Topology Riddles | Infinite Series

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Previous Episode
Building an Infinite Bridge
The Heart of Mathematics
Picture Hanging Article::
Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Made by Kornhaber Brown (
Find out why Topology is often called Rubber Sheet Geometry and try to solve these counter-intuitive topological puzzles.
Challenge Winners:
Alan Chang
Comments answered by Kelsey:
Louis JX

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  • This is awesome!

    Zeda ThomasZeda ThomasVor 26 Tage
  • miss you :'-(

    RamiroRamiroVor Monat
  • ADQRBOPqdgbapo

    Beacon BlasterBeacon BlasterVor Monat
  • First of all, you shouldn’t use nails, you should use staples; although they are the same if removed from the wall.

    David AsproudisDavid AsproudisVor 2 Monate
  • I spent a while at the beginning of the video. I paused the video as soon as I heard "if you were wearing really stretchy pants, could you remove them without lifting your feet." My answer is no, but let's see if I'm wrong lol. I was stuck for a while, but soon realized that the pants can be reduced to essentially a rectangle with two holes, where the two holes come from the two pant legs. The waist part can be expanded and flattened to the floor in the shape of a rectangle. The rectangular part isn't so important, but it is important to note that the pants are homeomorphic to something with two "holes". So from there, I envisioned standing with my left foot in one of the holes, and my right foot within the other hole - While the rest of the rectangular part lay around my feet, on the floor. From here, I guess you could lift the other hole up and over to the other foot, but from there, with the two holes stacked on top of one another, there is no way to remove it from both legs. And I think another thing worth mentioning is that, while the pants have two holes essentially, our entire figure (with out legs, hips and floor making a sort of triangle) has just one hole. The arms and torso, etc., do not contribute to any additional holes. Now if we take what we've learned from VSauce, we know that the body has a couple of "Through holes," such as the gastrointestinal tract. If we include this as a part of our solution space, MAYBE we can remove the pants! Let's see if I'm wrong! Edit: That wasn't even the right question. ;[

    Zach MosederZach MosederVor 3 Monate
  • 3:06 watch numberphile recent video

    Lincoln LiuLincoln LiuVor 3 Monate
  • You can turn a horshoe into a button! And vice versa!!! I solved a math problem good job brain! I want those pants!!!

    cassie martin-smithcassie martin-smithVor 3 Monate
  • I wouldn't mind stretching her donut

    Really HappeningsReally HappeningsVor 5 Monate
  • A pretzel and a bottomless cup with two handles.

    Iris AriolaIris AriolaVor 6 Monate
  • That question at the beginning is just how I greet people

    ZetapologyZetapologyVor 8 Monate
  • Mathematician pick-up line: "let your pants be topological"

    ImmortalcheeseImmortalcheeseVor 9 Monate
  • I really want those pants - they are amazing! Does anyone know where I could buy them? Don't know how to sow them myself unfortunately :D

    Max RosenthalerMax RosenthalerVor 10 Monate
  • @3:12 when you are inflating the main loop, where does its hole goes away????

    KhanabadosshiKhanabadosshiVor 11 Monate
  • i would try with anchors pants while she is wearing it...

    shubham modanwalshubham modanwalVor year
  • The fact that two shapes can be continuously deformed into each other implies that they are topologically equivalent, but the reverse is not true. Two topological spaces are said to be topologically equivalent if there is a continuous bijection between them whose inverse is continuous. For instance, all knots are topologically equivalent [to a circle]. It would be good to be precise in a channel about math.

    alonamalohalonamalohVor year
  • omg that fanart of Matt and Kelsey, tho lmaooooooooo

    Hugo GuzmanHugo GuzmanVor year
  • How is the nails problem related to loops

    Eduardo gilesEduardo gilesVor year
  • thats soooooo interesting 😍

    Nasir ShahNasir ShahVor year
  • pull your pants upward with enough pressure to rip the crotch/legs and then just take them off over your head. problem solved. will pbs be sending my topology phd via mail or do i need to print it out?

    lizardpeoplepoetrylizardpeoplepoetryVor year
  • pi no es la relación perímetro diámetro pues una circunferencia no es un polígono regular

    jhony angaritajhony angaritaVor year
  • Human being and dog are topologically same.

    MathstrokesMathstrokesVor year
  • Did anyone else come here looking for the logarithm reference???

    LavrineLavrineVor year
    • okay, i see it, heheh

      LavrineLavrineVor year
  • Another possible alternative, this time for the pants: 1. Pull pants down to ankles. Lol 2. Flip waist of pants downward, starting to flip the inside out. 3. Pull ends of pants up through the inside of seat of pants, extending the pant legs upward and inside out. They are upside down, but still inside out.

    Ryan BuchtaRyan BuchtaVor year
  • Alternative(?) For the figure 8: You could also 1. Shrink the arm between the rings until the rings appear to be still linked to each other, but now merged together still where they were joined. 2. Then, similar to the second move in the video, do a similar rotation of one of the rings, out of the other ring. 3. Finally, turn one ring until you get a figure eight.

    Ryan BuchtaRyan BuchtaVor year
  • For the first time, today I noticed that the picture hanging from two nails depicts Kelsey herself and Matt from SpaceTime!

    IlTrojoIlTrojoVor year
  • Humans are multi holed tori We are donuts yall

    PYXELPYXELVor year
  • Why would anyone want to hang a picture using two nails so that if either breaks the picture falls? Half the point of using two nails is so that if one fails there'll still be something holding the picture on the wall until it can be fixed.

    GgdivhjkjlGgdivhjkjlVor year
  • best book for topology

    Zeeshan Nawaz BalochZeeshan Nawaz BalochVor year
  • Ok, if cutting and gluing aren't allowed, what happens if you fold? *creases* *POOF!* Watch out, that was a sharp bend.

    Julian GouletteJulian GouletteVor year
  • Frequency merge gives topology. To remember topology know the frequency numbers. More than three is beyond scope of universe.

    Venkatesh babuVenkatesh babuVor year
  • Love u dear...

    Anayatullah NaikAnayatullah NaikVor year
  • a snake and a knotted snake are the same.

    Shiny MimikyuShiny MimikyuVor year
  • Loved everythining about your video except one picture ; ) one question: Why a circle is not topologically same as figure 8? i can squish a circle from center to make figure 8. Is genus here plays a part?

    Syed TirmiziSyed TirmiziVor year
  • Two shapes that are topologicaly equivalent? A human digestive system. A donut.

    András FogarasiAndrás FogarasiVor year
    • You read my mind, seriously.

      RVMJRVMJVor year
  • Anatomically correct human into a three holed doughnut (with air bubbles inside it, if you want to include things like blood vessels)

    beirirangubeiriranguVor year
  • Thank you very much to you and youtube.

    Saroj PandeyaSaroj PandeyaVor year
  • Pfft, Mr Bean has you beat. He changed out his underwear for swim trunks without taking off his pants.

    saeklinsaeklinVor year
  • Great session. Im terrible at all arithmetic disciplines,but I enjoy watching. Love the pants. Quite flattering. The colours well matched the form. I'll keep watching until I start to understand.

    Douglas WilliamsDouglas WilliamsVor year
  • what about n knots that turn into connected donuts......🤔🤔🤔🤔

    arrq1arrq1Vor year
  • I remember a pictorial essay in Esquire mag about prisoners figuring out a way to take their pants off while wearing ankle shackles. They did pick up their feet!

    Eliot BrownEliot BrownVor year
  • Serious question here, are males genus 2 and females genus 3?

    pa ptpa ptVor year
  • You kids and your topology

    Chilling OtakusChilling OtakusVor 2 years
  • The pants puzzle is easier than it sounds like. Just try it.

    Emperor Pingu's math channelEmperor Pingu's math channelVor 2 years
  • Hi! I loved this video. Back in the day, I couch surfed in the home of a UC Berkeley mathematician at the time when Grisha Perelman announced his proof of the Poincare Conjecture. It was all "yeah, we'll see" at the time. What ever became of it? I remember a hastily called meeting at the Uni.

    Grady BroylesGrady BroylesVor 2 years
  • A bit late, just saw your 11 May 2017 episode. Here are two 4D (or perhaps 11D?) topological shapes with unknown topological complexity which I am pretty certain are topologically equivalent, at least on a coarse grain scale. 1. The entire universe right now. 2. The entire universe ... just now. "Sketch Proof": Use the laws of physics time cobordism to deform one into the other, assuming a scale at which smoothness assumptions of general relativity apply and that no new Black Hole singularity was created in the intervening seconds.

    Bijou SmithBijou SmithVor 2 years
  • why did the topologist break their teeth? confused their coffee cup for a donut

    JessJessVor 2 years
  • This happens with my pants every time I try to take them off when I'm drunk😂😂😂

    Zachary AlbrightZachary AlbrightVor 2 years
  • but u destroyed the big hole! 3:09

    xo famxo famVor 2 years
  • 1:13:28 محاضرة العالم المصرى الكبير الاستاذ محمد النشائى بامريكا The Universe as a Golden Supercomputer Scorpion300100 2.4K views 5 months ago 2:48 Umov vs Einstein AlternativApproach 238 views 2 years ago 2:47 Physicist Stephen Hawking has died CNN 1.4M views 23 hours ago 5:28 Mohamed El Naschie at home in Surrey elnaschie 1.9K views 7 years ago 14:01 STEPHEN HAWKING | Before They Were GONE | BIOGRAPHY Michael McCrudden 46K views 3 hours ago 54:32 حوار مع العالم المصري د/ محمد النشائي ومسيرته العلمية على قناة النيل للأخبار بتاريخ 12-09-2016 Scorpion300100 193 views 1 year ago

    Mohamed . S. El NaschieMohamed . S. El NaschieVor 2 years
  • 12:47 "And they're being attacked by Pokemon". Thank you, Kelsey.

    Weretyu7777Weretyu7777Vor 2 years
  • Mathew O Dowd

    Delta kitchen.....Delta kitchen.....Vor 2 years
  • Instructions unclear. Took a bite out of a mug.

    Andy BriceAndy BriceVor 2 years
  • Topology zero is equal

    Kenichi MoriKenichi MoriVor 2 years
  • I figured I could just drop my pants, and then pull both legs up through the waist until they're inside out. You never said I had to be wearing the pants. Only that they had to end up inside out, and I couldn't move my feet.

    DanDanVor 2 years
  • 3:15 Is that not considered patching up a hole and therefore forbidden?

    Kom'rk OrdoKom'rk OrdoVor 2 years
  • take the pants off turn them inside out and then put them back on

    gabe juhaszgabe juhaszVor 2 years
  • What if I *don't* send anything to the challenge? Will I still win.? What about imaginary solutions?

    Tofara MoyoTofara MoyoVor 2 years
  • Is it ok if we thought of a different method for deforming the shapes?

    ReeveeReeveeVor 2 years
  • Does anyone else feel like they cheated with the figure 8? I mean they say no glueing/filling then glue/fill to make the figure 8.

    Matt ColinMatt ColinVor 2 years
  • Ive only watched about 2 videos of yours and i am addicted to this!

    RockBump ProductionsRockBump ProductionsVor 2 years
  • Could you imagine a topological donut in real life? It'd be the ultimate fidget toy.

    Albert NaveAlbert NaveVor 2 years
  • I wish she can read this message. I just wanted to say that I like the fact that she is super cute. Where were you when I was in my pure math courses?

    Mario ZMario ZVor 2 years
  • Topology is my new favorite math subject.

    Playlist KingPlaylist KingVor 2 years
  • wearing pants inside out!!! WOW ! interesting. I am actually a fashion designer. hahahha inspired by your video.

    TianTianVor 2 years
  • 3:07 fastest way: unentangle the two loops and contract the tube

    Bee Pin LimBee Pin LimVor 2 years
  • thanks to pbs and her for the extremely good videos. 5:37 thats herself in the pic ? :)

    aritra mukherjeearitra mukherjeeVor 2 years
  • 1:00 and 3:13 you said you cant tunt a donut into a sphere so.....

    גיל בלטנרגיל בלטנרVor 2 years
  • the auto play on DE-visions[for this channel videos only] always go to previous episode rather going to next episode please help.

  • I thought of legs, and the earth, being homeomorphic to a ring. Then I thought of pants, being homeomorphic to an underwear shape, with the "ring" "wearing" the underwear. push the ring up through the underwear rendering the underwear inside out

    John ReddickJohn ReddickVor 2 years
  • you are so pretty. thanks for this video

    Rock BalancerRock BalancerVor 2 years
Topology Riddles | Infinite Series