Drawing an Egg (with a Pentagon) - Numberphile

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  • @numberphile
    @numberphile  2 роки тому +223

    Don't miss the "egg-stra footage" over on Numberphile2 - ua-cam.com/video/tjyFw1BX4eM/v-deo.html

    • @chispun2
      @chispun2 2 роки тому +1

      Is that egg differentiable?

    • @SuviTuuliAllan
      @SuviTuuliAllan 2 роки тому +3

      I personally never get tired of egg puns. An eggcellent video. 👏🏻👏🏻👏🏻

    • @madscientist3544
      @madscientist3544 2 роки тому +1

      @@chispun2 Yes, twice. But not three times

    • @Tsai-Chieh-Huang12345
      @Tsai-Chieh-Huang12345 2 роки тому

      * wow ... *

  • @kanishkachakraborty
    @kanishkachakraborty 2 роки тому +424

    "Penta GONE, but it's here." 🤣

  • @6099x
    @6099x 2 роки тому +620

    Ah, Johnny Ball is such a wonderfully well-spoken host, pleasure to watch, thank you

    • @SlartiMarvinbartfast
      @SlartiMarvinbartfast 2 роки тому +9

      Agreed, always a pleasure to see Johnny. He deserves his own TV programme or UA-cam channel.

    • @rmsgrey
      @rmsgrey 2 роки тому +8

      @@SlartiMarvinbartfast He had his own TV show(s), appearing in at least one series of about 6 episodes pretty much every year from 1978 to 1994.

    • @johnrutherford2545
      @johnrutherford2545 2 роки тому +2

      What a lovely gent.

    • @ArawnOfAnnwn
      @ArawnOfAnnwn 2 роки тому +1

      @@rmsgrey What was it called?

    • @rmsgrey
      @rmsgrey 2 роки тому +6

      @@ArawnOfAnnwn One was called "Think of a Number". There were other titles... "Think Again", "Think It... Do It" "Johnny Ball Reveals All" and probably others.

  • @matildabryant8398
    @matildabryant8398 2 роки тому +267

    I worked with with laying hens for thirty years and I can tell you that the shell is placed on the egg in the uterus. It comes out hard unless the hen is very young or very old or is not getting enough calcium in their diet.

    • @graemep804
      @graemep804 2 роки тому +12

      If the egg comes out with a soft shell you can gently press your finger in the shell and leave an imprint of your fingerprint in it as it hardens.

    • @christosvoskresye
      @christosvoskresye 2 роки тому

      @@PeppoMusic Ever squeezed a bone right after it came out of the hen?

    • @DrBrangar
      @DrBrangar 2 роки тому +34

      @@PeppoMusic Okay, I want you to tell me how on earth the calcium carbonate crystals that make up the shell form in the half second between the egg leaving the chicken and hitting the ground? Eggs don't have flat spots, so it can't take any longer than that. When we make it ourselves, we bubble CO2 through calcium hydroxide, but that path isn't remotely viable because there isn't enough CO2 in the air, and calcium hydroxide is not great for most living things.

    • @Eddievargas1
      @Eddievargas1 2 роки тому

      @moi2833 I don’t think 30 years old is an old gator

    • @matildabryant8398
      @matildabryant8398 2 роки тому +43

      @Rapid Reckoner Nexus It is hard to let something that wrong stand when you spend your working life in education.

  • @ultimate0levels
    @ultimate0levels 2 роки тому +19

    I'm pretty sure the egg shell hardens inside the uterus, not when coming in contact with air...

  • @drskelebone
    @drskelebone 2 роки тому +1

    Has he been on before? I feel like I'd remember this calm soothing voice. In any case, please bring him back as much as he (and you) can allow.

  • @July-gj1st
    @July-gj1st 2 роки тому +3

    The Pythagorean Cult: HOW CAN IT NOT BE MAGICAL IF YOU CAN DRAW AN EGG WITH IT?!

  • @jimmykitty
    @jimmykitty 2 роки тому +8

    *Pentagons are the bestagons!*
    *I’d love to see this inside of the Pentagon.* ❤

    • @Pain-dr3hw
      @Pain-dr3hw 2 роки тому +3

      clearly you haven't watched CGP Grey's video about hexagons. They are the actual bestagons.

    • @jimmykitty
      @jimmykitty 2 роки тому

      @@Pain-dr3hw Hi

  • @IndyCotton
    @IndyCotton 2 роки тому

    Johnny Ball.. my childhood hero !!

  • @praveenb9048
    @praveenb9048 2 роки тому

    Just an hour ago, I found that a pigeon had laid an egg in the balcony. And now UA-cam comes up with this.

  • @stevefrandsen7897
    @stevefrandsen7897 2 роки тому

    Eggs are warm when they come out too. We fed our chickens broken seashells and baked egg shells for protein for the next shells. I love Johhny's books. Not too technical.

  • @jenschristiantvilum
    @jenschristiantvilum 2 роки тому

    Please make more videos with this gentleman and let him speak uninterruptedly. He has a perfect narrating voice.

  • @Veptis
    @Veptis 2 роки тому

    The golden ratio facts where never apparent to me. But it makes it Soo much more interesting

  • @jim40135
    @jim40135 2 роки тому

    The only thing that could make my day better than a new Johnny Ball video is finding out we both have the same type of year planner.

  • @jddes
    @jddes 2 роки тому +4

    Amazing, the math and the explanation. Johnny Ball really should do narration or asmr. His voice the perfect "wise man explaining" voice

  • @cabalistik
    @cabalistik 2 роки тому +1

    Great, now I'm hungry!

  • @EastBurningRed
    @EastBurningRed 2 роки тому

    Perfect for Easter

  • @recurvestickerdragon
    @recurvestickerdragon 2 роки тому

    Julia Drawfee LePetit: "Finally! Now I'll show them a true egg."

  • @angelodc1652
    @angelodc1652 2 роки тому

    I do the same, but the centers of the circles that form the sides of the thin end are on the endpoints of the lower semicircle
    By step by step
    1) Draw a perpendicular bisector crossing point O
    2) Draw a circle crossing the horizontal line at points A and B, and the vertical line at point C
    3) Construct and extend lines AC and BC
    4) Draw two with centers A and B both with radius AB, lines AC and BC at points D and E
    4) Draw the top of the egg by drawing an arc with center C and radius CD or CE

  • @marsulgumapu2010
    @marsulgumapu2010 2 роки тому

    A work of art

  • @octivia
    @octivia 2 роки тому

    Oh look, it's Johnny Ball drawing pentagrams and discussing the elasticity of a hen's egghole. Feels just like getting back from school again. :)

  • @laura1825
    @laura1825 2 роки тому

    That’s the easter spirit I like!

  • @frankharr9466
    @frankharr9466 2 роки тому

    Ahhhh! Pentigons are very important. There's a book size that has a pentagon at its heart.

  • @tekuaniaakab2050
    @tekuaniaakab2050 2 роки тому +1

    I didn’t think the image of how an egg gets pushed out of the chicken’s...um hole, was what i needed in my mind today. But alas...

    • @WanJae42
      @WanJae42 2 роки тому +1

      Imagine how it feels for the chicken! 🤣

  • @cedalege
    @cedalege 2 роки тому

    Nice watch!

  • @valtolhurst
    @valtolhurst 2 роки тому

    Johnny Ball! What a legend! Love this video!

  • @colinfew6570
    @colinfew6570 2 роки тому

    Math ASMR is amazing

  • @kevinelliott50
    @kevinelliott50 2 роки тому

    Matt Parker should review this in relation to a formula for an ellipse. : )

  • @elevown
    @elevown 2 роки тому +2

    Yes, but how would you go about drawing a perfect pentagon lol? If I did it freehand it would be WAY off.

  • @Evija3000
    @Evija3000 2 роки тому +2

    Lovely video

  • @tyleringram7883
    @tyleringram7883 2 роки тому

    Thats beautiful

  • @makessenseright
    @makessenseright 2 роки тому

    Almost fell asleep (in a good way) and then the camera guy woke me up :D

  • @karstenmeinders4844
    @karstenmeinders4844 2 роки тому

    Circumference and area? Happy Easter!

  • @bananafish3149
    @bananafish3149 2 роки тому

    This is ASMR gold

  • @thechristies3521
    @thechristies3521 2 роки тому

    John von Neumann famously said With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

  • @neutralface
    @neutralface 2 роки тому

    This made me feel good and smile hard! Cheers!😀

  • @williamcollins4049
    @williamcollins4049 2 роки тому

    As always clear as a bell.

  • @oafkad
    @oafkad 2 роки тому

    Wow. He is charming.

  • @hurktang
    @hurktang 2 роки тому +1

    This is an attempt to initiate us to witch craft !

  • @skyscraperfan
    @skyscraperfan 2 роки тому

    Is that really the exact egg shape or just an approximation? Usually if you connect two circle segments, the second derivative is not defined at the meeting point. That's why streets for example will never have a jump in curvature in a single point, but instead use a Bézier curve, which allows you to rotate the steering wheel smoothly instead of having to move it abrubtly in one point where the second derivative suddenly jumps.

    • @RFC-3514
      @RFC-3514 2 роки тому

      It's just an approximation, and only to chicken eggs, specifically. Basically, it's a construction to connect 4 separate arcs.

  • @rexlex7784
    @rexlex7784 2 роки тому +2

    EGGelent

  • @bobbob-vt3bw
    @bobbob-vt3bw 2 роки тому +2

    nice

  • @joebykaeby
    @joebykaeby 2 роки тому +1

    Egg-o-phile

  • @Rubrickety
    @Rubrickety 2 роки тому +12

    Beautifully explained for a lay audience. 😉

  • @archivist17
    @archivist17 2 роки тому

    This is great fun!

  • @khalilprince4527
    @khalilprince4527 2 роки тому

    You're a fantastic Human being...
    May Allah bless you 🤲

  • @skhan8244
    @skhan8244 2 роки тому +1

    Yeah. Eggs.

  • @MarioDiNicola
    @MarioDiNicola 2 роки тому

    Draw a perfect egg:
    Step 1: draw a perfect pentagon...

  • @AnalyticalReckoner
    @AnalyticalReckoner 2 роки тому +2

    Is that equation the shape of an egg in three dimensions?

  • @Edwin_Gan
    @Edwin_Gan 2 роки тому

    My 2-steps way to draw an egg:
    1. Draw a circle
    2. Draw the details.

  • @TheGodQuac
    @TheGodQuac 2 роки тому +1

    Why are you doing this?

  • @General12th
    @General12th 2 роки тому +1

    I just had a weird thought. If this video had been part of a children's educational program back during the '80s, especially in the US, would there be fundamentalist parents up in arms about seeing pentagrams on live TV? Or was the Satanic Panic overblown and that wouldn't have actually happened?

    • @SlartiMarvinbartfast
      @SlartiMarvinbartfast 2 роки тому +1

      I'm sure there would be a few deluded Karens making a fuss, as usual.

  • @jellymunoz8555
    @jellymunoz8555 2 роки тому

    how do i do a pentagon

  • @chrisg3030
    @chrisg3030 2 роки тому

    Beautiful. The pentagon (as opposed to pentagram) is already kind of eggy shaped with its pointy top and flat bottom. I've been experimenting with the shape you get on drawing successive circle radii each at a golden angle to the previous. At 5 you get 5 points on the circle, which don't form a regular pentagon however, but with 3 long and 2 short sides. As an egg It looks as if the pointy end got squashed closer to the flat end when emerging from the chicken. The long and short sides seem to be in the golden ratio to each other, on measurement anyway.

  • @CasualGraph
    @CasualGraph 2 роки тому

    egg

  • @beethovensg
    @beethovensg 2 роки тому

    Geometry is the basis of nature Grandpa. You aren't even aware of the magnitude of your deep understanding.
    G-D is number.

  • @MCLegoboy
    @MCLegoboy 2 роки тому

    Balderdash! No way the egg is soft as it's being laid! Clearly there's a goblin inside the chicken with a Straight Edge, Compass, Writing Utensil, and Calipers that makes sure each egg is perfectly shaped before it's finally laid. And if it doesn't match, the goblin eats the egg. Symbiotic relationships man, that's what's really going on.

  • @az362951847
    @az362951847 2 роки тому

    Golden egg

  • @Assassin_Droid
    @Assassin_Droid 2 роки тому +1

    What is this paper?

    • @Fummy007
      @Fummy007 2 роки тому

      Brown paper shows up better on camera.

  • @MichaelBerthelsen
    @MichaelBerthelsen 2 роки тому

    Despite all I have just seen, I'm left with one overwelming question...:
    WHAT'S A POULTRY ENGINEER?! AND WHY?!😂

  • @leandrogulrt
    @leandrogulrt 2 роки тому +160

    This episode was especially emotional for me. When I was just a child, my grandfather told me he knew how to draw an egg using a ruler and compass. Unfortunately I never asked him how this could be done, but that question never left my mind.
    My grandpa would have a birthday this month if he were alive. In a way, I feel good about imagining that maybe this was the solution, and that I no longer need to carry with me the anguish of never having asked what the method was.

  • @Smaug_le_dore
    @Smaug_le_dore 2 роки тому

    egg

  • @arranmcgown2386
    @arranmcgown2386 2 роки тому +355

    Such a relaxing voice, and a clear passion. Loved the video!

  • @stm31415
    @stm31415 2 роки тому +10

    This is biologically nonsense -- healthy chickens lay hard eggs -- but even mathematically, eggs are continuous curvature surfaces -- not made piecewise. What was this supposed to be?

    • @Volodimar
      @Volodimar 2 роки тому

      I think, it supposed to be a joke 🙂

    • @BlueEyesWhiteTeddy
      @BlueEyesWhiteTeddy 2 роки тому

      Although i dont believe him on the biology the curve he drew seems to be continuous as i understand the word.

    • @stm31415
      @stm31415 2 роки тому +2

      @@BlueEyesWhiteTeddy “continuous” and “continuous curvature” are different. Each place the circles touch, the *curvature* changes instantaneously, even though the points line up. Like a round rect vs a squircle, the drawing changes suddenly where the egg does so gradually.

  • @TomRocksMaths
    @TomRocksMaths 2 роки тому +115

    Met the legend Johnny Ball when I was a kid - I have no memory of it but I do wonder whether he’s the reason I now do what I do…

    • @deadbzeus
      @deadbzeus 2 роки тому +10

      @Euler Bhaisab He rocks maths

    • @ridinkulous2867
      @ridinkulous2867 2 роки тому +3

      @Euler Bhaisab He has appeared multiple times on the channel already, most recently with "ducks"

    • @m2QgCJb6tAnG11m8
      @m2QgCJb6tAnG11m8 2 роки тому +2

      @Euler Bhaisab meth

    • @Triantalex
      @Triantalex 8 місяців тому

      ??

  • @blenderfox
    @blenderfox 2 роки тому +127

    I immediately got taken back to my childhood listening to Johnny. He still has those mannerisms that made him such a memorable host back in the day.

  • @alainpbat3903
    @alainpbat3903 2 роки тому +30

    This is like math ASMR. I love this so much, with the wonderful soothing storytelling voice and the slow drawing of something mathematically complex. I love it.

    • @sujimtangerines
      @sujimtangerines 2 роки тому +2

      Came to the comments looking for an ASMR related comparison

    • @markiyanhapyak349
      @markiyanhapyak349 2 роки тому

      There's NO such thing like those four capitalized letters in the universe (, I assume)! *WHY* to use them‽‽

    • @markiyanhapyak349
      @markiyanhapyak349 2 роки тому +1

      “@@jaade9485”, *WHAT...‽*

  • @5thearth
    @5thearth 2 роки тому +64

    The shape of a bird's egg is evolutionarily influenced by how precariously the species' nests are built. A sphere is the topologically ideal shape for an egg, but it can also easily roll away. An egg shape rolls in a circle, and the "pointier" it is, the smaller the circle.
    Accordingly, birds that nest on the ground tend to have eggs that are close to spheres, while cliff-dwelling seabirds have extremely pointed eggs that reduce the odds of them rolling off the ledge and plummeting to their doom.

    • @bsharpmajorscale
      @bsharpmajorscale 2 роки тому +12

      The plummeting to their doom happens later when they get kicked out for their first flying lesson. :'D

    • @NotKyleChicago
      @NotKyleChicago 2 роки тому

      Was there a Numberphile that discussed this? I feel like I saw a video that discussed this before.

    • @iank2615
      @iank2615 2 роки тому +2

      Pointy eggs are less likely to roll down slopes too, and the blunt end, where the chick develops, stays cleaner than the pointy end. It seems to be a combination of all three things.

    • @finndriver1063
      @finndriver1063 2 роки тому +4

      This isn't true, but it's a common myth. Egg shape correlates with the ability to fly. In general, the 'better' a bird species is at flying, the pointier it's eggs are. This is thought to be a side-effect of evolving a more streamlined body.
      Penguins are the only obvious exception, as they don't fly but most species lay pointed eggs. They do need to be streamlined to swim, however.

    • @alouped
      @alouped 2 роки тому +11

      @@finndriver1063 "Egg shape correlates with the ability to fly" seems to be the factor in both explanations. Both body shape and tendency to have nests over ground will correlate with a birds ability to fly. But we can't know for sure what exactly was the evolutionary cause, maybe something else entirely.

  • @DrBrangar
    @DrBrangar 2 роки тому +42

    That bit about eggs being soft before the air gets at them is just flat false.

    • @DrBrangar
      @DrBrangar 2 роки тому +13

      @Nacho Rodríguez No, it is an urban myth. In fact, the shell being made is roughly equivalent to someone's water breaking, it is kinda the final signal to go lay. Further evidence is the fact when you dissolve the shell, the membrane that remains is still egg shaped, because the shape gets set internally. If it was naturally spherical (and somehow coated in some wild, rapid precursor to calcium carbonate that somehow works before the egg can travel the 2 cm to the ground, since eggs don't have flat spots) the shell would be holding it in tension that would be removed, returning the egg to a ball.

  • @ajmt13
    @ajmt13 2 роки тому +5

    IMO This should’ve been posted on April Fools Day 😅🤣

  • @murk1e
    @murk1e 2 роки тому +27

    I have so much affection for Johnny Ball. If the man doesn’t have a knighthood, he really should be on the next list.

    • @shugaroony
      @shugaroony 2 роки тому

      He's gave more to the country than half of these entitled eejits who get them.

  • @nulle8935
    @nulle8935 2 роки тому +2

    Only young chickens who are laying their first eggs will have a soft shell. Those chickens must've not have been getting enough calcium

  • @bitequation314
    @bitequation314 2 роки тому +63

    We NEED to persuade Johnny to set up an ASMR channel.

    • @nomadicrain
      @nomadicrain 2 роки тому

      Agreed…listening to him talk about eggs gave me all the tingles. Lol so relaxing to listen too.

    • @qzbnyv
      @qzbnyv 2 роки тому +2

      Imagine if a permanently running Johnny Ball streaming channel could be set up like it has been for Bob Ross.
      It would be amazing for future generations to have that at their fingertips.
      And if I ever become a parent, I imagine I’d leave it on a screen running in the nursery hopping he would rub off on my kids.

  • @OLBICHL
    @OLBICHL 2 роки тому +34

    meanwhile in the demon world, everyone is freaking out while the egg demon laughs at them hysterically with tears running down his cheeks, he mocked them with: "HA... you all didn't believe that I would ever be summoned, but look... after waiting for what felt like an eternity, because my summon ritual is very particular, I am finally called to the realm of the human beings... my time has finally come HAHAHA!!!"

    • @shruggzdastr8-facedclown
      @shruggzdastr8-facedclown 2 роки тому +2

      ...all thanks to his human summoner, Johnny Ball, for opening the portal between worlds not meant to be linked!!

  • @billr3053
    @billr3053 2 роки тому +8

    Thanks for including those honking formulas. I have yet to read that paper. I was going to comment that I highly doubt the true egg shape is a series of perfect circular arcs. Perhaps that shortcut is good enough to approximate it to a visual satisfaction.

    • @BurnabyAlex
      @BurnabyAlex 2 роки тому +3

      I agree, if you pause at 4:39 you will be able to notice the curves are close but not an exact match. We have the technology to 3d laser scan thousands of real eggs to compare them to mathematical models. I also doubt that a physical object will have 1 radius of curvature, and then hit a line where it has half the curvature projected around a rotated axis followed by a spherical endcap.

  • @youmaybebusy
    @youmaybebusy 2 роки тому +40

    "What was first: the chicken or the egg?"
    "Well, Satan of course."

    • @thomashauer6804
      @thomashauer6804 2 роки тому

      Phanes Protogonus hatched from the cosmic egg through the serpent..created by chronos. According Orphic Mythology at least, Then Prometheus became the Demiurge
      but yea its the same "fallen angel" arc
      .probably remixed from hindu and sumerian myhtology

    • @SgtSupaman
      @SgtSupaman 2 роки тому

      The pentagram was actually a holy symbol. The inverted pentagram is the satanic symbol, as it is a corruption of something holy.

  •  2 роки тому +13

    It's always a joy seeing a new video with Prof. Johnny Ball.

  • @Sirenhound
    @Sirenhound 2 роки тому +5

    Are we summoning something?

  • @WhosBean
    @WhosBean 2 роки тому +3

    If you told me a week ago that today I'd be watching a Numberphile video which discussed chicken vaginas, I wouldn't have believed you.

    • @fraenzchen85
      @fraenzchen85 2 роки тому

      It's not a vagina, hens and cocks got basically the same organ, one hole for everything, a cloaka.

    • @georgeprout42
      @georgeprout42 2 роки тому +1

      Cloaca. It's the original USB port.

  • @NatePrawdzik
    @NatePrawdzik 2 роки тому +5

    The Pentagon: "What, am I a yolk to you?"

  • @thenerdyouknowabout
    @thenerdyouknowabout 2 роки тому +5

    Braidy - "Presumably the hole in the chicken isnt that big"
    Tell me you're a mathematician without telling me you're a mathematician...

  • @jorgerowe8095
    @jorgerowe8095 2 роки тому +2

    Oh no, eggs don’t come out soft. He sounded too serious…

  • @geraldsnodd
    @geraldsnodd 2 роки тому +19

    "Yes , you can draw an egg with a pentagon "
    ~ Prof Johnny Ball

  • @varun_vidya
    @varun_vidya 2 роки тому +5

    He is like the David Attenborough of Geometry

  • @albertocattaneo4627
    @albertocattaneo4627 2 роки тому +2

    Only Johnny Ball can talk about something coming out of a bird's arse and make it sound fancy

  • @simonsaville9962
    @simonsaville9962 2 роки тому +4

    I was waiting for Johnny to ask us to "Think of a number"!
    He started in many of us a passion for mathematics.
    If you want more children to take up STEM subjects you need more Balls, as in Johnny Balls.
    Alas, I think he's unique, a one-of.
    Thank you JB!

  • @chrisweddle2577
    @chrisweddle2577 2 роки тому +3

    A hen is an egg's way of making another egg.

  • @jall3ri
    @jall3ri 2 роки тому +2

    Eggs from a Pentagram...could see a Conspiracy theory video out of this LOL

  • @danielstephenson7558
    @danielstephenson7558 2 роки тому +4

    Absolutely love that Numberphile has Johnny Ball on it now. Shaped my childhood, that man.
    More Johnny please!

  • @TommiHimberg
    @TommiHimberg 2 роки тому +1

    So for egg shape we have the geometric approximation presented here and the set of egguations presented in the linked paper. Gotcha. The question is now, which bird lays the most Pythagorean eggs?

  • @KekusMagnus
    @KekusMagnus 2 роки тому +1

    thats great, but it doesn't prove that the derivatives are continuous at the seams which would be the minimal requirement for it to be an egg

  • @camerongray7767
    @camerongray7767 2 роки тому +1

    This guy sounds like the David Attenborough of maths

  • @Schnabeltassentier
    @Schnabeltassentier 2 роки тому +5

    Johnny Ball is a lovely presenter, thank you for this episode!

  • @endlesswick
    @endlesswick 2 роки тому +1

    Peacewise. The first derivatives match at the intersections. A beautiful symmetry.

  • @John-mw3jf
    @John-mw3jf 2 роки тому +1

    To my eye the egg shape is very approximate. Seems like real eggs have more curvature from midline to the "pointy" end.

  • @zemariagp
    @zemariagp 2 роки тому +3

    “And I love them both both” - a life well lived

  • @eruhinmakhtar9162
    @eruhinmakhtar9162 2 роки тому +1

    Next do how to summon Satan with a pentagram please

  • @TristanMorrow
    @TristanMorrow 2 роки тому +1

    🥚 it must be Easter weekend in the UK timezones already to catch @Numberphile dropping this *Eggshell-Lent* geometric construction! 🥚

  • @xxMrPHDxx
    @xxMrPHDxx 2 роки тому +1

    Her: He must be thinking about other girl 😔
    Him: _I wonder if I could draw egg with pentagon using geometry_

  • @cosimobaldi03
    @cosimobaldi03 2 роки тому +1

    Eh