A New Discovery about Dodecahedrons - Numberphile

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Featuring Jayadev Athreya on a new discovery about platonic solids, in particular dodecahedra... Extra footage: • Yellow Brick Road and ...
Yellow Brick Road Sticker and T-Shirts: teespring.com/yellow-brick-nu...
More links & stuff in full description below ↓↓↓
PAPER: A Trajectory from a Vertex to Itself on the Dodecahedron: arxiv.org/abs/1802.00811
PAPER: Platonic solids and high genus covers of lattice surfaces: arxiv.org/abs/1811.04131
More great resources on the project: userhome.brooklyn.cuny.edu/aul...
More on Numberphile...
Platonic Solids: • 5 Platonic Solids - Nu...
Platonics is higher dimensions: • Perfect Shapes in High...
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
Learn more about MSRI in this interview David Eisenbud: • A Proof in the Drawer ...
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outr...
And support from Math For America - www.mathforamerica.org/
NUMBERPHILE
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Videos by Brady Haran
Animation by Pete McPartlan
Patreon: / numberphile
Numberphile T-Shirts: teespring.com/stores/numberphile
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9

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13 янв 2020

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Комментарии : 2,4 тыс.

@numberphile 4 года назад

Extra animations: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-hpNPPqm1EMc.html Yellow Brick Road Sticker and T-Shirts: teespring.com/yellow-brick-numberphile More resources on the project: userhome.brooklyn.cuny.edu/aulicino/dodecahedron/

@whatisthis2809 4 года назад

How was your day?

@jamesmuldoon1427 4 года назад

G'day

@kasajizo8963 4 года назад

Yo Numberphile what happened to James Grime

@anastasiaklyuch2746 4 года назад

How LONG did it take to make those animations? You really did a great job!

@ZeroOskul 4 года назад

A triangular hexacontahedron is also a regular solid.

@rif6876 4 года назад

Out on a 1st date. "So what do you do?" "I solved a 2000 year old problem on how to avoid your neighbors. Mathematically. My tattoo will explain it."

@uganasilverhand 4 года назад

Of course, there goes any non-mathematician date.

@jetison333 4 года назад

Oh man if my date did that, I would be in love.

@Ceelvain 4 года назад

@@uganasilverhand Many women would love a guy passionated about his field and able to explain it well.

@uganasilverhand 4 года назад

@@Ceelvain the wife's always asking me to stop talking about math, computers, and science

@rif6876 4 года назад

Didn't asteroids have a hyperspace button that transported you to a random spot? Sounds a lot like punching through a facet, traveling inside the solid, and punching out to the surface again.

@qlqnen 4 года назад

Jayadev: "Pac-Man might be a reference from too long ago." Brady: "Asteroids!"

@moth.monster 4 года назад

To be fair, Pac-Man is still a cultural icon. Most kids probably know about it still.

@korenn9381 4 года назад

@@moth.monsterYeah they do, there's a relatively new animation series about pac man.

@jacobdial2448 4 года назад

My mind did go to the half a press video

@chickeyy1792 4 года назад

@@korenn9381 Pixels?

@Joiner113 4 года назад

@@korenn9381 there is?? Why

@staglomagnifico5711 4 года назад

"One of the central tensions in the Little Prince, other than the loss of childhood innocence, ..." I love how he just glosses over that

@aaronwalterryse4281 2 года назад

Well... he has to stay on topic

@littlestonesadventures3939 Год назад

Because that is not important

@phodder 4 года назад

12:20 Was anyone else expecting him to turn around and lift his shirt to expose a back piece of 120 pentagons?

@matthuckabey007 4 года назад

@jocelynnielsen9154 4 года назад

@@matthuckabey007 but we did hope a little

@madkirk7431 4 года назад

·...·

@OrangeC7 2 года назад

I wasn't, but now I feel like I should have

@shaunlastname391 2 года назад

It's the reason I watched, had a feeling

@macnolds4145 4 года назад

The featured mathematician is a uniquely elegant and fluid communicator. Also, the animations were tremendously illustrative and enjoyable. Loved it.

@alveolate 4 года назад

including the animated Hannah Fry jogging?

@stuiesmb 4 года назад

macnolds you could tell how well he understood this subject by how he could break it down into discrete parts and explain each aspect simply. Very charismatic and obviously very intelligent guy. A real treat to watch

@sleepytimekoolaid 4 года назад

@@alveolate *especially* the Hannah Fry jogging.

@kemp10 4 года назад

Did you squint really hard when the jogger was on screen?

@NoName-zn1sb 4 года назад

... Kind of

@JNCressey 4 года назад

"There's the cube - everyone knows the cube." Just platonically though, right?

@PedanticAntics 4 года назад

JNCressey this should have more likes

@bonob0123 4 года назад

BIBLICALLY

@mal2ksc 4 года назад

Unless you're the Curator from _Gravitas._ We all know he's dry-humping the cubes instead of making new galleries, which is why the game is so short.

@subnormality5854 4 года назад

-sad cube noises-

@domlee5902 4 года назад

This is hilarious

@MeDoMeer 4 года назад

I love how his blackboard is so intensely clean

@alspezial2747 3 года назад

he does everything in his head, no blackboard needed

@shaunlastname391 2 года назад

Or he's a conman on the grift, making up shapes as he goes and glibly explaining it to get recognition and subsequent riches to pay for more body art. The conmans clean blackboard is a gullibility mirror 🤣

@emo6577 4 года назад

I love the way he talks about the subject. It’s easier to feel interested when he makes it seem so exciting

@cadeharris4631 4 года назад

Jayadev Athreya was my calculus teacher last year, super chill dude never thought I'd see him in a Numberphile video, small world I guess.

@samueltaylor9935 4 года назад

ayyyyy a UW fellow

@pentuplove6542 4 года назад

Shows the Rockefeller Education System works at making people unthinking.

@General12th 4 года назад

@@pentuplove6542 What?

@joshuarosen6242 4 года назад

@@pentuplove6542 Er, what? Would I be correct in thinking that you didn't do very well in the education system?

@iamcleaver6854 4 года назад

What os his nationality? Persian? That is a strange name.

@yourface4248 4 года назад

I like this man. he went through insane amount of mental gymnastics to show the world his tattoo.

@madkirk7431 4 года назад

Ikr

@webgpu 2 года назад

@Fremen unlike a certain "generation" of youngsters (and some oldass dudes too) who mark their bodies as if they were cattle. In the modern age, one of the first groups to mark their bodies were inmates, then whores, then the fkng nazis marked our brother jews, then these youngsters now.

@TheGamingLegendsOfficial 2 года назад

@@webgpu that's a bit of a slippery slope fallacy, isn't it?

@pappaflammyboi5799 2 года назад

@@TheGamingLegendsOfficial Yeah, it's pretty slippery, but possibly not too far off the mark.

@jimviau327 2 года назад

Well, He must be better than me, I have no tattoo to show off.

@espen990 4 года назад

I wish someone looked at me the way this guy looks at dodecahedrons.

@madkirk7431 4 года назад

OOF

@TheJwbooth 2 года назад

That's why his chalkboard is so clean, erasing all those naughty angles and planes

@klauspeter2199 2 года назад

“How many pieces can I cut it into? I don’t know! Let’s find out!”

@supertrampolinethebatpony3841 4 года назад

What I really find amazing is that their simplest answer is so simple that it’s easily visualized by the human brain; it’s not abstract at all like so many of the proofs or conjectures discussed on this channel. Like you could show that example to a mathematically inclined middle Schooler and they would understand what was going on. I think that’s so wonderful!

@UnkleRiceYo 4 года назад

2:28 Academy nominates Numberphile for best animated short horror film.

@volodyadykun6490 4 года назад

It's adorable

@namethathasntbeentakenyetm3682 4 года назад

@@volodyadykun6490 Are you blind!? Look at it!

@volodyadykun6490 4 года назад

@@namethathasntbeentakenyetm3682 and you are mean

@Alistair 4 года назад

@@volodyadykun6490 and you are trying to protect the feelings of a 3D model. Which happens to be possessed by a demon

@inigo8740 4 года назад

@@Alistair that mathematician may be meant to be Hannah Fry

@TheRetsekShow2236 4 года назад

"One of the central tensions in The Little Prince, other than the loss of childhood innocence" 😂😂😂

@tigershark8867 4 года назад

( ͡° ͜ʖ ͡°)

@loonycooney22 4 года назад

I don't know why, but I lost it when he said that.

@fictionmyth 4 года назад

@@loonycooney22 I wish you luck on finding it. :D

@Irondragon1945 4 года назад

_its a great read..._

@trickytreyperfected1482 4 года назад

@@loonycooney22 Oh gosh, you lost your innocence too?

@hughes2896 4 года назад

“Other than the loss of childhood innocence

@sahemali2204 4 года назад

Nice

@satyris410 4 года назад

That was what I'd suggest the path be called: loss of innocence path

@Om_1337 3 года назад

He quoted Ecclesiastes too

@lawrencedoliveiro9104 3 года назад

@@Om_1337 To show that the holy book was wrong!?

@brianbethea3069 3 года назад

3:01 "One of the central tensions in The Little Prince *_(other than the loss of childhood innocence)_* is that the prince has a sheep on his planet..." This made me laugh.

@DTHRocket 4 года назад

This guy probably never gets invited to play D&D with his friends. "Do you guys wanna know a cool thing about this D12?" "Here we go again..."

@ismailshtewi8560 4 года назад

i'd happily abandon D&D to talk geometry with this dude

@remixtheidiot5771 4 года назад

Ismail Shtewi who wouldn't? It is statistically proven that a majority of us d&d players are absolute nerds!!! (I'm a nerd and I play d&d so everyone else who plays d&d must also be a nerd!)

@TopLevelJiuJitsu 4 года назад

🤣

@CosmicPlatonix 4 года назад

@Cliven Longsight Quick, find a mathematician who can get super-excited about antiprisms and isohedra!

@percy6532 4 года назад

Thats is why my dnd party hates me.

@laurusschluep7464 4 года назад

When a video is called "a new discovery about dodecahedrons" you know you're in for a ride

@danielalba7651 4 года назад

Ahem, for a walk.

@zethyr8833 4 года назад

@@danielalba7651 jog

@SquirrelASMR 2 года назад

@@zethyr8833 a roll

@TheRojo387 2 года назад

Dodecahedra is the plural.

@Triantalex 6 месяцев назад

false.

@mnek742 4 года назад

Interesting! I had no idea something like this was unknown until recently. Just for fun I calculated the areas of the two pieces separated by the primary "yellow brick road". Apparently they're not the same in area, one piece is 9.66% larger than the other. The larger piece is 65-sqrt(5) parts out of 120...

@arnavrawat9864 2 года назад

how did you do it

@mnek742 2 года назад

@@arnavrawat9864 Hmm, it was a while back, but if you look at the video at 6:50, you can find the areas of the two halves of the surface by carefully measuring all lengths and angles, and finding the area of a certain right triangle whose hypotenuse is the red line. I could produce a proof in a youtube video if there was enough interest, but alas you're the first person to ask! But thank you for asking.

@Joao-uj9km 2 года назад

😀

@PedroSilva-re6ck 2 года назад

@@mnek742 Honestly, i would watch the proof 1000x, POST IT.

@steveparsons6719 Год назад

Well done for working this out. With the areas of the two surfaces being in the ratio of about 1·0966:1, I wonder whether the volumes of the two pieces are in the ratio of about 1·1483:1 ?

@torin1006 4 года назад

4:19 "It makes sense to go over a side, but it doesn't make sense to go over a corner." Me: **laughs in non-Euclidean**

@isaenzemilio5574 4 года назад

Cries in euclidean

@danielm.1441 4 года назад

Literally the cleanest blackboards I've seen in my life.

@hps362 4 года назад

...those _are_ blackboards...

@fringedwig4670 4 года назад

@Hoaxcrit yas

@sorrymyenglishbad2535 4 года назад

Never knew I'd be so interested in platonic solids and mathematical proofs. Sick video.

@ar_xiv 4 года назад

Well you have a truncated cube in your icon so that’s something

@DerpMuse 4 года назад

@@ar_xiv Its because only us cool kids use types of cubes in our pfp xD

@lhl2500 4 года назад

@@DerpMuse No need to be hyper about it.

@jeffvader811 4 года назад

@@DerpMuse Oi, do you have a licence for that 4th spatial dimension?

@Triantalex 6 месяцев назад

@cinnamonbeardstud 4 года назад

This guy is great, he is a very clear speaker and doesn't fumble words.

@shabblabbat 4 года назад

I could listen to Jayadev explain anything....so brilliant but easy to understand.

@octooopus 4 года назад

The line on the dodecahedron almost hitting the points is like the DVD menu icon almost hitting the corners of the screen.

@sirlight4954 4 года назад

It is the exact same problem, as bouncing is continuing towards into a mirror image

@wmhilton-old 4 года назад

Glad I'm not the only one who spent WAY to much time watching and waiting for a corner bounce to happen. I wonder if we had the same DVD player as kids?

@jekylhyde1843 4 года назад

I remember watching that and trying to solve it.

@CaptainWizard3000 4 года назад

No, you should be glad that your tv was not shaped as a pentagon, because then you could've been watching forever...

@HalcyonSerenade 4 года назад

It didn't surprise me at all when he said they've made educational materials about this for schools, because his explanations already sounded streamlined in a "for non-math enthusiasts" sense. Not just the words themselves, but his tone of voice implies much practice as well -- even compared to the Numberphile regulars, which is impressive!

@NoName-zn1sb 4 года назад

... kind of

@majinoyal 4 года назад

Deep love how you broke that down

@tristanrentz7687 4 года назад

Always great to see new faces on the show, but this guy takes the cake! His deep but light-hearted passion was infectious, accentuated by unique mannerisms that amounted to frequent full-body chuckling. A joy to watch. And the muse of his amusement: an outside-an-unexpected-Pandora's-box-of-a-realm, in the vicinity of the fundamentally familiar Euclidean solids! Great fun, many thanks..

@michaelstanley9960 4 года назад

I dont fully understand what your explaining but i love your enthusiasm and excitement on the subject. Shows that your really passionate for what your doing

@IanTanLK 4 года назад

Mathematician: Platonic Solids. The rest of us: Dice

@gavinclark6891 4 года назад

Ian Tan MY SPECIAL D12 CLICK CLACK

@emmybee5189 4 года назад

Ian Tan Ah, a man of culture I see. For this you get advantage on your next skill check

@404dne 4 года назад

EXOTIC ENGRAM

@uristmcdwarfington8863 4 года назад

@@404dne inDEEd

@shadycactus6146 4 года назад

the d10 is my least favorite die because it’s not a platonic solid

@unvergebeneid 4 года назад

Who would've thought that there are still things to learn about the good old d12 :D

@Fruitabat 4 года назад

So ddozen?

@J3rs3yM1k3 4 года назад

Not just for barbarians anymore. ;)

@QuantumFluxable 4 года назад

@@J3rs3yM1k3 great axe wielders unite

@kugelblitzingularity304 4 года назад

Ah the dirty dozens

@AlexJones-ue1ll 4 года назад

It doesn't have to cry itself to sleep anymore!

@thornorium8983 4 года назад

"The Dodecapath" for the simple path name?

@msg.timothy4914 3 года назад

I'm stealing this for a school assignment

@denismilic1878 2 года назад

I watched 19 min long video about Dodecahedron, and I want more. This guy radiates positive energy. Extra footage, here I came!

@lovelaugh7299 4 года назад

"So what's your job" "I imagine small living creatures on geometric objects" "Haha... no seriously what's your job" "This is my job for the past 25 years" "😐"

@adamfirst3772 4 года назад

....."get a real job".... one where hypothetical sheep and joggers HAVE WIDTH..... then a SIMPLE brain-fart, doesnt become a 25 year challenge!,

@chrisregman29 4 года назад

Let's assume a spherical cow...

@chadstratton4926 4 года назад

A genius doesn't waste the other person's time hiding deal breakers.

@dhoyt902 4 года назад

I don't know any of you, but when I watch Numberphile, I feel I am among friends.

@Simon-vf2bq 4 года назад

2:38 Its gonna haunt me in my nightmares

@bscutajar 3 года назад

Videos like this are prime numberphile content. Simple questions with interesting answers and can be clearly explained in a 15 minute video.

@pyglik2296 4 года назад

Important problems for mathematicians: how to go jogging witgout meeting other people :)

@dependsonwhosasking 4 года назад

And thus the treadmill was invented

@pentuplove6542 4 года назад

witgout? A Dutch / English word? Wit is out and out is out.

@supertrampolinethebatpony3841 4 года назад

Haha you never know when you’re going to run into a fellow Brony on the Internet!

@NotOneToFly 4 года назад

Suddenly, this is a relevant question for EVERYONE

@FPrimeHD1618 4 года назад

Next thing you know they are going to be telling us that a coffee cup and doughnut are the same thing!

@leadnitrate2194 4 года назад

The animation by Pete McPartlan is amazing. You guys have really outdone yourselves this time. Edit: Congratulations on the great discovery. A name for the simplest line could be The First Bridge of Koningsberg, I don't know

@jonathanlevy9635 4 года назад

Bridges of kongisbreg is already taken

@leadnitrate2194 4 года назад

@@jonathanlevy9635 yeah I know, I was saying that the original problem that Euler solved was to avoid going through a vertex (but a graph theory vertex, if you know what I mean), and this is a similar problem but with the vertex being a "real" one.

@luemas3219 2 года назад

Interestingly, I was building a wooden dodecahedron and as I was gluing and taping up the shape, I discovered this very thing. Great video.

@Theooolone 4 года назад

Thank you for letting me know that my sleep paralysis demon is an avid jogger.

@anonymouss8925 4 года назад

I wish I had 31 ways to avoid my neighbors

@TykoBrian7 4 года назад

Anonymous S move?

@s3cr3tpassword 4 года назад

Live on a dodecahedron then

@eyetube33 4 года назад

Use the back door or underground exit

@rafaelribas1027 4 года назад

Skip out the back, Jack; make a new plan, Stan...

@MarkusDarkess 4 года назад

Talk to them once and a while you will find that you will see them less.

@wokeupinapanic 4 года назад

Man, I hope he gets to do a lot more videos in the future! He’s fantastic and enthusiastic!

@heatblayze 4 года назад

Yes!! My mind instantly jumped to cutting and measuring the shapes too! Great video :D

@coopaloopmex 2 года назад

Everything about this channel is amazing!!!!

@ericsmith5919 4 года назад

"Here's a mathematical proof*!" *Some assembly required.

@trevorvanderwoerd8915 4 года назад

That's most proofs, but they usually word it as "left as an exercise for the reader."

@sk8rdman 4 года назад

@@trevorvanderwoerd8915 To be fair, that's the best way to get the reader to truly understand it. Force them to play around with it on their own.

@willowFFMPEG 4 года назад

Assembly? I thought this was numberphile not computerphile!

@user-jc2lz6jb2e 4 года назад

Can we get more of this mathematician? I love his explanations.

@CalvinHikes 4 года назад

Natalie made his idea clear he made it clear that he was the only one who had this idea. Which I appreciate it. Sometimes I'm not sure what the mathematician accomplished in this case he made that very clear as well.

@NoName-zn1sb 4 года назад

@@CalvinHikes Kind of...

@sarahpurol7710 10 месяцев назад

Very fun! Great job on the description. Thank you!

@jerberus5563 4 года назад

My geometry class in high school made 3D dodecahedrons out of paper, so seeing this 18 years later is really cool.

@TimJSwan 4 года назад

So weird! I recognized this guy. Sure enough, he was my math teacher at University of Illinois!!

@theatlasreport8046 4 года назад

Prove it !

@katherinewu3224 4 года назад

Ray Bois nah i think timothy was just saying where he teaches

@theatlasreport8046 4 года назад

I think you lie!!!

@Not.Your.Business 4 года назад

@@raybois what is "name dropping"? never heard that before my first language isn't english

@Not.Your.Business 4 года назад

@@raybois thx learn something new every day

@deanc9195 4 года назад

Round earth? NAH. Flat earth? NAH. Dodecahedral earth? YEAH!

@misc.endeavours8343 4 года назад

That'll shut them all up

@fuzziemusic 4 года назад

You forgot donut earth ;)

@talmage_ur 4 года назад

gratefully thank you for your uploads - great time to share such knowledge. Be well in mind heart.

@Prometheus720 4 года назад

I loved this video. Please have this man on again!

@DerpyLaron 4 года назад

Not sure if it was intentional but using the colours of the Zelda virtues/parts of the triforce for the corners on the net of the tetrahedron was a nice touch.

@zedex1226 4 года назад

And of course we all remember the side quest where you have to find the sheep that wandered into the lost woods.

@noahfine4820 4 года назад

I've been struggling a lot lately with a burnout in my passion for math. This video helped. Thank you

@EternalDensity 4 года назад

Wow. Fascinating discovery, so well explained.

@jekylhyde1843 4 года назад

I feel like this is somehow going to improve battery technology.

@nishan375 4 года назад

It might improve teleporting technology in 2000 years. Who knows

@Rahul-uk4su 2 года назад

Most of the theoretical physics in practical application is from maxwell's laws of electromagnetism and relativity which use math that is pretty standard for an undergraduate ,most of the pure math being worked on today ,ppl dont even know when and where it will be applied , mathematicians are stiving only to better the field so that when the time comes its ready for physicists

@jedh3721 4 года назад

The Dodecahedron has always been my favorite platonic solid, and I feel very justified seeing how weirdly different it is from the others even though I didn't know most of this stuff.

@sajateacher 4 года назад

I was actually thinking when I woke up this morning, "Gee, I really hope they discover something new about Dodecahedrons" and, well, there you have it. Could this day get any better?

@samaraisnt 4 года назад

Think not.

@arekkrolak6320 2 года назад

I have watched it second time after a break and I must say this scientist has ability to talk about maths with passion and involvement!

@man_of_many_pants 4 года назад

The dodecehedron has fascinated me recently and I was not sure why. I was learning mandala, and found a way to connect points on concentric circles to make an artistic rendition of a perfect dodecehedron. Interesting how you could both run in a straight line on both a sphere and the dodecehedron and end up In the same place.

@GummyGruffi 4 года назад

Let's call shortest path "Antisocial lazy jogger".

@alexanderf8451 4 года назад

Antisocial travelling salesman.

@androidwalle4932 4 года назад

@@alexanderf8451 unsuccessful salesman!

@jekylhyde1843 4 года назад

GummyGruffi ALJ

@Mattle_lutra 4 года назад

It is however, misusing the term "antisocial", and the term he's looking for is "asocial". Antisocial: meaning one who actively seeks out to destroy social relationships (a term often used when describing psychopaths and sociopaths) Asocial: meaning one who shys away from being social (often a term used to descripe depression symptoms)

@samaraisnt 4 года назад

yyyyyyyyyyyyyeeeesss! You _have_ to use/include the jogger's dilemma, to omit it is a crime!

@lawiez 4 года назад

this channel disappeared from my feed for more than a year, i'm glad it popped up again, gotta hit that bell icon!

@sander_bouwhuis 4 года назад

Very well presented video. This guy is VERY clear. Big thumbs up!

@TheDarthsphincter 4 года назад

"...my colleagues and I have been exploring a _facet_ of what would it be like to live on a platonic solid"

@colinnewton5254 4 года назад

Friendly I should think.

@lawrencedoliveiro9104 3 года назад

Very edgy. Did you get the point?

@Justifer14 4 года назад

Love the shape animations!

@Hard2heart2heart 4 года назад

Wow. Thanks for raising more questions

@The_hungry_vegans 4 года назад

Great job guys! Loved it

@BN-fi9wi 4 года назад

Starting my postgraduate studies in Mathematics this year and it's partly Numberphile's fault for featuring such well articulated topics. Hopefully one day I can articulate my ideas on the channel.

@SkillslliK 4 года назад

I can't thank him enough for his amazing proof that he submitted, what a passionate teacher. Need more of this type :)

@josephyoung6749 9 месяцев назад

rewatched to enjoy some abstract thinking, but also to admire the narrator, Mr. Athreya's gentle voice

@BlueGiant69202 4 года назад

Great video! I wonder if there is a relationship to the following: Synergetics by R. Buckminster Fuller 457.40 Spherical Polyhedra in Icosahedral System: The 31 great circles of the spherical icosahedron provide spherical edges for three other polyhedra in addition to the icosahedron: the rhombic triacontrahedron, the octahedron, and the pentagonal dodecahedron. The edges of the spherical icosahedron are shown in heavy lines in the illustration.

@benstapleton5319 4 года назад

How about 'Pathy McPathyface' for the shortest path's name

@numberphile 4 года назад

Don't be muscling in on my "Yellow Brick Road" idea! :)

@CalvinHikes 4 года назад

What a time to be alive.

@PopeGoliath 4 года назад

Came here to make this joke.

@ryanrising2237 4 года назад

This is immediately where my mind went when I heard the speaker suggest looking for suggestions in the comments.

@thatoneguy9582 4 года назад

what about ‘P’

@niekwesseling4355 4 года назад

Love how clearly this problem and solution is explained. Also the questions were spot on with helping to gain more insight and understand this better. Great work!

@stuartmacintosh4868 4 года назад

Amazing work. I can already imagine how this could be applied to 3D graphics optimisation problems.

@robinsonkaspar3395 4 года назад

When I thought of living on the point of a dodecahedron I thought about how steep a hill one would live on, and what that would look like perceptually, and how easy, if terrifyingly fast, if would be to bicycle over to a neighbors house (assuming a perfect bearings, lack of wind resistance, etc.)

@happydays3300 4 года назад

The code they did to solve this problem, is more impressive then the actual problem being solved, I just had a look, first thing I noticed was zero errors.😂

@moralboundaries1 4 года назад

Platonic solids are so fascinating and powerful. This is one of my favorite Numberphile videos. Great job Jayadev, Brady, and Pete! I felt a real sense of intrigue and mystery as you slowly explained the concept and revealed the story.

@PO-si4ty 4 года назад

Well done! Wow very simple but very intricate.

@StormTheSquid 2 года назад

This is the 3rd time in as many years I've been brought back to this video and I only just realized I commented two separate, very different responses as to why it does in fact make sense to go straight over a corner, and am starting to realize how my mindset has changed over these three years.

@rmreagle 4 года назад

"The Dodequator"

@AlwinMao 4 года назад

another suggestion: le petit path

@loganstrong5426 4 года назад

So, path in French is chemin (according to Google translate), but another word is trajet, and I like that better because of its similarity to trajectory. Le Petit Trajet.

@connorhamilton5707 4 года назад

Is there anyway we can make this have 12 letters? Other than swapping le with the, since The Petit Path sounds awkward with the french version of the word in the middle of english.

@didz65 4 года назад

Somehow i think La petite path is more appropriate because i assume the path is feminine (yep in french you assume gender for everything). But it really depends how you translate it. For example chemin and trajet are both masculine (le petit), but the first translation that came to my mind is trajectoire (la petite). Trajet and chemin are more like roads or itinerary, trajectoire is the word you would use in maths.

@iminni3459 4 года назад

Yes

@drawapretzel6003 4 года назад

do "mon chemin quotidien" or something bain/pain if theres a better french pun

@glyphiclive15 2 года назад

great video, well made and instructed

@luigidragonborn 3 года назад

I love how he teaches geometry ! now if he could explain algebra like this, I be sooo happy !!

@FlorianLinscheid 4 года назад

Jayadev is an incredibly good speaker, very concise and easy to follow thoughts. Please more of him!

@mxecho 4 года назад

"the Platonic Jogger"

@LordQueezle 4 года назад

Not only can you be a reclusive mathematician living on a dodecahedron... but you can also choose how long you want to run.

@roygalaasen 4 года назад

Lord Queezle Uh, I didn’t have time to watch till the end. Are you saying you could have an infinite run without passing through any of the corners? That is mind ... blown...

@jeremydavis3631 4 года назад

@@roygalaasen I haven't tried to prove it, but an infinitely long trajectory should be possible on any platonic solid. If you put the unfolded map on a coordinate plane, with at least two vertices on the x-axis, I conjecture that no trajectory with an irrational slope will intersect more than one vertex nor hit that vertex more than once (that is, it will intersect only one of the infinitely many colored points). It should be easiest to prove for the tetrahedron, since its map easily tesselates the plane. (If the map doesn't tesselate the plane, the slope might be different in different places because of the need to glue together sides that aren't touching, but it should always remain irrational.) A similar setup is often used to show how few rational numbers there are as compared to the irrational numbers around them.

@roygalaasen 4 года назад

Jeremy Davis yes, I think you are right. I realised that it should be possible short after posting my comment. Thank you for your explanation.

@Axacqk 4 года назад

@@jeremydavis3631 It boils down to cardinality. The path is completely defined by the starting direction. There is a continuum of possible starting directions, while there are only countably many directions where you will eventually hit a vertex (that includes non-solutions due to running into a neighbor's house). Therefore most paths are infinite.

@EllyTaliesinBingle 2 года назад

I wonder how much of this journey was computer-aided by tech and processing power only available in the last decade or so. :) It just makes me feel like I'm living in a special time when I see a new discovery about a platonic solid. Like, what???? lol. Amazing stuff guys, congratulations.

@davidk3849 4 года назад

This man is explaining how get a Fragment of Possibility

@timmytherobot2779 4 года назад

Yyyyaaaaaahhhhhhhhhhhhhhhhhhhhh be pleased

@PhysicsHelps 4 года назад

Beep Beep

@MichaelDreksler 4 года назад

Jayadev spoke so well in this video. Great job all of you.

@Sharklops 4 года назад

I'd buy a Numberphile shirt featuring that sheep with a rose in its mouth (aka, the Parker Sheep)

@rosiefay7283 4 года назад

Perhaps you could do it on a Parker cube!

@andrewkepert923 4 года назад

Wrong sort of dodecahedron for Matt

@Jahus 4 года назад

Amazing demonstration.

@YossiSirote 2 года назад

Loved this one!!

@IsaMorphic 4 года назад

I love how passionate these people are about their work. Keep it up!

@asmrtingletime4611 4 года назад

This series shows how wonderful and fun maths are in fact, though visual explanation is so important. Great work!

@adwe9912 4 года назад

Thanks for video! My favorite is dodecahedron. My companies’ logo has pentagon in it and i use the dodecahedron for my interactive webpages! Awesomeness 💯

@ioannis-johnmizithras 4 года назад

great video as always!!!!

@TheMrvidfreak 4 года назад

Numberphile: platonic solids Me and my crush: solidly platonic

@anotherone9460 4 года назад

Oof.

@afinafina 4 года назад

Name suggestion for class 1: Lazy Prince Path Name suggestion for class 31: Drunk Prince Path LE: and have a spectrum from 1 to 31 going from Laziest to Drunkest