How many ways can circles overlap? - Numberphile

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T-shirt and poster details below. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ Featuring Neil Sloane from the OEIS: https://oeis.org And thanks to Jonathan Wild: https://www.mcgill.ca/music/jonathan-wild OEIS A250001 - Number of arrangements of n circles in the affine plane: https://oeis.org/A250001 3-Circles T-Shirt: https://teespring.com/three-circles-numberphile 4-Circles Poster: https://teespring.com/four-circles-numberphile Other merch: https://teespring.com/stores/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Animation by Pete McPartlan Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9

Comments

AbovetheLoft : 4:38 *whispers* "Look at these. This is a very delicate...configuration..."

Henrique Sucupira : Today I'm sleeping early 3 am: _in how many ways can circles overlap_

Jonathan Fishman : “Jonathan wild took this series out to 5” Oh that’s actually not that impress- “3: 14, 4: 173, 5: 16,951” Oh never mind

Zatanna Zatara : circles not kissing is pure shapeophobia brought about by the squares

CryMor Gaming : I like how this video went full circle.

Oliver Sansum : 4:30 sounding like a mathematical Attenborough

Keith Foo : The 4 Audi and 5 Olympic rings cannot be formed because of copyright violations.

Peter Flatenthwack : Me: do you speak gallifreyan ? Neil: 😏

AstroTibs : Well you have a _soft_ lower bound for 6. It's just 5's count.

lasaga eater : How much paper do these guys go through

Philippe Carphin : @8:19 I see a triangle and a hexagon wearing a bikini.

Alexander Ram : 4:20-4:45 when no one but you understands your doodling

ninpo : 4:35 ASMR

kaslon05 : Like some weird Venn diagrams trying to explain UK leaving the EU Sorry but I couldn’t bring myself to say the B word

Andrew P. Roberts : 0:58 **Super Smash Bros theme gets increasingly louder*

Jindra Vysocký : I love the UNIX book behind Mr. Sloane :)

retepaskab : Let me give a lower bound for 6: 16951.

TheAguydude : "We don't have a lower bound." Of course we do. Just make an arbitrary number of arrangements (e.g., 0) and you now have a lower bound. A slightly less useless lower bound is 16,951 (draw a circle around every arrangement of 5.

J J : On the opposite side of the spectrum, my dog will turn around in circles trying to get comfy to sleep. But that’s his second choice. He chooses lap over circles every time.

charles0 : In 5:32 he said 'Does A meet C?' and you put X on the row corresponding to B meeting C

Alistair Smith : This is pure asmr. With the added bonus its really interesting

/dev/null : Every time I watch one of Neil's videos, I just want whataburger.

macleadg : Is it the same for squares?

Charlie Angkor : I think doesn’t specify enough what it means configurations are identical or different.

Undertaker : I get hyped every time they upload a video

Sarah Bear Draws : Does anyone know what is on his shirt? I saw Don Knuth wearing it as well and I can't figure out what it means.

NyAn CaT : Maths is not just about numbers its about understanding

Walking Guy : 3:03. don't tell me i'm the only one that noticed this

Nestrislia Crystal : I wonder if the Time Lords/Ladies from doctor who thought of this when writing their modern language.

MC cashMax : Following the criteria he layed out about the five circled I found an arrangement in about 10 minutes.

Kian Ellis : 3:02 - 3:05 Antman in End Game in a nutshell

JB Lewis : The Mathematica book behind Neil Sloane intrigues me.

Dustin : I thoroughly enjoyed this

Abdega : 4:16 it looks like Futurama Alienese

♫♪Ludwig van Beethoven♪♫ : Not only the equation is hard, but also writing a program to brute force in efficient way is hard

thelittlesagg2 : Circles: *exist* Audi: It's free real estate

Archanfel : What about spheres? And extension of this problem to higher dimensions!?

CheesecakeLasagna : If Bob Ross was a mathematician, he'd be this guy.

road to 100 MILLION subs without videos : imagane not being able to move the center of the circle out to infinity to get a straight line - this meme is brought to you by the projective plane gang

DaxHamel : At some point you can cherry pick arbitrary rules the suit whatever situation you're looking for. The whole exercise becomes meaningless.

♫♪Ludwig van Beethoven♪♫ : Each way after 6 was its own plot twist

Andras Libal : Is there a way of mapping these on Feynman diagrams or something similar and giving a physical meaning to your question?

VECIOKEPAVA : The video isn't even that interesting to be honest but his voice is so relaxing that it's basically ASMR.

Crash : Dr Sloane has one of those wonderfully relaxing-yet-compelling voices that are just ideal for podcasts.

Mara K : The n=4 animation reminds me of cat’s cradle

John Thomas : How it is different from "How many ways can SPHERES overlap"? 1 sphere 1 way 2 spheres 3 ways ...

Bruce : Neil Sloane (is that his name?) has the mind for math and the voice for story telling !

Zebulon Virginia : I love your voice, & thank you for sharing this beauty. I'm going to have to look up affine plane again. I'm sure it made sense to me at some point in the past, but these days I only understand projective, as I've been obsessed with the projective plane for so long.

Elessar Strider : You left out when each one is bigger than the other two. I call it the Escher configuration.