Dip the edges in ink, roll it. What shape does it make? Can you mathematically describe it? I want to know this.
@mohammedyassin80643 жыл бұрын
I feel that going to be an interesting thing
@yingo40983 жыл бұрын
@@mohammedyassin8064 it's gonna be a line segment
@carlosandleon3 жыл бұрын
two parallel wavy lines with sharp crests
@Daspletophysis3 жыл бұрын
Since the contact points occur along at most a semicircular portion of each disc, I imagine the trace of where these points contact the table would approximate 2 cycloids that are perfectly out of phase with each other.
@Ziphoroc2 жыл бұрын
It would make lines. Duh
@DavidRichfield9 жыл бұрын
The center of mass of a rolling square doesn't go in a zigzag; it goes in a series of circle arcs.
@ianwubby62719 жыл бұрын
+David Richfield I'd imagine the zig-zag was just easier to animate.
@ARP2wefightforyou7 жыл бұрын
David Richfield Vsauce made a video about this.
@ky-gp4sz7 жыл бұрын
David Richfield if you look closely you can tell it moves a lot more than the lines
@kaina54677 жыл бұрын
Looking for this
@Pulpaldabadies6 жыл бұрын
Indeed. A rolling Parker square makes a zig-zag :)
@TheBigBigBlues10 жыл бұрын
"Ah a new numberphile video, great!" *Watches Video* *Spends £30 on book and maths gear* "Cheers Brady, Beans again for me tonight."
@numberphile10 жыл бұрын
TheBigBigBlues money well spent and nothing wrong with beans!!!! have steak on the weekend, but next week you can support us on Patreon and have beans again! :)
@Number-cz1rd10 жыл бұрын
Numberphile For convenience he could perhaps offer a premium package that includes both a signed book and a supply of beans.
@PeterBarnes27 жыл бұрын
+Number 5 But it's the beans they used to teach you about counting at school.
@Triantalex Жыл бұрын
??
@TheNefari10 жыл бұрын
Now for a little artistic experiment take these discs and put them into paint or ink and then roll them on white paper the line you will see is quite amazing :D
@boaz25784 жыл бұрын
Tell me, what will I see?
@Beesman8810 жыл бұрын
Instead of Pi or Tau we should make a compromise. Pau = 1.5 Pi
@epajarjestys99817 жыл бұрын
It's a Ti(e).
@munjee26 жыл бұрын
Wau
@frechjo5 жыл бұрын
From the perspective pi, 1.5pi is 50% away, from the perspective of tau, it's only 25% away. To be fair, it should be 1+1/3pi or 2/3tau.
@jacobr77295 жыл бұрын
That was an 0ld XKCD joke...
@GeodesicBruh5 жыл бұрын
Fuci
@electroislove5 жыл бұрын
Matt has this subtle sense of humour, which is lovely You rock man!
@jodyze54138 жыл бұрын
''let's remove this mess of root 2 here'' *proceeds to add more root 2*
@ob3vious4 жыл бұрын
In maths we add to subtract
@h-Films4 жыл бұрын
no he has an abomination of root 2 not a mess =D
@salmachi98368 жыл бұрын
I love this mathematician , so lovely and smiley guy .
@bruinflight10 жыл бұрын
Thanks Brady, Matt and everybody else on the Numberphile team for the great videos! You all rock and... as this video shows, roll!
@miikeV339 жыл бұрын
"45° is π/2..I mean you could say, 'That is τ/4', but you'd be an idiot." Oh, the irony.
@blackmephistopheles22736 жыл бұрын
Nah, it wasn't irony...it was Matt using his big brass ones!
@mydemon4 жыл бұрын
Truly amazing. Only way it could've been better if he said "tau/8"
@pedroivog.s.68704 жыл бұрын
Actually 45° is π/4
@kutsen393 жыл бұрын
For those that don't get it, tau is 2π
@dielaughing733 жыл бұрын
I think he was talking about Parker Pi
@hpekristiansen10 жыл бұрын
You nicely prove that the center of mass is at the same height in these two positions. -but you forget to prove, that the center of mass does not oscillate up and down in between.
@numberphile10 жыл бұрын
hpekristiansen hi, there is a second video coming to Numberphile2 where Matt touches on this, although a proof is not show. It is proven.
@naequs10 жыл бұрын
Numberphile ha, homework ! i'm gonna try to prove that myself before the next video comes out :D
@Yldron10 жыл бұрын
1:06 That square's center of mass does not move like this!
@Epikification10 жыл бұрын
Yeah, it moves in arcs, right?
@anothermoth10 жыл бұрын
Epikification and the thing that makes it roll really badly is not the up and down motion of the centre of mass, but the sharp corners it turns at the bottom of it's path where it must instantaneously change direction from rotating around one corner to rotating around the next.
@UMosNyu10 жыл бұрын
Epikification Circles around the corner that is to the ground.
@Epikification10 жыл бұрын
Yeah, that's what I was thinking, but I wasn't certain enough to comment. A college make a square wheeled vehicle and a track composed of semi-circles to demonstrate it at some point.
@JamesCoyle9510 жыл бұрын
anothermoth What you just described is the center of mass having to move up instantaneously when it gets to the edge. It doesn't roll well because you need to add a force to lift the center of mass up over the corner.
@classyname4210 жыл бұрын
Please feature Matt parker more often. He's the funniest man on earth.
@numberphile10 жыл бұрын
jediknightonearth we'll try
@AdrenalineL1fe10 жыл бұрын
Numberphile also James Grime
@Triantalex Жыл бұрын
false.
@AceTheBraveIT10 жыл бұрын
5:02 - 45° = pi/2 ??? WAT??? Great video though!
@Fogmeister10 жыл бұрын
LOL! I thought exactly the same thing! :D
@nonoymanoynoy10 жыл бұрын
He even dissed Tau. haha
@MegaJORB10 жыл бұрын
He's talking in radians where pi=90 degrees
@Fogmeister10 жыл бұрын
MegaJORB Good point... except Pi = 180degrees. 45degrees = Pi/4
@StephandaSilva10 жыл бұрын
MegaJORB except that pi is usually 180 degrees.
@davidsweeney11110 жыл бұрын
I suspect this guy is a mathematician.
@christianchristian34678 жыл бұрын
Did this with two circular place mats before in a pub, just stumbled upon it by accident, loved it and no no clear answer why, until now!
@axelrosalewski10 жыл бұрын
I love how all the phds and professors on numberphile are so happy when solving those problems! It really gives me the fun on maths back :)
@HYEOL10 жыл бұрын
that's why you use τ in the first place :D made my day.
@burpie32588 жыл бұрын
"But then you'd be an idiot."
@Scerttle8 жыл бұрын
burpie Shots fired.
@burpie32588 жыл бұрын
EssThree Indeed.
@robknightfilms7 жыл бұрын
Yup. Especially because that's tau/8 (or pi/4).
@trickytreyperfected14827 жыл бұрын
Which immeadiately backfires since he said "Pi on 2" when it should be "Pi on 4"
@isavenewspapers88904 ай бұрын
To be fair, one would indeed be an idiot for confusing a 45-degree angle with a right angle. He was not, on technicality, wrong.
@Will140f10 жыл бұрын
Hurray! New numberphile! Double hurray!! Featuring Matt Parker!!
@KingLarbear2 жыл бұрын
I never really put together that that is why circles rolled I thought it was because they're round but this makes sense too
@frasernicol886810 жыл бұрын
Love this guy. He's brilliant
@mikecannon379510 жыл бұрын
Thanks for the video, Brady and all Numberphile educators!
@GoldenSax9 жыл бұрын
Did... did we just reinvent the wheel? O.o
@MarksAwesomeness9 жыл бұрын
Golden Sax Perfect.
@dispatch13479 жыл бұрын
Golden Sax Going to be a lot harder to attach an axle to that centre of mass.
@AlucardNoir10 жыл бұрын
Messy physical reality, what a typical mathematician thing to say.
@ricardojbatista10 жыл бұрын
Great video, as always. Just bought a signed copy of Matt's book.
@DOSTalks10 жыл бұрын
I love this guy! more matt on numberphile!
@karl13105810 жыл бұрын
Nice video :) Another tiny mistake: in the animation showing the rolling square, the path aof the center of mass should be a series of circular arcs (because the center is rotating around the corner of the square which is on the ground) instead of a series of straight lines (1:03 - 1:10)
@krisinox88810 жыл бұрын
Parker is one of my favourite people on numberphile
@pad9201110 жыл бұрын
Great video, I was about to complain about the lack of an annotation but then remembered what Brady always says: "Nobody ever checks the notes." so I did.
@DesmondAltairEzio10 жыл бұрын
i paused the video to solve for myself but i used sine instead even though his way was probably easier, and he was right- i got the same answer. i love how math always works itself out like that.
@DaveScottAggie8 жыл бұрын
I look forward to receiving my signed copy.
@MrTurkmenistan100010 жыл бұрын
I didn't know I needed this in my life until now!
@SebBrosig8 жыл бұрын
You showed that 2 positions of the slotted-circle-assembly's rolling path have equal height of COG. That doesn't prove that it _will_ roll freely inasmuch as it's necessary not sufficient criterion. intermediat angles could be higher/lower, no? However it's enough to calculate the slot depth.. and physically playing with the toy shows it must be true! Mathematicians get a woozy stomach at this point but can work out the proof for arbitrary angles, while the rest of us just get on and play with the toy for a bit.
@ravenlord410 жыл бұрын
Loved the anti-tau jab! It's icing on the cake of another sweet video :D
@fsakdhfksajhf10 жыл бұрын
A zig zag line is used to show the change of center-of-mass of the rolling square. The CoM would actually describe circular arcs with a center at the corner touching the surface.
@michaellikeaboss9 жыл бұрын
I just made one of these from 11 gauge stainless steel and they work great!
@mancheaseskrelpher84199 жыл бұрын
Oh Matt, no matter how much you think pi is better than tau, the truth shall always be that tau > pi.
@you_tube6189 жыл бұрын
You win
@DaddyKafkaesque10 жыл бұрын
I think it's hilarious that he disses on Tau after falling prey to the dumb Pi conversions. Congrats, this is why we people who like Tau advocate for it.
@soupisfornoobs40813 жыл бұрын
It's called misspeaking, everyone does that. Do you really think 360/8 is less hassle than 180/4? For a mathematician? Doing live unscripted commentary?
@ZardoDhieldor10 жыл бұрын
"You could say it's tau on four, but then you'd be an idiot" Of course you would. It's obviously tau over _eight_. :D
@uforob56013 жыл бұрын
and pi/4
@1GoodRiddance10 жыл бұрын
That's mesmerizing.
@zxwy378 жыл бұрын
In his attempt to diss Tau, Matt managed to illsutrate exactly why Tau is better than Pi :-P
@TheOneTrueIgnus8 жыл бұрын
That diss was a classic Parker Square
@austinglugla5 жыл бұрын
@@TheOneTrueIgnus Parker Circle in this case
@shambosaha97274 жыл бұрын
A Parker pi
@vangildermichael17678 жыл бұрын
so cool. Such an absolutely awesome idea, about yoking up two circles together at a right angle. And yet have them roll. And after i am so amazed with the whole idea, then you come and dissect the maths about how it is all possible. So I don't have to. thankx
@andvil0110 жыл бұрын
I called the cut c. The large triangle hypotenuse is 3r-2c. The small triangle hypotenuse is 2r-d. That gives (3r-2c)/r=(2r-c)/(r/sqr2). With a little algebra we have c=(1-sqr2/2)r=0,2929r. A little faster way.
@GEM4sta10 жыл бұрын
Obvious mistake in the video. Many people wrong in the comments as well. Theoretically, if we only consider gravity and a force applied to the... we'll call it a "wheel", the square would roll just as efficiently as the circle. Yes, potential energy is gained when it rises on it's tip. However, potential energy is lost when it's center of mass goes back down. The kinetic energy will oscillate between two numbers, like the little graph you saw in the video. You could simplify the problem by approximating it to a straight line. Friction takes away energy, otherwise energy is usually constant.
@freshrockpapa-e77997 жыл бұрын
And more energy is taken when you move the center of mass.
@lukedig1110 жыл бұрын
45 degrees is equal to pi/4 , not pi/2 as mentioned (so it is also equal to tau/8). Who's the idiot now eh Matt? :P
@numberphile10 жыл бұрын
***** I'm not sure Matt will not reply because he's already outside sticking forks in his eyes.
@anticorncob610 жыл бұрын
Numberphile I hope that's because he realized he screwed up and not because people are "overreacting to his joke" or whatever.
@kovanovsky22336 жыл бұрын
OOF
@CsharpPreza10 жыл бұрын
I understand it can happen once in a while that someone says something wrong but calling someone an idiot for using tau seems way too inappropriate to me.
@kingsizedmidget72949 жыл бұрын
Well than you seem pretty thin skinned, and need to learn how to take a joke. If you watch this channel at all you'd know the ongoing tau vs pie debate and find gat remark quite humorous.
@soupisfornoobs40813 жыл бұрын
True,
@seanehle832310 жыл бұрын
A square will roll perfectly well, without slipping - provided the surface it rolls along is curved appropriately. In the case of a square, the surface would be scalloped with repeating cycloids. How's that for a topic? "Square wheels could be real." I bet most of your viewers would find this fascinating.
@williamrutherford5536 жыл бұрын
Didn't they cover this in the shapes of constant width video? Also, by mathematical definition, a wheel cannot be square, because a square is not a shape of constant width. If you want to say that there's a possible surface on which a square could roll, fine, but that doesn't make it a wheel. A wheel is an object that can roll on a flat surface.
@JktuUekmw6 жыл бұрын
Matt: I have some circles today. Me: *shivers with anticipation*
@zozzy46308 жыл бұрын
5:07 "You could also say that it's tau on four, but then you'd be an idiot." Quite right, Matt, considering 45 degrees is an eighth of a circle, so it's obviously tau over eight.
@williamrutherford5536 жыл бұрын
Right, because that's the most important part of the identity of Pi, is whether it's simple to convert from degrees to radians.
@robertdarcy62105 жыл бұрын
@@williamrutherford553 indeed, since pi is defined in terms of diameter,and radians are defined in terms of the radius
@Leibowitz10 жыл бұрын
This is fabulous, might have to try this with my math class..
@JonJeffels9 жыл бұрын
***** elegantly describes maths in ways we can understand. Thank you! Also, thank you for my signed copy of your book :))
@benkao82534 жыл бұрын
When squares roll, I think about whether a side of a square simultaneously touches the ground after each flip, or whether the edge touches from base all the way up to the next tip not instantly
@belgaer49432 жыл бұрын
this
@TeamDragofied6 жыл бұрын
Parker draws a lopsided circle in a video about wobbly circles that came out on 8 September, 2014. The Parker Circle video came out on 18 September, 2017. This predicted the Parker Square addition known as the Parker Circle.
@njw704 жыл бұрын
One day I will understand these equations
@inothernews10 жыл бұрын
Matt hasn't let go of Pi vs Tau, great vid haha :)
@xDMrGarrison7 жыл бұрын
Does anyone else find it really adorable the way this little contraption wobbles ahead? xD
@kasuha10 жыл бұрын
Center of rolling square moves along circular sections, not straight lines. Every time its corner is on the ground, the center follows a circle around that point until another corner touches the ground.
@Roman_CK2 ай бұрын
Kind of tempted to give this one a try. 🤔
@daddymuggle Жыл бұрын
'Wobbly circles'. I was expecting cute Parker circles of some sort. The interlocked discs wobbling along were even cuter than that! Who ever said that maths wasn't fun?
@il2xbox10 жыл бұрын
once again our hero sqrt(2) saves the day
@hersirirminsul4 жыл бұрын
Note to animator: 1:03. The centre of mass of a rolling square would trace a scallop form not a zig zag.
@iCrAz33luVmuSiC10 жыл бұрын
You should have clips of these brass circles on the next Hello Internet podcast on KZbin. They're mesmerizing! 😁
@Formulka10 жыл бұрын
he should be called Math Parker :)
@fakjbf10 жыл бұрын
The irony of calling t/4 idiotic when he wasn't even right.............
@jasing888810 жыл бұрын
Nice video :)
@saichaitanyakudapa95544 жыл бұрын
2-√2 = √2(1-√2)... So u can simply cancel 1-√2 on both sides and u are done!!!...
@hssh86986 жыл бұрын
11:02 the centre of mass may not move up and down but still it moves sideways as you can see which does take a lot of kinetic energy out of the forward movement
@praisethyjeebus7 жыл бұрын
I love what happens if you click on the link for the signed copy now.
@LucidEnigma2110 жыл бұрын
I like the calm theme. :]
@Garbaz10 жыл бұрын
Going to buy the bonus edition of the book, hope it ships fast to germany ^^
@LittleBoilover10 жыл бұрын
I suspect I'd be playing with this for HOURS
@kyledoyle986410 жыл бұрын
Great video guys 😁
@RazvanGabor10 жыл бұрын
how can you say it was a great video if the video was uploaded 4 minutes ago and it has 11 minutes.You didn't even watched the video omg!!!WHAT A LIAR!!SHAME
@kyledoyle986410 жыл бұрын
Razvan Gabor I agree I've placed a large amount of faith in my Australian brothers, but I doubt I'll be disappointed
@markzero82913 жыл бұрын
Here's a comment that's 6 years late: 1:02 those should be circular arcs centered on the lower corner of the square, with half the square's diagonal as their radii! But other than that minor detail, great video!
@Ariel-ps8je7 жыл бұрын
wibbly wobbly- circle wircles... Matt Parker has always reminded me of the 11th Doctor when he's doing his stand up
@nsajko19 жыл бұрын
At 8:30 a sqrt(2) just has to be factored out of the right parentheses, instead of all the nonsense. It's easier to notice that if you look at the numbers inside of parens as powers of 2.
@chhayapatel40983 жыл бұрын
Very nice Thank you
@lucasmontec10 жыл бұрын
Tau > PI and you MUST agree with this.
@ericcartmansh9 жыл бұрын
His sketching skills are very impressive in addition to his equation solving skills :D
@mattvw928710 жыл бұрын
At 11:03 you see LuLu Numberphile? Wow that office is cluttered, and where's the shredder? all for our leader CGP Grey
@lucarnauddunoyer505810 жыл бұрын
Awesome work! I like it every time more, please keep going :-).
@JohnDobyns10 жыл бұрын
Very cool!
@AnkhArcRod10 жыл бұрын
There was no proof offered for why the height of center of mass must stay the same in all rotations. We solved the situation for 2 specific configurations and showed that the height of center of mass remained unchanged for the two configurations shown. The really cool part was, in fact, the proof that this stays unchanged regardless of the configuration of rotation. Incidentally, for any randomly chosen flat shape, there will always be at least two configurations for which the center of mass is at the same height (proof lies in the continuity of path of center of mass and that center of mass must return to the same value after 360 degree rotation).
@jony77798 жыл бұрын
The statement "you could say its tau on 4 but then you would be an idiot" is even more hilarious caus its wrong haha
@_helium_7 жыл бұрын
4:13 he says "Two times the radius" Someone must not be a fan of defining their circle constant by the diameter🤔
@MEZNAY7 жыл бұрын
Parker circles
@No-10 жыл бұрын
Omondi Akura He multiplied both sides by sqrt(2), not 2 * sqrt(2). Sqrt(2)^2 = 2, so sqrt(2) * sqrt(2)(r + d/2) = 2(r + d/2) = 2r + d. He just shortcut through some of the repetitive steps.
@TimVerweij10 жыл бұрын
I'm pretty sure that at 1:03, when the square is 'rolling', the red line segments should be curved.
@pasunurusaivineeth37395 жыл бұрын
0:33 PARKER CIRCLE, Thanks for stopping by!
@andrijadragovic74708 жыл бұрын
1:46 I love it when mathematicians try to describe the imperfect world of physics
@Pengochan8 жыл бұрын
(sqrt(2)-2)/(1-sqrt(2))=sqrt(2) obviously since sqrt(2)-2=sqrt(2)*(1-sqrt(2)) . The interesting part is where you explain why the two disks center of gravity stays at that height in all other positions too, why did i miss that? For now you only showed it's the same height every 45°. :)
@breathless7927 жыл бұрын
at 5:32 (approx) he mentioned pandigital numbers, but had already showed one at 3:31 : 8326197504 is a pandigital number using all 10 digits and it wasn't pointed out
@EviIDuck10 жыл бұрын
...45 degrees is Pi/4 not Pi/2
@KeZkinOG10 жыл бұрын
AMAZING
@007bistromath10 жыл бұрын
τ>π Not even the most diehard pi fanatic can argue this.
@letsgetsomeshoes123910 жыл бұрын
x
@007bistromath10 жыл бұрын
letsgetsomeshoes1239 ...That's adorable. Leaving aside that Prof. Parker clearly started it, WOOOOOOOOSH
@RQLexi10 жыл бұрын
letsgetsomeshoes1239 Tau vs pi is an ongoing (harmless) discussion on this channel, partially because of the practical aspect of it, partially because of the humorous aspect of treating the matter far more seriously than necessary. In this video, Matt quite clearly referred to it for reasons of humour, knowing full well that a lot of the viewers are familiar with the debate and where he stands in the matter. I choose to believe that 007bistromath 's comment tried to reply in kind ("pi fanatic" being a clear hint). What I have more trouble justifying is your reference to toxicity, comparison to the LoL community and the use of "shitheads". Are you sure you aren't overreacting a bit? Or am I missing a joke here?
@007bistromath10 жыл бұрын
John Smith +letsgetsomeshoes1239 is probably swept up in the zeitgeist of current events in gaming. It's a good thing I wasn't saying anything mean to vihart. They'd probably be calling me a misogynist, too. :V ...Huh. Can't get the markup to work.
@QuadfishTym10 жыл бұрын
letsgetsomeshoes1239 While I don't blame you for missing such a shamelessly geeky joke like that, there's no 'toxicity' here except what you're bringing with your own comment.
@Toastwig10 жыл бұрын
1:52 jaw drop....why was that so amazing??
@U014B4 жыл бұрын
*_ˈæk_*_ ˌtʃu ə li,_ it's about halfway between ¼ and ⅓, so it's really (¼+⅓)/2, which is 7/24.
@glenthemann10 жыл бұрын
Numberphile It would be cool to extend this to calculate the ideal curvature along the edge of the discs. As the discs grow thicker the rolling would become inhibited, necessitating the need for curved edges. What sort of curve would give a perfect rolling action? I wonder. I'm going to work this out ;)
@eltyo34010 жыл бұрын
Gotta love Matt's sarcasm xD
@raidedsalt71106 жыл бұрын
"You could say that it's tau on four, but then you'd be an idiot." We got the best person to explain everything.