Funny Fractions and Ford Circles - Numberphile

Farey Sequences, Ford Circles and a strange addition sign...
Featuring Francis Bonahon from the University of Southern California.
More links & stuff in full description below ↓↓↓
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[@EpicFishStudio]

let's talk about *fR̸̵͇̹͍̰̗̫̭̠͈̮̳̞̫̬͎̼͉͕ͫ̒̿̏ͤ̾͘͞actions*

[@shadowbane7401]

Dat Epic Fish ikr

[@robsbackyardastrophotograp8885]

How do you even type an R like that?

[@v6790]

@@robsbackyardastrophotograp8885 he hacked his keyboard

[@Maxence1402a]

@@v6790 With a butcher's chopper.

[@lyrimetacurl0]

FR̸̵͇̹͍̰̗̫̭̠͈̮̳̞̫̬͎̼͉͕ͫ̒̿̏ͤ̾͘͞ench

[@shell_jump]

I had no idea it was possible to write numbers with an accent. This man is my hero.

[@veertsucks]

First time watching this video, and yes, how he writes his 2's has made my life!!

[@conanichigawa]

Such a French way of writing numbers.

[@112048112048]

Average "One over Two" fan VS average "Ouonne over Toux" enjoyer

[@lyleandres1510]

instablaster

[@jhoughjr1]

I noticed his 2 had a curvey line but his q looked like a nine.

[@ThePaull3d]

Mathematician, Mustache, Accent, Clothes ... He nailed life.

[@noahshomeforstrangeandeduc4431]

ThePaull3d true

[@zofop2891]

I forgot my clothes

[@genericusername4206]

ThePaull3d why would you not wear clothes

[@mrsamsun912]

And life nailed him back

[@asheep7797]

@@zofop2891 you lost life and sanity

[@10mimu]

"I wanna talk 'bout frrrrractions".

[@columbus8myhw]

Istari Pallando f-gh-gh-gh-actions

[@thatoneguy9582]

Human Effigy “You can add them up, or you can mooltiply them”

[@gratux]

@@thatoneguy9582 mülitplai

[@TheWikiMax]

he is like Mr Hollande :P

[@AmonAmarthFan609]

"Fr🇫🇷r🇫🇷a🇫🇷ctions"

[@totallymcmylastname9077]

He is so French the rice on my table turned into a baguette, and so does the water into wine.

[@hughstout]

And your rock music turned into romantic music

[@sooosooo100]

Water into wine is the speciality of a certain middle eastern man..

[@mrl9418]

I didn't see that coming, and I only have myself to Blame!

[@asheep7797]

The hole in my wall goes to Britain.

[@GuyWithAnAmazingHat]

When I saw this gentleman on the thumbnail, I knew right away this is going to be an awesome video.

[@gabrielkellar1935]

To me he looked like an american dad

[@Triantalex]

??

[@aychar]

Could this man be any more french?

[@lifeproofminds]

hr Haha Ikr? Even his first name is Francis.

[@vianneymonnier7660]

hr If we added a bottle of red wine and bread on the table, plus him complaining about the government and going on strike, yep, we should get something representative of French people. From France with love ;)

[@TacoDoesYoutube]

hr I thought he was German :/

[@luisadrian327]

TacoDoesKZbin Me too and I'm german XD But the accent is french I guess... :)

[@GuyMichaely]

hr Yes. He's German.

[@JustASnack]

What I love the most about Numberphile is how enthusiastic all the mathematicians you bring up for show are!

[@13gondolla37]

I would listen to an hour long video of this guy just saying "fractions" over and over and over...

[@NoriMori1992]

"Fkhrakhchons"

[@zorm_]

That's quite how we say it in french lol (except the "on" sound is different)

[@pj4717]

ASMR

[@geoff7936]

Nailed it!

[@zorm_]

frakcheunze

[@antonino30]

the "I cannot completely explain the details"@13:52 broke my heart... This video needs a second part! It got me on the edge of my seat the whole time! Numberphile Lives!

[@TakeWalker]

One of the most amazing Numberphiles of late!

[@BarclaySmith]

Take Walker Totally agree - I was watching with mouth agape for much of the video.

[@kkira22]

Right?! Moustaches and accents are awesome but there's really nothing better than the peculiarities of this particular reality.

[@7000000th]

Take Walker I'm sorry to say, it was painful for me to watch this video, even though the content had the usual amazingness. It's just that I can't take him sereously with his accent. I just notice every influence from French, because I'm french too.

[@pabloricardodetarragon2649]

7000000th If you are stopped by a so trivial detail, never do studies. He is perfectly understandable, speaks slowly, and explains clearly. Besides he has a very nice pedigree in mathematics, probably far better you'll never have. Go in UK in some university I won't name and try to understand a mumbling Scottish guy writing undecipherable signs on the chalkboard about Navier Stokes equations. That's true pain, specially when you know that the exam is within 2 months.

[@7000000th]

Pablo Ricardo de Tarragon if you're trying to vent your frurtration, go do it to someone else, because I not responsible for it. I was just trying to remark upon his accent, and how French it was, and as I said, I understood every word of it and enjoyed the content. Even, I felt a bit of pride that a fellow Frenchman should be on this channel, no matter what his accent is

[@tanukigalpa]

this guy's accent gives me life, I could listen to him all day. If I had his accent I'd never stop talking. It's so energetic and mildly entertaining

[@Triantalex]

??

[@TheJaredtheJaredlong]

"Where's this guy from, Switzerland or something?" Looks at description: Southern California. "Oh."

[@lbzimmerman96]

TheJaredtheJaredlong Well he is from France originally, just now works in SoCal

[@mikecsiy]

TheJaredtheJaredlong That's what all Southern Californians sound like. He haz zee clazzic valley aczent.

[@pedrodemello3666]

Somehow I don't think he was born in California... just sayin'.

[@zorm_]

he is french, he talks with a french accent and he was born in france... He's probably californian

[@loganallomes4305]

A quick google search shows that he was born on the 9th of September, 1955, in Tarbes, France

[@123Joack]

4:04 "Pussyball" k

[@NebulusVoid]

Verlenzius possible m8 lol

[@axelord4ever]

Blake T My mate is possibly laughing out loud? Are you a seer?

[@NebulusVoid]

***** Yes. Yes I am lol

[@VincentKun]

404 stopped working

[@TheSummoner]

Verlenzius damn you almost made me choke myself with food

[@Box-of-hats]

Glad to see some Welsh mathematicians on Numberphile!

[@Box-of-hats]

I'm joking :D

[@john117950]

Stuart Hull You can tell when a frenchguy is speaking english...

[@edwardbottle1018]

Stuart Hull Poe's Law, amirite?

[@pabloricardodetarragon2649]

Lucas Nakach You can tell also when a American guy is speaking French. Then best is when one southern guy is trying to speak French to a Canadian from Quebec with a heavy joual accent.

[@yannchereau3630]

***** I am french and I bearky understand what he says. A funny thing is that in France, when people don't know how the pronounciation of a word or when they are not sure of it; they don't even try to because they don't want to be ridiculous but it is even worse !

[@gammaknife167]

My brain just exploded. AMAZING VIDEO. WE NEED MORE OF THIS GUY TOO

[@DJAbrahamLincoln1]

This guy is by far my favorite Numberphile guest solely based on voice.

[@jamirimaj6880]

Even the greatest comedians and humorists can't be more French than this guy even if they try their hardest, all he needs to do is write "2" and it's all over.

[@VictorChavesVVBC]

The "Farey addition" (mediant) is very interesting. I once did a work about the Stern-Brocot tree (sometimes called Farey tree) and its applications to number theory. It has many interesting properties: it generates all rational numbers exaclty once (and you can estimate the maximum height it should appear), many simmetries and pn - mq = 1 relations useful for factoring numbers. Very interesting video to me, I've never seen the geometry on this. Geometry has this weird habit of making algebra look nicer.

[@rosselur]

at around 1:10, i distinctly heard the word puttiply. awesome.

[@raumaankidwai]

rosselur More like 1:16

[@raumaankidwai]

raumaan kidwai "Wanta puttiplyt wit tree ovar seven, aye puttiply dem noombars ondas top, aye puttiply dem noombars ondas buttum, andaye putty it togeder"

[@raumaankidwai]

raumaan kidwai 1:20 and on... "KHOWEVER"

[@carloshiguera9221]

raumaan kidwai I laughed more than I should have

[@jeremylawrence6041]

Carlos Higuera me too, i'm in tears

[@ZincAddict]

I just love listening to him say the word "Prime"

[@BonDonJuan]

Pggghhheim

[@BlackBirdJacobo]

This is all french stereotypes in just one person.

[@Jkirek_]

that's german, not french. please learn your stereotypical foreign english accents

[@DerSim688]

@Jasper Kole I hope you are not serious?

[@BlackBirdJacobo]

+Jasper Kole I know but I assure you that guy's English is French af.

[@DerSim688]

+Jasper Kole +Jacobo Pinadado well, as a german who also speaks French let me tell you: obviously French Dialect ;) if you still dont believe me just google his name.

[@RubALamp]

Jasper Kole PLeASe LeARn YouR STeREoTyPicaL ForeIGn EnGLisH ACceNtS.

[@ramata1962]

What a positive and happy professor. It helps get over the accent. His personality is very clear ie, he's clear.

[@mythbusterman8541]

One of the best guest appearances in numberphile history. What a legend.

[@skroot7975]

Cool maths! His moustache is magnificent. Also, Putin ancestor at 9:26? :p

[@matteochancerel9332]

I was exactly thinking the same thing xD

[@johnchessant3012]

Especially the one in the background! :D

[@HawtDawg420]

Right??

[@edancoll3250]

At 3:10, I was really hoping to see a ≡ sign. I f***ing love those.

[@EcceJack]

Wow... at the very beginning I was like "meh, just playing around with fractions", but by the end *mind = blown!!* :O

[@hyperghoul]

learning math with super mario

[@Jhauty]

I'm INSTANT LAUGHING OF YOUR COMMENT

[@stefanschacht3322]

He looks a bit like Saddam Hussein...

[@Ivan_1791]

Hahaha. xD

[@franekpiechota6514]

After video he is going to save queen pich

[@almarkowbender]

Mario is Italian not French...

[@9cool10]

i love this guys accent, cant quite put my finger on why. also i learned a thing today ^^

[@basbas192]

9cool10 French Accent. Pretty much have the same.

[@9cool10]

ahh yeah, now i can hear it XD its a really cool accent though.

[@CastelDawn]

***** yeah, it's weird to hear when you're french

[@CastelDawn]

***** really? well, that explains the clothes

[@pedroheck3667]

I start laughing for no reason watching this, it's so incredible

[@johnchessant3012]

6:02 - 'Something to do on a rainy day. List all fractions p/q with 0 < p

[@davidgillies620]

There's 16691 of them. Partitioning them into triplets yields 16689, all of which are Farey sequences. In Mathematica a simple-minded way to do it is: Select[Partition[ Union[Sort[ Select[Flatten[Table[p/q, {p, 0, 234}, {q, 1, 234}]], #

[@jonahdavis7833]

His 2's are written so fancy, they even look French

[@zorm_]

he is french :p by the way he has a huuuuge french accent when he speaks english

[@Ian-nl9yd]

+Zorm we know

[@zorm_]

pipi prout

[@Triantalex]

false.

[@lukeusperez8585]

"I thought that we could talk about ghfrakkktions"

[@darkmage07070777]

This video would have been worth watching to learn about the circle-plus sign trick alone. The fact that the entire thing is full of interesting stuff puts it over the moon.

[@andrewmole745]

This is one of my favourite Numberphile videos. He has such a joy in his subject and in explaining it, coupled with a great sense of humour.

[@tg13fire]

I have watched this video like 40 times. the way he writes down the numbers is so different from everybody else. 2 and 9 are the most unique out of any of them

[@AmonAmarthFan609]

Am I the only one that thinks his (obviously French) accent sounds like it has some German influence?

[@Dave-iz6lh]

Maybe he lives in Strasbourg!

[@antonanairamendoza7193]

He is Californian

[@maximmillennia]

Now I cant unhear it

[@gamingcat341]

Mar'kusi Rosenburg same

[@nbrader]

My first thought was that he looked German and my second thought was that he sounded French. I think the way he looks probably influenced you.

[@SmappleMcWingers]

Is he using "my pinky told me" as the idiomatic equivalent of "a little bird told me?"

[@CreepyHandedMan]

Matthew Kelley Yep. In french, we say "mon petit doigt me dit". It's a bit old-fashioned though, but this guy nails it with his overall attitude and appearance, he's amazing.

[@kentoutcourt]

Might be old fashioned in some places (I guess you're in Europe) but it's still very popular in Quebec

[@flynnwilliford980]

This guy looks like Jeremy Clarkson's clean-cut Belgian cousin.

[@bcubed72]

He looks like Vicente Fox. Doesn't sound like him, though.

[@paulgillespie542]

He's so deliberate and clear in what is clearly not his mother tongue.

[@pecabokem4345]

I would love to know the deeper explanation for this.

[@coosoorlog]

I hope this guy also has a video about the mathematics of yodeling

[@cchimozmin]

My new favourite Numberfile video. Blown away. Classic Numberfile. I was so excited watching that. It's like magic. There must be something fundamental about patterns like that. What field of mathematics is that? Pure maths? Gonna do an OU course I think. Never too late.

[@RotundRager]

This guy is super energetic about math. I'm glad he seems to genuinely enjoy it that much. I can't get that hype for math, but I can appreciate someone who does.

[@maklasik]

Braum, is that you?

[@newgoredan303]

Ahahahahah

[@123FireSnake]

maklas ho ha hahaha

[@archmage1999]

maklas There will be a new skin for Braum, his shield will be a blackboard =D

[@MenwithHill]

Kil'Jaeden "Big Professor Braum", now available for 975 RP.

[@ItsSansom]

maklas Braum is here!

[@BlooregardQKazoo-ff6wb]

Really liked this guy, you should have him on more.

[@XTeaOrCrumpetsX]

"Pages and pages and pages and pages." This guy is awesome haha!

[@WandRindustries]

The neatest handwriting of any individual you've ever had on this channel. He's definitely breaking the stereotype of mathematicians with poor script.

[@Adamas97]

This was amazing. I would have nothing thought about this but seeing it happen was mind blowing for some reason. Great video! (As always)

[@kojuha1]

Guys, please, I didn’t get the statement, Every triple of what is a farey sum? I’m serious

[@jacefairis1289]

'I thought that we could talk about frrractions.' Great way to start a video. c:

[@veggiet2009]

when you got to 13:14. My eyes got wide. That's awesome!

[@imrcorp1]

We need this man to return and save 2020

[@TheMaplestrip]

This guy is awesome - I hope we'll see Francis more often! :D

[@TheHomeless87]

Cauchy looks like Vladmir Putin

[@igesio]

My exact thought

[@BugSunder]

YESS i thought this

[@FreeScience]

TheHomeless87 Was about to say, but I had to search the page for "putin" first :P

[@freddykrueger5503]

TheHomeless87 man I just posted that exact same message a minute ago.now I scroll down, see your comment and realise I was not the only one who thought so!

[@daisshitpostclub1239]

TheHomeless87 more like stalin

[@IDthief1]

honestly this guys smile makes me so happy, like he looks genuinely happy throughout all of this.

[@aidabit7554]

Warm... fuzzy... feelings!! This must be a rare sighting of the time traveling Favorite Grandpa/Great Uncle Francis

[@123paddy09]

That French accent

[@alexpigeon692]

More videos with Francis Bonahon, please

[@AnimusPrime87]

This guy is one of my favorites.

[@guycomments]

One of the more interesting videos in a while for me. Hoping we get more videos with Francis.

[@Nuke_Gunray]

This Ford Circle Packing... it's a fractal, isn't it?

[@Yoreni]

it looks like one

[@uPenguin]

Fractions is very niiice, high-5!

[@AzazeoAinamart]

Well, this is amazing. Such connections in math always makes me think how beautiful our universe is

[@antoniedepotter3371]

Best video ever on Numberphile. Amazed by all the conclusions that were made. Just brilliant!

[@TheRealFlenuan]

J'adore son accent !

[@renaared]

Sincèrement, on dirait une parodie de notre accent haha

[@iagocasabiellgonzalez7807]

Awesome! This might be my favorite Numberphile video to date! I've been drawing those kinds of circle patterns for years. Many thanks Brady! : )

[@treespunk]

As I see it this is the most authentic French accent of English ever spoken by a human being

[@reedplaysgames]

Ah yes, *myootiplication*

[@Henrix1998]

Still waiting for Toyota Circles

[@GeorgeRPope]

Well we could be sure that they'd be more reliable.

[@1DInciner]

Audi one

[@ibrahimaswade42]

My best numberphile so far !

[@gfx2006]

I can't stop listening to this repeatedly :) 5:41 "bages and bages and bages and bages..." Love his accent and his looks. He's just like a cartoon character comes to life!! Seems like a super nice guy to hang out with too!

[@ben1996123]

cool. the circle thing is like the dirichlet function

[@Deathranger999]

A serious comment from Ben? What is this?

[@JonhamYT]

ey ben

[@ben1996123]

Kieran Kaempen this is maff ***** ello

[@goingquentin]

ben1996123 hi ben the slidy man

[@monk_marius4338]

The Dirichlet function is 1 when x is rational and zero is irrational which doesn't seem related to Farey addition.

[@DaKnightsofawesome]

Dat moustache doe

[@FireyDeath4]

It's just so satisfying when mathematics fit in together SO. WELL.

[@AKhoja]

The way he says "prime" makes my day!

[@nogahlerman6137]

Who needs an ark??? I Noah guy!

[@user-cn5pm7zg1u]

bad

[@Slithy]

This guy's accent is dope as f. Where's he from?

[@rhysappa]

France.

[@Slithy]

rhysappa Thanks.

[@theproofessayist8441]

"Let us break the rules": YEAH LOVE PURE MATH ANARCHY!!!! To quote Heath Ledger's Joker, "upset the established order, and everything becomes chaos. I'm an agent of chaos. You know the thing about chaos??? It's fair!"

[@eldizo_]

The circles being tangent like that is just amazing. Hooray for funny fractions!

[@JonhamYT]

n-th comment

[@bitchslapper12]

What are the chances of me meeting this man totally wasted, beyond his mathematical mind, on this year's Oktoberfest? (Answer in a fraction please).

[@spheal4754]

number ------------- number

[@AnCoSt1]

He not German...

[@CubeBag]

p/q

[@LawffleCopter]

CubeBag now puttiply number/number by p/q

[@bitchslapper12]

AnCoSt1 Sorry, I now believe he's French after further investigation of his accent.

[@blazebluebass]

That was beautiful! It is so fantastic that there are all those weird connections in mathematics in fields that do not appear to have anything in common. It is even better if those can be displayed by some geometry - then it is just pleasure to watch.

[@Cold_Ham_on_Rye]

I was like, oohh this will just be a boring basic fraction thing... but no it turned out to be the insane fractions are magical and beautiful thing. We need more of this guy.

[@icrin_]

I really want to know which programs were used to do these graphs and calculations.

[@RamsesTheFourth]

Icaro Vasconcelos I think he made them himself... its easiest way, I would use probably Python :)

[@Blistio11]

Icaro Vasconcelos probably something specificaly made for this. a pretty easy application to make, at that.

[@janvarhol]

Icaro Vasconcelos most of programming languages have graphical library. on top of that there is a lot of educational and academic SW. just google it if you are interested. when I was at school we used to do clickable fractal expansion of various sorts. this should be the same. it was a few lines of code, nothing special.

[@icrin_]

thank you all

[@JanM351531351]

Icaro Vasconcelos Possibly mathematica.

[@gfetco]

Eyy, Luigi funny fractions eyh?

[@jonasbindslev9894]

I think it is crucial that we have this amazing person explaining this, because otherwise it would probably be pretty boring, as well as being just silly. It needs a funny personality to talk about a funny fraction. P.S. I am absolutely in love with his handwriting

[@Bourbonismbeta]

This man is amazing. We need more videos of this man.

[@tom7]

This guy is so amazingly charming! And I learned a cool new thing!

[@dgtlrn]

I think everyone has a new favourite mathematician on KZbin!

[@yungml]

This was truly amazing, more of this great guy!

[@gruingas]

This guy has the most amazing accent ever and this is the most amazing thing about fractions I have even seen.

[@JackSassyPants]

His handwriting is absolutely immaculate, especially the way he writes the numeral 2.

[@Ounaide]

Finally a french mathematician on Numberphile ♥

[@JoelLeBlanc]

You had me at "FRACTIONS"! What a marvellous character!

[@berkeleycreager3601]

No one's talking about how beautiful this man's penmanship is

[@robbyroth18]

I don't currently know the exact reason, but this is my favorite numberphile video.

[@MrDrewbies]

This blew my mind, I love stuff like this

[@yuvalne]

The way he says "prime" is incredible

[@Keyywiii]

Holy shit this guy is the best. I could listen to him tell me math things all day.