (ngl those are some awesome gifts imo, personally Id have the same reaction if someone buys me one of those periodic tables which have the elements inside them

[@Eic17H]

@@nuzayerov not just a sphere, a truncated icosahedron

[@scottwatrous]

Find someone as excited about your curves as this guy is for the abstract mathematical concept of negative curvature.

[@ehkbv]

My bf bc he cheated on me

[@livedandletdie]

Don't you mean Find someone as excited about your negative curves as this guy is for the abstract mathematical concept of negative curvature. Because if you're shaped like a Pseudosphere then man would the scientist be into you.

[@subh1]

what's so abstract about negative curvature?

[@Bryan-fl5ve]

Waists and cleavage are nice examples of negative curvature.

[@ogrxdy]

3:10 He’s so excited and it made me smile. I love this guy.

[@JustAWorms]

Easy Maths no me

[@supersharpshots]

Vertigo, Under dat.

[@Tommy20136]

Just A Worm nobody asked

[@martiddy]

Vertigo I know right?, I'd wish my math teachers were that enthusiastic in class.

[@Kapin05]

This dude's voice makes me so inexplicably happy

[@zucchi6195]

"The universe appears to have negative curvature" video ends right there wtf man

[@LeoStaley]

More recent studies have overturned that and it seems it really is more likely to have no curvature.

[@thanhngangproduction]

Came for the conclusion, left with more confusion.

[@MrParry1976]

For all those who didn't get his last line about space having a negative curvature... Gravity basically warps space, so the way the space is warped is a negative curvature... If u still didn't understand go and look up the image of gravity bending space on Google... The shape made by the bent space is basically the same shape that he made to draw a five sided square

[@georgelionon9050]

@@MrParry1976 He said the universe, not space in the vicinity of masses. And as we know it is wrong. At least the curvature of the universe if not flat is below our currently ability to measure the curvature if not being flat. Right now we only have an upper bound to 0.. which gets closer to 0 the better we measure.

[@MrParry1976]

@@georgelionon9050 Thanks for the info. I guess I confused the two 😅 But yeah I guess what you say makes sense since a warped universe would have many crazy effects lol

[@balthazarnaylor5874]

This man is so jolly it literally made my week

[@XanTheDragon]

I love math, don't get me wrong, I love my numbers. But DAMN. Cliff really loves math, and he's beyond anything I've seen. I'd be surprised to see someone who likes it more than him.

[@kookyflukes9749]

Hannah fry

[@oybekoyhonim]

Carl Friedrich Gauss

[@Tentin.Quarantino]

You should see him with a slide rule!

[@NarutoUzumaki-fz3sl]

I love math too

[@AndriyVasylenko]

2:16 for a moment I seriously thought it'd be the Klein's bottle again

[@OllorbidaComment]

Andriy Vasylenko you too ? :D

[@prajwalv5712]

Andriy Vasylenko man go play bass

[@AndriyVasylenko]

Prajwal V you nerd

[@traktortarik8224]

I kind of wish it was

[@boumbh]

Klein's bottle aren't far away (in the background ^^)

[@setblink6200]

"a sphere, not to be confused with a ball" I'ma google that real quick and be back, then you can show me your 3d witchcraft.

[@kwarqe]

tell us, what did you find?

[@kwarqe]

nvm, I googled it myself. A sphere is a surface, an empty object, and a ball is a volume, a solid object.

[@marcellomarianetti1770]

In maths usually the ball is actually only the inside, without the border, for example the points P = (x, y, z) that satisfy x² + y² + z² < 1 make a ball in R³

[@JdeBP]

At which point he holds up a flask that is neither sphere nor ball. (-:

[@sdm000]

*I'll attend every math lesson if my teacher is this amazing dude*

[@terminatortot4421]

So would I! This guy is the reason I actually like math lol

[@martinpast2187]

I would actually want to go to college idt this mans teaching xD

[@danielhawk5390]

I’m not sure I’d qualify

[@jassipapayucatan7278]

Same

[@harold121]

Sadly that's just a hollow dream. Most and most contents in ANY field are dull and prolonged even with entertaining teaching skills, and these fun things in the posted videos are just rare sweet sprinkles that keep the people going.

[@rovio6445]

I dont understand you but your enthusiasm is universal!

[@renjia3504]

Rovio 64 MK47 saitama

[@ZacabebOTG]

Cliff Stoll is so awesome. He's excited like a little kid, and that has me excited like a little kid. If I'd had maths and physics teachers like this, I'd have remembered so much more. 🙂

[@ajayghangas1090]

Yeah you would have remembered so much fake and false knowledge.

[@requiem6465]

@james lewis the wait continues for a response.

[@jjrulez1596]

@james lewis over 6 months, abd still nothing.

[@jadethejoker1029]

@@jjrulez1596 I'll @ him

[@jadethejoker1029]

@@ajayghangas1090 Are you going to explain yourself or nahh?

[@RenegadeScooter]

"5-Sided Square" Math teachers: Wait, that's illegal.

[@rleroygordon]

My problem with this claim is that a square is a quadrilateral, i.e. a four-sided figure. What he's describing is a pentagon (a five-sided figure).

[@Hurrican444_]

@@rleroygordon The claim is that it should be impossible to have a Pentagon with all the angles at 90 degrees when they ususually have 108 degrees. So in a 2d plain this would be impossible. There are multiple different ways you could describe a square, but one of them is that all the angles are 90⁰ and all the sides are the same which only applies to squares in the 2d plain. So you could make the point that these are squares when obviously they are not because they are 3d

[@BetaTestingUrGf]

We must also remember that the definitions of geomitry of shapes in 0 gausian curvature, doesn't all translate when you have a negative or positive gausian curvature. You could properly also make some funny looking boxes, if you were allowed to bend into some 4th spaceial dimention

[@bulba1561]

This man's excitement for this topic makes me happy.

[@av28379]

Me too

[@OrangeC7]

"Our universe seems to have something of negative curvature..." *video ends* _Biggest cliffhanger ever_

OrangeC7 A *cliff*hanger indeed.

[@NotaWalrus1]

I'll un-cliffhang it. It's not actually true. To the best of our measuring ability it seems to be flat, but there's obviously a margin of error so it may have slight curvature.

[@jubileeYAVEL]

NotaWalrus, Well I don't know about that

[@Kapin05]

This guy makes everything really exciting. This just proves that it ain't maths that bores kids, it's math teachers.

[@thegamer5367]

Kra Z Kapin Its a teachers job to make a student willing to learn if you act happy and exsited the students will reflect that in the fact that they are willing to show atension

[@andrewkim9090]

Kra Z Kapin I can't blame the teachers; most of them are trying their best to make things interesting. They're just confined by a uniform, uninteresting curriculum. In my opinion, common core is one of the most useless things created for education.

[@RanEncounter]

While I agree that some of the fault is in the math teachers corner, you cannot make an assumption that all of the fault is in the teachers corner. You would never teach the kids how to learn by themselves if you always needed an enthusiastic teacher around. It is a balance act and most kids do not want the same thing.

[@Kapin05]

I understand that. I'm just saying that teachers hold a somewhat large amount of the blame for bad education.

[@howardbaxter2514]

Agreed. I’ve had great teachers and horrible teachers. The great teachers have significantly helped me along the way and actually got me engaged on subjects that I either love, like math, or hate like English. The bad teachers have openly discouraged me from pursuing other subjects like chemistry (chem professor and chem teaching assistant in high school), and English (I’ve only had one amazing English teacher, and he was my Russian I/II teacher).

[@queenaunt4531]

It's so refreshing to see someone so exited about math/geometry/physics. I love this man's excitement!

[@Emilamlom]

"Our universe is something that has negative curvature." You can't just drop a bomb on us like that and end the video! What does that mean?

[@megasparklegoomba6807]

Tim K it means that math and science are fake and the earth is flat 😂

[@rainydeestar4806]

@@megasparklegoomba6807 Nah it means the earth is a negative globe

[@demenion3521]

it is actually in principle easy to measure. as for two-dimensional surfaces, you can use the sum of the angles of a triangle, you can use the solid angles of a tetraeder to determine if the space you life in is flat (no curvature) or has positive/negative curvature. the problem is just that the differences to no curvature in our universe are very minute and hard to measure with an actual tetraeder. but as far as i know, there is an experiment planned using satellites to probe exactly that

[@metanightmare1]

Omg yes bruh

[@Josephsamuelinniss]

I understand the theory to be, that if the universe was finite, it would have positive curvature, closed like a ball. If the universe is infinite then it would either be flat or have negative curvature. Like the opposite of closed, an anti sphere. We hypothesise from relativity, mass and energy bend space time, we also hypothesise that the universe is expanding (as we have observed). As the universe expands the density decreases, there is a critical point where the expansion of the universe and implied average density will flip curvature, in effect the universe will go from positive curvature (a finite ball) to negative curvature (and infinite exploded ball). This is all subject to the total mass energy in the universe which is unknown as we’re trapped in what we can observe. Maybe there is dark matter and the universe has enough energy to be constantly expanding (which is the theory alluded to with “the universe has negative curvature”) maybe the universe doesn’t in which case the universe probably has positive curvature (implying that there might be something outside of the universe). You could easily get lost thinking about it...

[@DrJohnZoidberg]

This is what happens when you have Charisma 10 *and* Intelligence 10

[@SuperNikio2]

+0 modifier in both :(

[@drano9862]

It should be CHA 20 and INT 20.

[@dusty6299]

and wisdom 10

[@mabus4910]

10 is the human average in D&D and Pathfinder

[@dusty6299]

@@mabus4910 who said we were talkimg abt dnd

[@MisterAppleEsq]

I'm going to start saying that things have “delicious properties”.

[@H457ur]

me too. As soon as I heard that I was going to comment but you got here first.

[@sethgrasse9082]

I've been doing that on my own for a long time. 🙂

[@astro2191]

I think he explained curvature using a slice of pizza once, so curvature is indeed delicious

[@ClickBeetleTV]

At first I thought you wrote "deciduous properties" which I am also going to start saying now

[@blinky_52]

MaxPeck lol i remember. It changed the way i eat pizza haha

[@Etobio]

I love how enthusiastic and excited this man is! He is truly passionate and it shows.

[@evynmclellan6755]

At 3:14 anonymous made the most inspirational quote. “Jfbdbdhdhdh” If I do say so myself, astonishing!

[@gonati3051]

**happ noises**

[@son9798]

@SpongeBob13579 I think not

[@skylardeslypere9909]

How did you get the sound so correctly tho

[@jackdog06]

“You know as well as I do” *explains something I’d never thought about before* Me: uh... yeah... I sure did know that...

[@rebelsouljaz]

he was speaking to the cameraman not you specifically

[@oivamickelsson3864]

rebelsouljaz brady's no cameraman

[@northbaseuk882]

*coughs* I knew this.

[@jackdog06]

Erik r/iamverysmart

[@legendgames128]

I knew about that

[@xSungamerx]

Cliff Stoll, the singular reason glass blowers make enough money to live.

[@SS-cc2cv]

The Sungamer that and bongs

[@dmaster254]

Don't forget NurdRage's tendency to destroy tons of borosilicate glassware trying to make metallic sodium and protect the glassware from the sodium hydroxide. And after months of experimenting, he finally did it!

[@JESSEverything]

If they ever make a new Back To The Future movie, I know who will star in it.

[@ijemand5672]

Who

[@whirrrl]

he looks exactly like doc it's incredible

[@SKYL1N3]

2018: 1=2 2019: a square with 5 sides 2020: *EARTH IS A CUBE*

[@Hasan...]

2021: F**k Cube Earthers!

[@maverick-n6x]

Hahah.. see

[@stulora3172]

2025: TV screens are spheres

[@dx8pi6o48]

Minecraft

[@CieMaKat]

Wait? Did I missed some "revelation" regardint 1=2? Have you made that up or there's some paper?

[@nono7105]

Teacher: How many sides does a square have? Me: Eh, 3 to 5.

[@moritzheinzel815]

no no probably 1 to infinity

[@Melkoh02]

@@moritzheinzel815 how would you have just one?

[@petrmatko6628]

@@moritzheinzel815 Were you even thinking while writing that?

[@darkienl5886]

@@petrmatko6628 nah, thinking is for rookies

[@petrmatko6628]

@@darkienl5886 I actually red that first time like: reading is for *cookies*

[@jchry3688]

I love this professor, he always hyped

[@MrB33keeper]

Same

[@cordlefhrichter1520]

Same, you love this professor, or same, you're always hyped!? Inquiring minds must know!!!

[@timseguine2]

I think he isn't a professor, actually.

[@MrB33keeper]

Liam McIrishman - same as in I love this guy's enthusiasm. But I love learning new things too.

[@macaroni9496]

Person: why do you need a 5-sided square? Him: *my goals are beyond your understanding*

[@OddWorlderer]

Make a 6-sisded square, just so I can see you smile more :)

[@enragedmoosemedia]

Deca-square. We have the technology...

[@MrRobert27k]

Try making it on a mobius torrid

[@tron7_]

cube

[@gappity]

@@tron7_ lol

[@xplodingmuffin3092]

A six sided square..... hmm

[@KB3TLR]

if this guy was my high school or college math teacher i would probably be a mathematician lol

[@missionpupa]

He teaches 8th graders university level physics. He doesnt have to teach children, but he understands the importance of doing it.

[@LincolnChamberlin]

I have a couple teachers this enthusiastic, unfortunately after usually bad teachers

[@jubileeYAVEL]

collegebandi, I know right? this just made me so happy, glad I can learn from people like him through the power of the internet.

[@ramanibai1426]

Next Pythagoras probably

[@flamingeddge782]

@@muskawazin2484 mathmatize

[@devangliya7131]

7:37 "It's trying to pop out of the bottom of the table" Cliff is amazing!

[@alexhinz5681]

“It’s trying to pop out the bottom on the table”

[@dennisolari9886]

When you’re on your computer doing nothing and you mom calls you down for pi 3:14

[@freezeburn1]

*p i*

[@Mr.Reality]

lol

[@derekpoland9374]

When your mom calls you down for a pizza pi

[@shadowbane7401]

Happy time

[@RandomMan-nv2qh]

GAUSS CURVITURE

[@tasosjw]

The title is very funny in Greek. Because "square" is translated "τετράγωνο" which means four corners.

[@XXLandorinXX]

same in Japanese. 四角 (pronounced shikaku) is Japanese for square. 四 means four and 角 means angle

[@danielcastillo591]

Can I make a five-sided four-sided?

[@benjaminnewlon7865]

Sooooo, its funny in all languages except english

[@Kajws]

They aren't all necessarily translations for the word square. As each of you have pointed out, each word in each language can be broken down into 2 parts: "four" and "angle/corner", so why is it that in English this does not happen? I believe the translations from each language into English would be more correct as "Quadrangle", "quadrilateral" or "Tetragon". Whilst the accepted definition for square is specifically four equal sides and corners, I've never liked it because it does tend to fall apart in more complex planar geometry. Equal sides and corners without a specific quantity would be how I would want it defined

[@CostcoComrade]

Do you believe in greek gods?

[@chillerup5709]

07:05 Trying to fit sleep, social life, studying and working into my program

[@simonwedel7905]

Genius

[@wheat8789]

True

[@aromorguy]

Why not do all of it at the same time?

[@sebastiendeseglise7571]

R/woshhhhhh

[@alive03330]

Sebastien Deseglise r/whoooosh*

[@Jacob-il3nu]

3:13 This guy gets so excited for math because he loves it so much

[@gameknight5051]

Little did I know the shape of squidwards clarinet was the most mind blowing thing I’d hear today

[@nebojsanikolic254]

Wait... 👀

[@elonmusk6205]

*Makes a 5 sided square* Wait, that's an illegal move

[@Neris-of-the-other]

From the moment he started to project 2D shapes, onto the 3D surface, he was out of Euclidean geometry and operated in non-Euclidean. So, it was a pretty legal move.

[@naverilllang]

Outstanding move

[@spin.chicken]

As far as my definition goes a square needs to have FOUR sides. . . I've never heard any definition that operates outside of that. Euclids work on geometry is something we should follow...otherwise I can say I made a 6 sided triangle, if I wanted...

[@remirousselet6867]

The definition of a square is "Has at least 3 corner of 90deg and each side have the same length". So this technically fits the definition.

[@anonofyesterday4650]

@@naverilllang It's an older meme, sir but it checks out.

[@thescoobymike]

So... the Bermuda triangle is really a square?

[@menjii4833]

well according to him if its 90° on each three side than it is but i think its just less than 180°

[@menjii4833]

wait i think its more than 180° not less sorry

[@sairentov]

No. It's too small for it to be curved along the earth surface.

[@nickgismo]

In reality: Probably not, since there isn't enough space between each point for the lines to curve (Meaning you would only see some small change in the angles but not enough to really make a difference) In theory: Yes. The earth as we now it, is not sphere (S^2 (unit sphere)). It is actually an oblate (Ellipsoid of revolution). And if i remember correct from my topology classes: "A Spheroid (General term for the shape) is a sphere where there have been some affine transformation (Geometrical way of saying that each point, line and plane on a space is preserved under some deforming)". So in theory it should hold, but that would not be true, because if you take a shape like the Bermuda triangle, then you will notice that the lines in between the points, aren't actually parallel to any longitude/latitude lines. And since they themself aren't longitude/latitude lines, they won't have a property of angle preserving (conformal) under any affine transformation. (Can't actually remember the topology term for angel preserving, so i use the word from Complex Analysis) So in conclussion: No. Hope this help EDIT: So the mapping that preserve angels is also called conformal. Took a peek in my book. And also what i meant to say in both parts was: "The angle between the lines in the bermuda shape would not have the same angles if you where to map it from the Spheroid into the sphere, since the map is not conformal, except if the lines where longitude/latitude lines, which it is not. And since our point have different longitude/latitude coordinates, that would make the angle, form such transformation, different and there the wouldn't have the same angle between the lines, and therefore not a square.

[@angrynpc5477]

It's not a perfect square , but if we grossly simplify, yes.

[@bryantherocker]

HE SHOULD BE OUR MATH PROFESSOR ..... I SEE PASSION IN HIS EYES

[@sudoscoobs1373]

478 flat earthers disliked this video

[@jesisdavila4063]

580

[@TheMilwaukeeProtocol]

Sudoscoobs Slam dunk

[@JasonV845]

616

[@valkrieg9660]

I Ruined your 444 likes

[@vrasch5354]

760

[@wyatta7442]

I love how excited he gets all throughout the video. I could only dream of being that excited about something

[@user84074]

MARTY! I was hanging a clock. I fell and hit my head. When I came to, I drew THIS! (3-sided square)

[@jmag579]

3:14 When I remember I have cookies n cream in the freezer.

[@lilaloweree5908]

You mean when you remember you have pie

[@mkalyan4289]

@@lilaloweree5908 pi*

[@mkalyan4289]

@@lilaloweree5908 the time stamp is 3.14 too

[@nuzayerov]

​@@mkalyan4289OMG THAT'S SO PERFECT

[@lawrencecalablaster568]

The Internet's goofy uncle returns :)

[@AndysTransformerCrisps]

Easy Maths that’s old

[@ankitb3954]

You can see the love and respect he has for the beauty that math exerts on this world

[@970357ers]

ANKIT BATCHALI math is not a force, just a language to describe phenomena.

[@melon4249]

“Ahghjhahj!!” I love this old man. He’s so happy all the time.

[@Kerminshermin]

Cutest moments: 1:57 2:13 3:13 5:40

[@david_ga8490]

Kawaii desu ne

[@sharqstep]

doing gods work eh

[@david_ga8490]

@Nicholas Natale nanitteruno?

[@david_ga8490]

@Nicholas Natale I don't get it

[@yuegodelg]

thank u

[@karthiksmanian]

When you love math to such extent you could say this 7:37 I can see this man's childishness and enthusiasm towards maths so much !! Lots of love!

[@jubileeYAVEL]

karthik sankar, I know XD I wish he was my uncle or grandpa or something:) but I mean it's true, it really IS trying to pop out the bottom of the table, that doesn't mean it has any ability to, but it is trying

[@yeln4tsmusic]

I WISH I had this guy as a calculus professor.

[@inanjarif1388]

Therapist: It's okay,five-sided square can't hurt you,he isn't real. Five-sided square:

[@soychivaspues6375]

Oh my, I Loved this man instantly. The passion and the love he dedicates to his findings. Barbaro(amazing)

[@richardsantalone9380]

"90 degrees, 90 degrees, 90 degrees, 90 degrees," people in the sahara counting their temperature

[@stulora3172]

oooor, people in the USA

[@dx8pi6o48]

Or USA depending on which system you’re using (the normal one or the one that doesn’t make sense)

[@CrittingOut]

@@dx8pi6o48 poor america stuck with the primitive imperial system

[@dx8pi6o48]

@@CrittingOut ikr

[@CrittingOut]

@@ohquicksey9545 They use imperial

[@johnchessant3012]

It should be mentioned that when you draw "lines" on the curved surfaces, they must be the shortest path (called the "geodesic") connecting the two endpoints on the surface (kind of like how the shortest path between two points on the earth is part of a great circle). When making these polygons, you can't just draw your lines and angles any which way, which makes the five-sided square even more awesome. Great video Mr. Stoll!

[@chrisg3030]

Isn't the longest path between two points also a geodesic if it's a length of string pulled tight, just going round the other way?

[@johnchessant3012]

Chris G Yes, I think so. This is definitely well-defined on spheres and similar shapes. On the Euclidean geometry, it'd only be defined by adding a "point at infinity", which is sometimes called the one-point compactification; then every "longest-geodesic" would pass through the point at infinity.

[@chrisg3030]

When a given distance on a Euclidean plane is measured off by pulling tight a given length of string from a fixed point and fixing it at the other end does it become the longest path?

[@johnchessant3012]

Chris G No, that would be the shortest path (a line). But, the longest path would be to go "the other way" on the line, out to infinity and "around" infinity, coming back on the other infinite part of the line. This isn't precise, of course, and the way to make it precise is to add the point "at infinity" to the Euclidean space. Then it's possible to show that infinity is no different than any other point, and all lines are "infinite circles", so you can define a "shortest geodesic" and a "longest geodesic". (The longest geodesic would always be infinite; just think of a Euclidean plane as an Earth with really, really big radius.) Hopefully this clarifies what I said above a bit.

[@abdulsamadansari222]

Why is everybody a nerd in here?

[@lucass430]

This guy's enthusiasm made this day a better one!

[@abel8787]

Start of the video: triangle with 90 degree angles End of the video: *out universe has negative curvature*

[@chasebh89]

"5 sided square made of 90* angles" *Middle School geometry teachers* "STOP, YOU'VE VIOLATED THE LAW"

[@johnnyparellax491]

Grandpa vsause with enthusiam

[@ep.]

Albert Einstein

[@pending-WW2000]

The embodiment of anti-depression

[@minijoe8059]

2:13, i thought he was going to explode or sth

[@quaso0000]

More like 3:13

[@Pigen_]

He is such a precious boi ;)

[@carsonlodder948]

And a wrong one because a polygon can’t have a curved edge

[@OrangeC7]

​@@carsonlodder948 It doesn't have a curved edge on the surface it's on, although it curves in 3 dimensions (mostly because the surface itself curves in 3 dimensions). The whole idea is that we are talking about 2 dimensional surfaces and the properties of those surfaces. I would recommend VSauce's "Which Way Is Down?" video for a method of determining truly curved and truly straight lines. Wait a second what are you even talking about no one mentioned polygons in this thread

[@lewisbotterill4948]

Honestly love this guy's energy and enthusiasm.

[@Deeema]

Whats next? 8 sided ball? Half Life 3?

[@minidreschi2]

nah... Half Life 3 is impossible

[@cctrollz5706]

Now we just need that 8 sided ball

[@35571113]

Actually, the 8 sided ball is easy. Just take a ball in the Manhattan metric in 4 dimensions... :P I'll show myself out.

[@tinydiccbandito4953]

@@minidreschi2 so you say, huh?

[@Tony_Goat]

We, we got uhhh, Half Life 3 now, soooo....

[@jochen4207]

This guy is having so much fun with squares and angles... It fits his look perfectly

[@spicemasterii6775]

Great video. Love your enthusiasm and passion sir. I have only come across ONE other person with similar passion and enthusiasm. But for some reason he was always going "1.21 gigawatts" and "88 miles per hour"

[@gabrielrockman]

I think he reminds me more of Vizzini from the Princes Bride. Especially in the scene where he "outsmarts" Wesley with the wine cups.

[@zacharytaylor190]

Cliff Stoll. Contagious enthusiasm for topology, astronomer, electronic musician mentored by Moog himself, not to mention discovering and aiding in the capture of a KGB Computer Hacker! Absolute legend.

[@hecko-yes]

So, a Parker square?

[@PhilBoswell]

I vote we call this a "Stoll Square" ^_^

[@Slithy]

Let's call it "Cliff Square (not to be confused with square cliff)".

[@TKNinja37]

A square that doesn't have 4 sides, but all angles 90°, and all sides equal. That's not a Parker square. It's still somehow perfect in its ways. I like "Stoll squares". Further, I like trisquare and pentasquare for those two.

[@leandrogulrt]

Cliff Square sounds better.

[@EchoHeo]

Parker pentagon

[@michaelmartindale3184]

His admiration and enthuse for this subject is infectious.

[@danielgagliardi727]

What a delicious property!

[@EpicFishStudio]

wanna hear more about hyperbolic MADNESS? you can have any number of sides with any angle you wish if you only stretch the object to be big enough. you can even extend the size count to infinity. and you can tessalate them as freely. in simplest of such cases you can perfectly evenly put pentagons side by side without any gaps, and from that you can go on for tessalating infinity number of infinity-sided objects. and then you can go on for more dimensions than two... huh. geometry is weird.

[@neoxus30]

Chew)

[@maythefool9904]

I live for the way this man gets excited about maths. It makes me excited too.

[@19TheChaosWarrior79]

Dammit Cliff is just a happy bloke. He should Klein bottle his enthusiasm and sell it 😁

[@falxonPSN]

But.... Then... How would I get it out of the bottle???

[@CGoody564]

Considering he makes them... I'd say it's as close to doing so as one could get

[@economixxxx]

Wait WHAT ??? UNIVERSE HAS NEGATIVE CURVATURE? WHY END THE VIDEO THERE?? WHERE'S PART 2 ????

[@__-cx6lg]

It's actually a famous open question in theoretical physics, if I remember correctly. Measurements indicate that it's approximately flat. Einstein showed that crazy curvature is allowed in our universe; it doesn't HAVE to be flat, as you might initially expect. What's more is that gravity, as you may know, causes weird spacetime curvature (though again, contrary to the video, the net curvature of empty space is approximately 0).

[@JaccovanSchaik]

Talk about a Cliff-hanger.

[@daksh8747]

There's an entire branch of mathematics called "Non-euclidean Geometry" about this!

[@NFITC1]

It's more of a wave than a sink-hole.

[@daksh8747]

NFITC1 It'd be best if the OC looked it up rather than learn the finer details from youtube comments

[@mikesteffen3378]

I love seeing all the complainers. He's intentionally being imprecise. This is an example of learning through paradox: present a set of assumptions, show how that can lead to an "invalid" result, and then...the viewer has to *think* (and learn!). Typically targeted at non-experts. Maybe the definition of square wasn't rigorous enough? Maybe his definition is rigorous, but only in 2D? Maybe there is a whole set of mathematics that can explain things further we can learn about? Maybe we just say "neat - math is cooler than I thought!"

[@zoz0boy]

Finally, someone with mind.

[@austen407]

How is he being imprecise? This is spherical geometry, not euclidean geometry. In spherical geometry, the definition of a square is a polygon with great arc curves of equal lengths and equal angle measures.

[@jonathandpg6115]

He's being imprecise overall by not getting into depth with all the differences and people are mad about it but this is what the channel is for. It's not for learning everything rather than sparking up interest for people who don't normally do as much math.

[@OMGclueless]

He's imprecise because he doesn't introduce all the things you would need to if you wanted to treat this rigorously like a mathematician. For example, what does "straight" mean on a sphere, or on his pseudo-sphere? What does "equal length" mean?

[@mike4ty4]

An alternative interpretation though is it shows how you can take a specific concept and then generalize it in reasonable, and yet surprising, ways, to contexts where it would not have applied before. Thereby showing you that you can be a bit less dogmatic or rigid about how it comes to understanding certain concepts, like that of the square, and how that then new possibilities open up you could not have imagined before, making you think in a way that _expands_ your mind and your imaginative horizon. (That's essentially "small to large" or "narrow to broad", whereas you are imagining "broad to narrow". Both ways of looking at it work, and are valid, depending on what you want to emphasize - precision or generality, stricture versus openness.) (And analyzing both perspectives, and both Euclidean and non-Euclidean geometries, one can actually prove that the existence of a square as defined by a Euclidean definition, four equal sides with four _right_ angles, is, for spaces of _constant_ curvature, equivalent to the statement that that curvature is zero, i.e. the space is Euclidean, or in terms Euclid would have recognized, that his fifth postulate holds.)

[@xenofeild983]

nothing makes me happier than to see a man go giddy over math. So pure

[@Shulkerkiste]

The last sentence was quite interesting :)

[@shrine115]

Completely agree, made me curious

[@TheBlablawww]

It is sad that the video ended at that point

[@airro3672]

isn’t it stated in the inflationary universe theory that the universe has a positive curvature??

[@CosmicCitiZenOfficial]

playing at x2 this professor looks a mad METH-matician :D ;)

[@sarthakshah1058]

x2 gang

[@-Jed]

METH-magician*

[@Sanglierification]

Where is marty mcfly???

[@LordShenanigan]

Even better at 1/2 speed. He becomes a Marijumatician.

[@drabberfrog]

5 sided square: Exists My Math Teacher: Impossible

[@theemeraldman6580]

The most wholesome mathematician I've seen in my life!

[@kcwidman]

We need a "Delicious property" T-shirt with a pi shaped cherry pie on it.

[@LedCROwbar2]

Fantastic video. Please make more videos with Cliff Stoll, I could listen to him for days.

[@LessThan3___]

Did he just throw in a btw the entire universe has negative curvature. monkaS

[@nebojsanikolic254]

Litteraly I thought the same, I don't know if that information is suposed to be well known(probably not) but it blew my mind 👀

[@PradeepKumar-tk5iv]

Looking from inside of a sphere, the inner surface has positive curvature! So according to Cliff we are not inside a spherical Universe.

[@JrgenHelland00]

Take a look at models of gravity wells if you want to get an idea of what he means with negative curvature. They kind of look like the trumpet shape he was drawing on.

[@Jamsaladd]

wtf monkaS

[@skepticmoderate5790]

@@PradeepKumar-tk5iv We're talking about curvature of a 3D 'surface' though. This has nothing to do with the spherical appearance of the edges of our universe.

[@VictorDiaz97]

Imagine if everyone had this man as their teacher. People wouldn't hate math so much.

[@DanielGallagherMusic]

0:16 "But wait, you know as well as I do..." No, sir... I do not.

[@enragedmoosemedia]

Had the same thoughts, dude. I'll catch myself watching this channel from time to time, and then realize I barely passed pre-algebra in school. 😂

[@K.D.Meyers]

Same

[@M3dicayne]

I do understand it and still have the problem of having an unsolved equation in my head... Laws of geometry seem to have been broken legally.

[@emerald_greeen]

He's so happy while explaining it. It makes me smile too. My heart is happy💖

[@SHASHANKRUSTAGII]

When you feel so much excited to explain some concepts. You are definitely the master. Respect for the man

[@altf4magic332]

I love how at 5:41 the camerman moves away from Cliff

[@kylemichaelledesma2766]

3 words. I LOVE THIS. I honestly dislike mathematics but this man has made me love it

[@raidedsalt7110]

this dude's enthusiasm for squares makes me enthusiastic for squares how the frick.

[@jahsjk4954]

Me: a square has 4 sides Numberphile: hold my beer Edit: Wow, I have NEVER reached 1000 likes for a comment. Thanks everyone I really appreciate it. Honestly, most my comments get one like, from me.😢

[@ligitadventurez]

Cool video but deceptive. A square is a four sided shape by definition, not just a shape with 90 degree angles

[@itrex2438]

@@ligitadventurez wrong, correct definition is a figure with four equal straight sides and four right angles

[@daemonskycloak6818]

antonio uta technically not wrong you just have the specific definition. You supported what was said.

[@calebplaysgamesofficial]

THATS WHAT I SAID

[@Mrhistory-nb5jb]

My life. 🤣🤣