Find yourself someone who looks at you the way this guy looks at circles. This is true love. It's beautiful.

@fyradur

3 жыл бұрын

Ain't nobody who touches you tangently like him

@koendos3

3 жыл бұрын

Both thing have 1 thing in common, they kiss

@baras9700

3 жыл бұрын

boi, u haven’t watched his question 6 video have u😂

@OrBIT_learn

3 жыл бұрын

@@baras9700 I have. He said he literally cried after solving that question because he was too happy.

@joshdoyle182

2 жыл бұрын

I keep looking at girls like that, and they freak out.

This video has instilled me with the very bizarre experience of knowing exactly what you are doing whilst also having no bloody clue what the fuck you are doing.

@robertvermillion6816

7 жыл бұрын

I know it's called "circle inversion" but I too do not have the foggiest idea what circle inversion actually does.

@justclosing

7 жыл бұрын

When it's finished..what do you do with it?

@shaideshe4150

7 жыл бұрын

Imagine you're inside a circular mirror and you draw a shape on the floor, the inversion of this shape through the circle is how you'd see it in the mirror

@TebiByyte

7 жыл бұрын

Welcome to the world of math!

@wansichen3743

7 жыл бұрын

try searching for something called hypobolic geometry,hopefully it helps

this is a 26 minute video of a man trying to find the relative radius of a circle, and he is very happy too.

@YtseFrobozz

5 жыл бұрын

It's a long way to go just to get the radius of a circle, but it's kinda worth it for the look of pure, distilled insanity at 21:50.

@TakaExc

5 жыл бұрын

He's like the Bob Ross of mathematics

@patxmcq

4 жыл бұрын

@@YtseFrobozz 😂😂😂

@tomwallen7271

4 жыл бұрын

The one thing I got from this video is that there are many many circles, and this guy is having a great time.

@mehmetcy84

4 жыл бұрын

Ytse Frobozz 🤣🤣🤣🤣

“If you kiss in real life you have to kiss in the inversion too. Exactly”

@wknw1442

2 жыл бұрын

i feel bad for my inversion now

@nrm224

2 жыл бұрын

@@wknw1442 i pulled a few muscles trying to kiss my inversion IRL.

@PC_Simo

Жыл бұрын

@@nrm224 I presume that was before you figured out you just go right up to the circle of inversion, and kiss the perimeter.

@davidgould9431

Жыл бұрын

"Kiss" is a terrible way to describe two lines being tangent to each other. In real life, kissing still keeps the two people or things separate: just very close together. Tangents actually share a point, so the kissing point is necessarily the same in both the real and inverted world. I've watched this video a few times and this question always bugged me.

You should really ask for consent before touching tangentially.

@cameronwilliams7930

4 жыл бұрын

13:52

@peterparker-or2os

4 жыл бұрын

And don't get me started on the kissing circles...

@SriRamDasariChandra

4 жыл бұрын

Say no Mohr...!!

@thomasd2444

4 жыл бұрын

@@SriRamDasariChandra - nudge nudge

@steamer1

4 жыл бұрын

Ever been kicked in the tangetiallys?

8:35 "Gee you've got good instincts" is my favorite part of the video, the dynamic between these two is hilarious

@conkrcstf6405

3 жыл бұрын

Im thinking Simon originally thought I'd be an oval

11:59 He said 'Circle inversion!' with the same level of happiness how Hulk said 'Time travel!'.

@sicapanjesis3987

2 жыл бұрын

I see this as a absolute win

@TeganCantEven

Жыл бұрын

Omg. And not only with the same enthusiasm but practically the same cadence!

@BMLBiz

Жыл бұрын

​​@@TeganCantEven and body language... well it was similar

For anyone wondering, the general formula for the area of the nth blue circle (and the nth number in the sequence) will be 1/(15+4*n*(n-1))

@maulwurf9414

5 жыл бұрын

Chausies thanks I might need this eventually

@ayaipeeoiiu8151

4 жыл бұрын

Fluffy Boi pretty simple it turns out that you have to add 8*n at the denominator each time

@g.tucker8682

4 жыл бұрын

Finally, some actual information! Thanks.

@matthewcare9731

4 жыл бұрын

sat thru the entire thing, even tho it is absolutely beyond me. however, despite not understanding the circles per say, the pattern jumped out within seconds, but i could only think of it iteratively. well done finding the general. i wish he had related the geometry to that closed form explicitly. anyway, learning about the inversions was cool.

@asarnatskiy

4 жыл бұрын

@@ayaipeeoiiu8151 exactly my thought indeed. I was satisfying hearing the 1/95 at the end, because it was a predictable sequence from the beginning.

Funny to note that 1/95th is also the portion of this demonstration I've understood.

@-42-47

5 жыл бұрын

It is also 1/95th as efficient as just measuring the tiny circle. Though a video where they just do that would only be about 1/95th as interesting to watch.

@coolgarrett17

5 жыл бұрын

@@-42-47 Measuring the tiny circle isn't efficient because error gets amplified at small distances

@alexalt2630

5 жыл бұрын

Haha yes. I wish he was clearer

@gjermundification

5 жыл бұрын

@@alexalt2630 Which part needs to be clearer?

@gjermundification

5 жыл бұрын

@@alexalt2630 What he shows should make you able to do unlimited iterations of this if you have enough paper; or pixels.

I'm glad the whole thing came full circle in the end

@error.418

8 жыл бұрын

+charles paradise *groan*

@fluffycritter

8 жыл бұрын

+charles paradise I see what you did there

@sabitalam5277

8 жыл бұрын

+fluffy I'm an app developer and I'm absolutely *APP*-auled by your statement - I'm afraid I'm going to give you a *PUN*-ishment. *bad trombone sounds*

@aceman0000099

8 жыл бұрын

*dies from pun

@NickiRusin

8 жыл бұрын

+charles paradise It's a shame this video doesn't circulate online more. It deserves a round of applause.

I just love how happy Simon is the entire time, this is a man who truly loves what he does

@shahchintan420

8 ай бұрын

He's just high

Beautiful construction. I suspected the final result from the other denominators: 15, 23, 39, and 63. From 15 to 23 is 1*8. From 23 to 39 is 2*8. From 39 to 63 is 3*8. From 63 to 95 is 4*8. But it's worthwhile to watch him construct the inverted circles and enjoying it.

@matthewziemba7526

2 жыл бұрын

I did the same thing! It was very satisfying to see that I worked it out correctly! I definitely would need to study it a bit more to understand how the circles all worked though... 😂

@Achill101

2 жыл бұрын

@@matthewziemba7526 - thank you for reminding me of that video. I watched it again :-)

@B.M.0.

2 жыл бұрын

kind of seems like a waste of time really when basic sequence math gives you the result in 5 seconds not 26 minutes. I bet the analytics on this video show no watch time between 3:37 and 26:24

@Achill101

2 жыл бұрын

@@B.M.0. - I see the meaning of that video in introducing the Inversion At A Circle and giving an example. While I find the inversion elegant and appealing, there seem to not many examples, unfortunately: Ptolemy's axiom, Pappias circles like here, geometrically constructing circles that touch other circles. I would like to know more examples. But I found the construction here marvelous from 14:00 on. Have other watched it, too? If not, I consider it their loss. Watching videos is often "wasting time", but it can be also very entertaining. . . . About basic math giving you the results instead: you would still have to prove it. Also here, some steps are cut short, like the radius of the inverted circles being R/16. Yes, I can prove it myself, but they should have added it to the video, I think.

@PC_Simo

Жыл бұрын

Same here 😅.

I like the part when he said circle

@danielhricmail

5 жыл бұрын

So the whole video pretty much

@andycheng4436

5 жыл бұрын

I like the part when the pen was on the paper

@teakfreeman3543

5 жыл бұрын

the part where h

@birb1686

5 жыл бұрын

So did i

@maulwurf9414

5 жыл бұрын

I liek potamto

this guy scares me, he's eroticly in love with maths.

@FairyNuffMuffin2

4 жыл бұрын

You might say he's a numberphile

@amineabdz

4 жыл бұрын

@@FairyNuffMuffin2 badum tssss

"This is epic. This is seriously epic... This is absolutely epic."

@maxwellsequation4887

3 жыл бұрын

It is epic

I love hearing smart people talk it makes me feel smart

Just imagine trying to solve the initial problem, and you think, "quadratic mirrors" and it works

@jobliar937

5 жыл бұрын

think it is a series look for a common difference in the denominators. I mean you can even write the equation for f(n) of it

@ahmeduygun7320

4 жыл бұрын

@@jobliar937 it must be a series since as you see towards the end what changes for each of those small little blue circles is just one addition of purple circle that is between two parallel lines

@PercyPortland

4 жыл бұрын

Ahmed Uygun Still trying time figure out how to describe the formula, but am I off in thinking the next in the series should be 1/135?

@jimvj5897

4 жыл бұрын

@@PercyPortland You are correct. As others have pointed out, the general formula for 1/radius of nth circle is: (2n+1)^2 + 14 where the first blue circle has n=0.

@russellfautheree4650

4 жыл бұрын

@@jimvj5897 I know it might not be prettier to everyone in an "a*n^2+bn+c" form, but I did it anyway. 4n^2+4n+15. I hope. Been a long time since I touched algebra. I like it in a form that hides the magic.

Beautifully explained. I was excited as a child when the purple cirlcles began to align! hehe.

@numberphile

9 жыл бұрын

Francisco Ibarrola glad you enjoyed it

@user-qq6si7zv3t

8 жыл бұрын

+Francisco Ibarrola Purple crayon much

@CTJ2619

8 жыл бұрын

+Numberphile awesome video guys. brilliant

@842Mono

7 жыл бұрын

I wish I could watch that when I was younger really!

@e1woqf

7 жыл бұрын

me too!!

Rewatching this a year later and man there are just too many great lines (both in terms of geometry and dialogue ;)

@SuperReznative

4 жыл бұрын

trequor Hah..yup. Shalom

@sudheerthunga2155

4 жыл бұрын

Me too!

Genuinely one of my favourite videos ever on this platform. The pure joy is infectious

@toferg.8264

Жыл бұрын

For sure!

I can't pretend that I understand it, but I do so much enjoy this guy's enthusiasm! He is absolutely loving it!

@xavierpaquin

7 жыл бұрын

Phew!!! This is epic!

@Beremor

7 жыл бұрын

I was thinking the exact same thing! In honor of his enthusiasm, I might actually really try and really understand what's going on. :)

@MGmirkin

5 жыл бұрын

Frankly, he's doing that which is the sole function of GOVERNMENT... Taking something **SIMPLE** and **needlessly complicating it** ... ;) (Yes, that's a reference to Burt Gummer from Tremors...)

@joshuajames78

5 жыл бұрын

Yes, Adam! I agree!

Professor: "Show your work" Me: "NO."

@cooling9953

7 жыл бұрын

Standard

@ReZort

7 жыл бұрын

lol, if I had this problem, then i wouldn't do it either

@eliasthememelord

7 жыл бұрын

Kitty Forest fires

@y0Luda

6 жыл бұрын

why though..? that's just disrespectful.. just remember how much effort he puts into teaching you things. that's valuable time...

@Fudmottin

6 жыл бұрын

It's my time. I paid for it.

26:29 *Laughs in Mathematician*

@SuperReznative

4 жыл бұрын

Rusty Shackleford : )

13:52 *vigorously rubs hands* “This is the reason why I came.”

@kakonya2994

4 жыл бұрын

Read this exactly when he says it.

It's just adding an arithmetic sequence. 15 + 8 = 23. 23 + 16 = 39. 39 + 24 = 63. 63 + 32 = 95.

@gregor849

6 жыл бұрын

Same idea...

@adb012

6 жыл бұрын

Here you have another one 15 23 15+23+1=39 23+39+1=63 39+63+1=103. Ooooopsy.

@howardg2010

4 жыл бұрын

Me 32 seconds in: "1/95" 26'35" pass Me: "Yup."

That brown paper should be framed and hung on a wall. Beautiful!

It's been 4 years since I first watched this video. I was in high school. Numberphile gave me so much passion for mathematics that I'm now in university. Now, 4 years later, I can finally understand this video.

I love how the spiral of circles inverts to identical circles in a straight line

I have no idea what I just watched but now whenever I close my eyes all I see are circles.

@derciferreira7211

9 жыл бұрын

LittleMikey this is related with hyperbolic geometry.

@davecrupel2817

7 жыл бұрын

LittleMikey Regrets?

@GamingMCUniverse

6 жыл бұрын

derci ferreira Euclidean geometry is not the same as hyperbolic geometry

@hiromiarash172

6 жыл бұрын

I don’t understand....

Please purchase this guy a compass which you can mount pens and markers in.

@outtabubblegum7034

6 жыл бұрын

I recommend a computer.

@maxnullifidian

5 жыл бұрын

DarkArachnid, that should've been rather obvious, no? LOL

@silentgolden8507

5 жыл бұрын

He didn't use it for a reason could you guess the reason......?

@YorranKlees

5 жыл бұрын

Doesn't change the way your brain computes. Besides, you still need a decent algorithm from your brain for the computer to compute.. That is, if you're the one actually giving it a thought. Personaly I would recommend a brain before getting the computer. Which surprisingly gets all back to the original point : where is Numberphile going today ??

@clementlefebvre9835

5 жыл бұрын

He actually already has one, he just doesnt use it ^^' :D Painful to watch ^^

I've learned something new today: Complex maths makes me cry.

@mariuswisser1555

4 жыл бұрын

Just my thoughts

@clockworkkirlia7475

4 жыл бұрын

Oh, this isn't *complex* maths, precisely... "i" shudder to think. :p

@clockworkkirlia7475

3 жыл бұрын

@@merge3550 Oh, that's okay, I can probably do something silly (yet strangely elegant) with exponents to fix it.

5:58 - "So the radius is 60." -> Every math teacher: "60 what? Apples? Bananas?"

@jared8515

4 жыл бұрын

At first I thought it was mm but I got super confused when it looked more like 3cm and not 6

@PaulPower4

4 жыл бұрын

I suppose the thing about maths teachers is that they're not just teaching you for maths, they're teaching you for physics, engineering, etc., where having specific units of distance is important. In pure maths, it's enough to say "60 arbitrary units of length" or even just "60".

@pranavlimaye

3 жыл бұрын

@@jared8515 6:24 dude it's clearly 6cm.

@andreasschelfhout3472

3 жыл бұрын

@@PaulPower4 In engineering you often find that parameters are "non-dimensionalized" to obtain a general solution, and then you slap on some scaling factors to get the result that fits your needs.

@snbeast9545

3 жыл бұрын

Not the higher ones. IIRC mine stopped caring beyond Algebra I (or whatever equivalent), unless the problem calls for units (How much thread? or How long of a fence? when your numbers have units).

The editing was really nice. I'm sure that explanation took forever in real time. Really cool stuff.

@MathHacker42

9 жыл бұрын

The explanation took forever after editing, it's nearly a half an hour long.

@Bluemilk92

9 жыл бұрын

MathHacker42 You'd have to be a rather impatient type of person to consider a half hour as "forever"

@RichardHoman9009

9 жыл бұрын

Bluemilk92 Maybe in normal circumstances, but this is a KZread video. They tend to be "long" at just /ten/ minutes. (Mind you, I don't necessarily disagree with you. It's just worth considering.) I, for one, loved this video :)

@MathHacker42

9 жыл бұрын

Bluemilk92 Yeah, I may have been a bit hyperbolic, I just meant that it was much longer than a typical youtube video.

@Bluemilk92

9 жыл бұрын

MathHacker42 I guess it just matter what type of content you watch. Since I often watch video-game related videos, I rarely watch anything under 20 minuets

He keep using the word "simple", but this is the inverse of simple

And this is how Alfa Romeo came up with their wheel design

18:06 "... these two circles are lines ..." was about where slipped out of consciousness

my head just exploded

@numberphile

9 жыл бұрын

Ernesto Roybal ouch

@ernestoroybal3682

9 жыл бұрын

I don't recommend it.

@lucaspluijgers2975

8 жыл бұрын

Ernesto Roybal MY HEAD JUST EXPLODED 100 TIMES MORE! why? well you can see 1 on 15, 1 on 23 (plus 8), 1 on 39 (plus 16), 1 on 63 (plus 24) and 1 on 95 (plus 32). so at the start i thought "is it 1 on 95???" at the end "OMG I FRACKING KNEW IT!!!!!!!".

@myravied7965

8 жыл бұрын

Lucas Pluijgers i had the same, the question is what has that progression with 8*n to do

@lucaspluijgers2975

8 жыл бұрын

Awesome

23:40 Pirate does math

@PeterBarnes2

7 жыл бұрын

Not as exciting as a pirate becoming a student union president.

@sul4509

7 жыл бұрын

d:^)

@tristancollins8789

7 жыл бұрын

LOLOL

@mirko5250

6 жыл бұрын

best comment so far

@fergusfisher1315

5 жыл бұрын

AAAAARRRRRRRRRRR

I am not at all exaggerating when I say that this video was what put me on the path to becoming a math major. Thank you

I was wondering as to how many people figured out at one glance that the radius of the inverted blue circles was in fact R/16. He totally glossed over that detail. It is a fun little exercise to confirm that it is indeed the case. Also, following this derivation, it is not that difficult to arrive at the general form for the nth circle radius. This has to be one of the sweetest numberphile video I have watched!

I've watched this 4 or 5 times now, and I really feel like I understand it. I use geometry at work constantly (I make custom stairs and handrails, nothing but triangles, circles and the occasional ellipse) and the more I watch this the more I know that this doesn't help me to do with anything with my job, but I love it anyway.

@stephenparker7478

6 жыл бұрын

Perhaps if you were a watchmaker :)

@SWIM5QUAD

5 жыл бұрын

Functional

@alexalt2630

5 жыл бұрын

Stephen Parker True point! Didn’t think about how gears are kissing each other in a similar manner

Touching tangentially sounds naughty.

@Ludix147

8 жыл бұрын

or like the name of an indie rock band

@sfpt

7 жыл бұрын

+Kazza FDM genital*

@LuukvdHoogen

7 жыл бұрын

It does sound kinkier than kissing, now that you mentioned it.

@justclosing

7 жыл бұрын

You're mixing up tangent with tanga and the string theory

@Kebabrulle4869

7 жыл бұрын

what is this comment chain

Beautiful! I love explanations where I get lost, but end up understanding.

Of course, you can give the next number in the sequence immediately, just by noting that the denominator increments by 8 more each time. 23-15=8, 39-23=16, 63-39=24, and so 95-63=32 --> 95 is the next denominator. But nonetheless, this was just an incredibly fun video, and our man's enthusiasm is just amazing and contagious.

When you watch and listen to someone like this guy who is SO passionate about something, you cant help but become interested. I love people like this. I wish all the teachers of our children could have this kind of drive.

@1:24 From now on when I wish to use the word: "kissing" I will substitute the expression "touching tangentially".

@mercybellafiore3677

9 жыл бұрын

Yeah, I got to first base last night... I touched Sarah tangentially. No big deal...

@EmdrGreg

9 жыл бұрын

Unfortunately, that would have to exclude touching where anything happens to cross the tangent line--

@manioqqqq

Жыл бұрын

Bro, i had a dream that i touched my crush tangentally (r/outofcontext)

if you have a chrome sphere you can actually watch this happening with real reflections

@canal000

2 жыл бұрын

how is that?

I thought the title of the video was the guys's name: Eric Circles I'm not that bright lol

What did I just watch.

@davecrupel2817

7 жыл бұрын

something... _sniff_ ...beautiful....

1/15, 1/23, 1/39, 1/63, ... 15, 23, 39, 63, ... the difference between each number forms a pattern: 8, 16, 24 the next difference would be 32 63 + 32 = 95 the next number in the series is 1/95 the series continues: 1/95, 1/135, 1/183, 1/239, 1/303, 1/375, 1/455, 1/543, 1/639, 1/743, 1/855, 1/975, 1/1103, 1/1239, 1/1383, 1/1535, 1/1695

@danlmd1

8 жыл бұрын

The equation to solve for it is 1/4(4+(n-1(n)))-1 when n= the place in the sequence you are solving for

@JacobShepley

8 жыл бұрын

danlmd1 try 1/( ( 2n+1 )^2+14 ) n starts at 0

It's been a while since the first time I watched this, but after seeing it again I think it's my favorite Numberphile.

There's something really gratifying, satisfying and fulfilling about seeing you folks do mathematics in these comments. It feels like you're using your keyboards to the extreme. Flexing almost. While having fairly enlightening, very intelligent, nerdy conversations! And as a nerd myself, i love it!

New drinking game, everytime he says circle, take a drink

@sonofnone116

5 жыл бұрын

I dont want to die.

@sebastiantinsley9812

5 жыл бұрын

ill be pickled

@TheTenthBlueJay

5 жыл бұрын

Drink orange juice

@TheAechBomb

5 жыл бұрын

I'm not playing, but I died from alcohol poisoning by proxy

@antirediska5454

5 жыл бұрын

Like Russian-Russian roulette? :D

Epic circles but every time Simon says circle it speeds up Video only last 2 minutes

@TheJFARod

4 жыл бұрын

Even less!

@themrflibbleuk

4 жыл бұрын

I read this comment at the perfect time.

@FairyNuffMuffin2

4 жыл бұрын

That's how long the video where he only says circle is

@cecillemilitante3115

4 жыл бұрын

Speeds up by what number?

@Palladox22

4 жыл бұрын

what if you drink every time? 😂

Watched this when I was still young at 2016, so I didn't understand much, thinking that it wasnt that impressive. Watching this video again made me realize how amazing this actually is. Dayum.

This is my favorite video on numberphile i wish i could see more constructions from this dude, Australia represent

This guy's enthusiasm is the best =)

I thought it would be 95 because the difference between 15 and 23 is 8, 23 and 39 is16, 39-63=24, so 95

@yyGODyy

9 жыл бұрын

yyGODyy Ha i was right. Bitches!

@mattmarsh1566

8 жыл бұрын

yyGODyy yeah i thought the same thing, lol no need for the 20 minute explanation

@shadrack1701

8 жыл бұрын

yyGODyy But what he showed us was the way to prove this using geometry. We could all reasonably assume 95 was the answer (as did I) but using this method it shows the poof of that, very cool.

@rasowa2958

8 жыл бұрын

+yyGODyy Yeah, I spotted the same thing (+8+16+24+32). Geniuses like us don't need to draw any circles :)

@andrewxc1335

8 жыл бұрын

+yyGODyy Right-o. Now prove it by induction.

11:25 When the lecturer asks a question

@Mswordx23

3 жыл бұрын

You don't expect to be asked a question so your brain momentarily short circuits even though it's an easy question xD

Wow, if I had known this it would have made...something...much easier to figure out. Maybe. Probably not.

"Yo Dawg, I heard you like circles so I put circles in your circles" :o

@liltunwin

8 жыл бұрын

+Justin Lew (MC Gamer) That are touching the circles you put in your circles.

@hannesjvv

8 жыл бұрын

+Justin Lew (MC Gamer) Reminds me of XKCD 855. Before all the other "great" minds of the web, Zombo.com's designers used the awesome of circles.

@paulinethegreat1

8 жыл бұрын

+Justin Lew (MC Gamer) You still don't sound nearly as suggestive as Simon saying the circles are kissing... I will never think of tangents the same way again...

@tangobravo5752

6 жыл бұрын

Ellipse My Ride!

From the thumbnail, I thought it was Matthew Santoro with a wig on.

@RelatedGiraffe

8 жыл бұрын

+STaSHZILLA420 Lol, me too.

@Ken-zd4pv

8 жыл бұрын

+STaSHZILLA420 I thought a much younger Bob Ross

@oliverpage2833

8 жыл бұрын

you beat me to it!

@ethanweber5182

7 жыл бұрын

KILLER KEEMSTAR

I'm here again 6 years later, having watched the most recent video on how inversion works, and I can confirm, this is much easier to follow! Still got a little bit lost at the end, but the general idea of how things come together is understandable :)

22:08 he even bruised his finger doing this. Creds to that. Totally LOVE this video, probably the best thing on youtube. SOOO awesome and satisfying.

For all you commenting about adding 8s repeatedly to the denominator, the most important thing you have to realize is that noticing a pattern does not amount to a proof. The techniques he showed in the video (applied a bit more rigorously, albeit) certainly do. That's the important part. He proved the result, and in quite a marvelous manner.

@RYFAMO

8 жыл бұрын

+Kieran Kaempen I might not be a mathematician, but isn't mathematical induction a valid and accepted proof technique? I mean, yes, you could draw a lot of colourful circles for a few hours, but inducing the theory is a lot more practical - especially in real life, when you don't have the time (or even the skills) to elaborate a fancy (and in this case quite unconventional) proof. Nevertheless this was a very interesting approach to the topic and encourages to think out of the box more often.

@santoriomaker69

6 жыл бұрын

I think that Simon (the guy from the vid) shouldn't reveal that many numbers in the pattern, since I can also see a pattern among it (nevertheless, a really beautiful and epic proof). If he did, like say reveal 2 numbers, then the general audience wouldn't be so cocky about it having to SuDdEnLy have the next number. Side Note (a REALLY late reply to RYFAMO): The proof Simon presented is a problem WAYYY back when geometry is the algebra of ancient math times.The chain is called the Pappus chain and it was obviously discovered by Pappus of Alexandria on the 3rd AD century. So Pappus actually proved this using the Inversion method, without ANY mathematical induction. So technically speaking, it's a practical proof from ancient times.

@semajxocliw

6 жыл бұрын

RYFAMO noticing a pattern and testing it repeatedly is not induction. induction is testing base cases and then showing that because the base cases worked, the next case will also work. Just saying "here's an observed formula for the nth case" doesnt prove anything.

@jeffreyblack666

5 жыл бұрын

How does it constitute proof? He noticed the pattern matches the circles. That no more constitutes proof than noticing it matches a formula. So his "proof" is no better than simply saying the nth number is 1/(4*n^2-4*n+15). All his "proof" actually amounts to is the equivalent of saying 1/(4*n^2-4*n+15) is 1/95 when n=5. He has failed to show that this pattern should correspond to the circles rather than simply matches. And that is something that it would be impossible to do as does not fall into the realm of proof.

@mapetlv

5 жыл бұрын

The issue here is that the question was introduced in a form of find a pattern question. And then he started drawing circles. So technically all those "adding 8s" are correct answers to the question.

Brady, this video isn't too long, at least not for me. I have always had a love for circles, so this is right up my alley. It looks like this video could have been two hours long. I would have still watched it multiple times.

This is why mathematicians+graphing programs=LOVE. I'm sure it's the same feeling as when Lotus 1-2-3 came out for the accountants.

Taking a class on Neutral and Hyperbolic Geometry and inversions now make a lot of sense to me! I love this!

Dude is by far the best Numberphile guest.

just wow. that structure is truly beautiful. so many amazing properties.

this is so amazing, he does not overstate how beautiful this is

This was the first Numberphile video I saw a few years ago. I think I've seen them all now, and it came back up in my feed. I've gone full circle on Numberphile, on a video about inverted circles! I may get this as a tattoo!

But why is it 1/15? :(

I wish I had the programming skill to write some drawing software for this! It would allow you to draw a circle of inversion first, then you could draw whatever shapes you liked inside or outside it. I'd want to see what happened if I drew squares or triangles... they'd probably come out really weird and distorted. **gasp** and then someone would write the 3D version, with a sphere of inversion. And you could pop cubes and pyramids and stuff into it or around it... it would be like a freaky hall of mirrors on acid.

I love how much this dude loves circles!

This is my favorite video on the entire internet.

@kenbrunet6120

4 жыл бұрын

Proof that you've only seen one video on the entire internet

my formula is: 1 diveded by (15+(X*8)) and X is the number of which circle you wanna no the ratio... and the first one is Nb=0

Brady, You should sell these brown papers at a charity auction or something along those lines.

Since the release of Tenet this video takes on a whoooole new meaning

Amazing. I'm a university maths youtube vlogger and I can't tell you how much numberphile has helped and inspired me over the years! :)

"We're gonna do this quite rough, Brady, if that's alright." Fueling lemons.

This is the firat time I truely craved the brown paper as art for my wall.

Those tiny tea cups on the background stole my attention!!!

Fave Numberphile by far. It’s adorable mathematician tv 💖 the best is their offices/background details 😂 amazing people

Syrio Forel escaped and became a mathematician.

@NotMeInc

8 жыл бұрын

***** BUT NOT MINE!

Guys, I'm not kidding when I say this, I did the procedure while watching the video, and it was the most satisfied I have ever been! This is just a wonderful way to show connections between different parts and areas of mathematics. I love these videos, please keep doing the world a favor by making videos like this!

Hands down my favourite numberphile video

Hi really appreciate his enthusiasm when doing these amazing demonstrations.

ok, now add the 3rd dimension...... I dare you.

@ifcoltransg2

7 жыл бұрын

People seem to stop when they get to three.

"If two lines touch at infinity...well this is kind of tricky stuff here" My favorite part of the video. :)

This is the best numberphile video ever

This was incredible, I was looking for a physical construction of Descartes' device for the construction of geometric sequences and this solution took my attention train off the rails. I HAVE BEEN INSPIRED TO BUILD A SCULPTURE USING THIS DEMONSTRATION. only I am going to expand the planes to spherical and other appropriate extrusions. Thank you for this beautiful solution.

@DavidSartor0

8 ай бұрын

Was this completed?

Where is CGPGrey's first?

@LostLargeCats

8 жыл бұрын

+Niklback1 Yeah I just started listening to HI.

@ghillies3796

5 жыл бұрын

At the bottom just keep digging

Now Brady! Look Brady!

One of their best videos!!!!

That's actually amazing how he works that out. Amazing

If you raise each term of that sequence to the power of -1, then add 1 to it, then divide it by 8, you get the Fibonacci sequence starting at the term of 2.

@vvalph9483

5 жыл бұрын

lol i thought the same thing

@linkAKAdude

5 жыл бұрын

I thought of Fibonacci numbers at first also, but the denominators seem to follow triangular numbers (times 8 then plus 15) which is how I predicted the 95 in the beginning.

@guillaume5313

4 жыл бұрын

@@linkAKAdude the first few denominators also seem to have a wierd pattern: the nth term is the sum of the two previous terms +1, but that doesn't work for 1/95 though, is there a particular reason for that or just a coincidence?

@whywelovefilm7079

4 жыл бұрын

Are you all serious? Or speaking nonsense just to be funny?

@guillaume5313

4 жыл бұрын

@@whywelovefilm7079 We're simply pointing out weird patterns, most of them are probably useless but asking questions is how maths work

At 22:17 he just states that the blue circle is R/16 without any proof or reasoning. :-(

Favorite Numberphile vid

Best video intro I have seen yet "amazing"