Incredible Formula - Numberphile

Рет қаралды 1,786,378

7 жыл бұрын

Dr James Grime discusses a couple of clever formulas which are pandigital - using all the numbers from 1-9.
More links & stuff in full description below ↓↓↓
More on pandigital numbers: • Why 381,654,729 is awe...
More on e: • e (Euler's Number) - N...
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Пікірлер: 1 600

@nichrun 7 жыл бұрын

Numberphile. The only channel where a formula is described as "cute". So adorable.

@henryyang478 7 жыл бұрын

it is quite 'cute',for its not mathematically complicated,yet gives a interesting result.just like a adorable magician preforming a simple trick,you know it's simple,but got amazed anyway.

@xuanlan6062 6 жыл бұрын

No clue if this is a compliment or not.

@bradhammond7540 6 жыл бұрын

Its not even a formula, it's an expression. So...

@cheeseburgermonkey7104 6 жыл бұрын

*turns minecraft person into real person into candy, then eats it*

@lulube11e111 6 жыл бұрын

nichrun we use that in my class very often

@wilkatis 7 жыл бұрын

How to remember e to more decimal places than you'll ever need? It's 2 point 7 followed by birth year of Lev Tolstoj (1828) followed by birth year of Jules Verne (1828) followed by angles of isosceles right triangle (45 90 45) e = 2.7 1828 1828 45 90 45 ... Now you can't say I didn't learn anything at mathematics class

@AuroraNora3 7 жыл бұрын

whoa

@garlic-os 7 жыл бұрын

Thanks!

@Reydriel 7 жыл бұрын

wilkatis Yeah, it's just basically 2.7 1828 1828 45 90 45 Incredibly easy to remember lol

@ragnkja 7 жыл бұрын

My maths teacher gave the same kind of grouping for the first ten digits, except that he only used one author born in 1828, namely Henrik Ibsen. Thanks for the triangle mnemonic for the next six digits!

@Ulkomaalainen 7 жыл бұрын

I had a colleague (teaching maths myself) who told me it's "Two-Point" and then the Andrew Jackson sequence: 7th president, elected in 1828, elected in 1828. Which didn't help me remember e that much, but I know more about Andrew Jackson now than I did before :) (Oh, yes, not the US here)

@rajajinnah3478 7 жыл бұрын

0:14 So 'Zero' is basically me during my friends' road trips 😂

@suave319 7 жыл бұрын

I feel you bro

@MrTVx99 7 жыл бұрын

Raja Jinnah at least you have friends. Feelsbadman

@rajajinnah3478 7 жыл бұрын

Ace Reaction Hahaha 😁

@Supware 7 жыл бұрын

Fun fact, it's also the number of friends I have :D

@kosmozaut 7 жыл бұрын

Me too tanks.

@itsnotcharan 7 жыл бұрын

To blow your mind: 81= 9^2= 3^4=70+6+5

@dramawind 7 жыл бұрын

No. Way.

@itsnotcharan 7 жыл бұрын

Also, this is kinda cheating but still... 49^1=07^2=85-36

@badmanjones179 7 жыл бұрын

0≠1≠2≠3≠4≠5≠6≠7≠8≠9 *bam*

@itsnotcharan 7 жыл бұрын

badman jones You sir, deserve an applause and a cookie

@quarkyquasar893 7 жыл бұрын

How about (9^8^7^6^5^4^3^2)^0 = 1?

@Anamnesia 7 жыл бұрын

4:15 "I Love e SO much..." Me too, but I don't go around telling everyone about it!

@minimosern 7 жыл бұрын

Anamnesia I do

@MichaelHeide 7 жыл бұрын

Anamnesia It's Adam and Eve, not Adam and e!

@Nishant-ko3uy 5 жыл бұрын

Anamnesia . Well u just did tell everyone that u love e.

@davutsauze8319 3 жыл бұрын

Hah, you should!

@goutamboppana961 2 жыл бұрын

@ganaraminukshuk0 7 жыл бұрын

Can we call approximations of e E-proximations?

@PeterJavi 7 жыл бұрын

Ganaram Inukshuk You must be pun at parties.

@anorangewithacapybaraunder2370 4 жыл бұрын

PJ Vis You bet he Vis

@randomdude9135 4 жыл бұрын

Russian accent

@miasma529 4 жыл бұрын

You aren’t so lim-ted xD

@ballelort87 3 жыл бұрын

Yes

@patrickhodson8715 7 жыл бұрын

1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100

@F3V3RDR3AMS 7 жыл бұрын

123 - 45 - 67 + 89 = 100

@OfficialHuMan 7 жыл бұрын

12345 - 6 - 7 + 89 = 100

@maximelaplace1467 7 жыл бұрын

-1 * 2 + 3 + 4 + 5 - 6 + 7 + 89 = 100 (1 - 2 + 3) * ( 4 * (.5 + 6 + 7 + 8 - 9) = 100

@shreccc9326 7 жыл бұрын

OfficialHuMan ummmm no

@SamuelKristopher 5 жыл бұрын

@@shreccc9326 I see you're too serious to get the joke. Also, 1+2^3456789=100

@Halosty45 7 жыл бұрын

Yeah the formula for e is much nicer.

@reblogo 7 жыл бұрын

And far more accurate

@generaltopix7228 7 жыл бұрын

SuperWifiBattler The problem is that you are only allowed to use all numbers 1-9 only once...

@druid_zephyrus 7 жыл бұрын

SuperWifiBattler if anyone can do that why was it only ever done recently, and not say the day of e, as a constant, being applied

@funnydogman9534 7 жыл бұрын

but it isnt pandigitallllllllllll

@suqmadiq3462 7 жыл бұрын

would like your comment if it did not have 314 likes

@steliostoulis1875 7 жыл бұрын

love Dr Grime. ...his enthusiasm is so relatable

@ImaginaryHuman072889 7 жыл бұрын

For those asking for full steps: 3^(2^85) = 3^[2*(2^84)] = (3^2)^(2^84) = 9^(2^84) = 9^[2^(2*42)] = 9^[(2^2)^42] = 9^(4^42) = 9^[4^(6*7)]

@rjohnson8ball 4 жыл бұрын

Thanks. My only concern was 3^[2*(2^84)] = (3^2)^(2^84) but after some deep thought, I understand why.

@saoirsedeltufo7436 4 жыл бұрын

@@rjohnson8ball It's a general rule that a^(b*c) = (a^b)^c = (a^c)^b

@besarsinghbhardwaj7012 4 жыл бұрын

Just exlain it briefly

@GtaRockt 7 жыл бұрын

2 Dr. Grime videos in a row? It's almost like it's Christmas!

@MarioFanGamer659 7 жыл бұрын

Ba dum tss...

@GtaRockt 7 жыл бұрын

@MarioFanGamer well when I wrote the comment it was still the 23th in my place so..

@Blazervitch 7 жыл бұрын

23th or 23rd lol

@Robostate 7 жыл бұрын

I am sorry I had to vote up your comment. You had 227 up votes, and that is a prime number. Quick, please, someone else vote it up to its twin!

@aifesolenopsisgomez605 5 жыл бұрын

479!! prime likes again :D

@codediporpal 7 жыл бұрын

1:20 I case you were wondering, Dr. James Grime was actually calculating that number on the fly, from the equation, while talking to you.

@alaaalzahrani8104 5 жыл бұрын

whattt

@castor2000 4 жыл бұрын

lol

@indian_scouser_ynwa 7 жыл бұрын

james is my favourite on numberphile

@Pankaw 7 жыл бұрын

sing with banana

@adamfrenkel1719 6 жыл бұрын

Wrong

@andrewkovnat 7 жыл бұрын

I wonder what that paper feels like... That is life's biggest question.

@Oscypex 7 жыл бұрын

Andrew Kovnat If your question may be rephrased as "what is this paper feeling?", the answer is "nothing", because it's paper and it doesn't have a working nervous system. If it's "what's the sensation of touching this paper?" instead, then I suggest you hand over your life savings to Numberphile and ask for a sheet of their paper in return.

@minimooster7258 7 жыл бұрын

Andrew Kovnat I think its just brown wrapping paper. You should be able to find some pretty easily, if you don't already have some lying around.

@andrewkovnat 7 жыл бұрын

Interesting.

@zoranhacker 7 жыл бұрын

I imagine it's like one of those chill giving materials (not pleasant to touch)

@andrewkovnat 7 жыл бұрын

That's what I was thinking originally.

@david-yt4oo 7 жыл бұрын

I smiled when he mentioned how accurate it was

@kcwidman 7 жыл бұрын

dani gómez likewise

@jeromesnail 7 жыл бұрын

dani gómez me too! I'm still smiling !

@AlexRomanov1 7 жыл бұрын

he gets so happy about numbers, its adorable. lol

@SirtubalotTX 7 жыл бұрын

I know.. right? Dr. Grimes has an incredible mind. It's not fair really. I like numbers too but they vex me more often than not, so they don't make me happy sometimes.

@DanB-sh3wt 3 жыл бұрын

About noombahs, you mean.

@panzer1896 6 жыл бұрын

4:16 "I love e so much" - Dr James Grime aka J-Grizzle

@EclecticSceptic 7 жыл бұрын

Wow that's an amazing formula. The precision is remarkable.

@Philgob 7 жыл бұрын

Amazing! So simple yet it's very impressive that he was able to do this.

@astropgn 7 жыл бұрын

If you put e / ((1+9^(-4^(6*7)))^3^2^85) on wolfram alpha, the result is "e"... weird

@twwc960 7 жыл бұрын

I think what's happening is that it is rounding the (1+9^(-4^(6*7))) to 1, since it can only work with a finite precision. Then 1 raised to any power is 1, so the denominator is calculated as 1 rather than e.

@Trias805 7 жыл бұрын

However, it properly calculates ((1+9^(-4^(6*7)))^3^2^85) itself...

@astropgn 7 жыл бұрын

It might be, but as Trias00 mentioned, if I don't put it on the denominator (or even on the numerator, which also gives a wrong result) it can calculate to a fair precision.

@KuK137 7 жыл бұрын

It doesn't. Raising that to power of 85 would take a lot of time, my guess is that it's hard coded to recognize that number and simply return e, which is why it breaks when the number is in different form, like in OP formula...

@vijuarez3859 7 жыл бұрын

Wolfram Mathematica gives me an overflow and underflow error, it's too much for the pc. I tried with Python because it keeps trying even if it's too much data, but it's been going for a while I don't think it's going to finish.

@r0kus 7 жыл бұрын

I agree, that pandigital piquation (hey! if the other was a pandigital equation, we can do this now) was not all that impressive. just 10 places? Heck, the well known fraction 355/113 is accurate to 6 places.

@geoffreywu4304 7 жыл бұрын

Have you ever tried (9^2+(19^2)/22)^(1/4)? Pretty accurate... I think Ramanujan found the approximation.

@r0kus 7 жыл бұрын

That is a nice one, @Geoffrey_Wu . It is accurate to 8 places. I'm not sure I'll remember it the way I remember 355/113, though.

@r0kus 7 жыл бұрын

alysdexia well, obviously. I even had to look up _nescient_. 🙄

@filipsperl 7 жыл бұрын

I don't see why everyone has a problem with the 6*7 not just being 42. First, the mathematical curiosity explored in this video is not a formula, but a number. The whole thing can be expresed as one number, which is very close to e. Every part of the number can be expressed differently and it doesn't matter what signs, brackets or symbols are between them. If 4^2 were to show up in these type of expressions, of course you can write it just as 16, but you need the digits 4 and 2, just as you need 6 and 7 in this case. Why would that be considered cheating?

@goutamboppana961 2 жыл бұрын

well cuz that wouldn't be pandigital anymore

@efulmer8675 2 жыл бұрын

The point is to make all the digits show up in the formula, so while there are ways to express numbers in other ways, by specifying that 42 is 6*7, he avoids any accusations of cheating by forcing the formula to look a certain way.

@yaboi7034 2 жыл бұрын

Well you could write e like that, but i doubt it just stops, so this way is simplified.

@L4Vo5 7 жыл бұрын

That last formula was such a parker square...

@jesseacummins 7 жыл бұрын

L4Vo5 This is the most apt use of that term.

@hsl8251 7 жыл бұрын

I love videos with this guy because he so excited about this. You can see the joy in his eyes

@camilohiche4475 7 жыл бұрын

Those pandigital formulas are kinda parker squared though tbh...

@Azrage 6 жыл бұрын

Not the one on “e”though. That was neat. The others were parker formulas.

@duarteromano2702 4 жыл бұрын

This statement is false: l

@TheSnelly101 7 жыл бұрын

I love these guys' enthusiasm for math!

@MannuDGr8 7 жыл бұрын

I am in love with this channel.. it teaches me so much and in such an interesting way.. you guys are doing a great job ! cheers.

@SNNTV3000 7 жыл бұрын

4:15 James loves his pills This joke's been done a trillion trillion times hasn't it?

@MrCyanGaming 7 жыл бұрын

If you're reading this, have an amazing Christmas! 🎄🎄🎄

@thanosaekk2449 7 жыл бұрын

So now I will see you at Numberphile videos too? I have already seen you at every Mumbo Jumbo video!

@Zwijger 7 жыл бұрын

CyanGaming | ᴹᶦᶰᵉᶜʳᵃᶠᵗ ⁻ ᴳᵃᵐᵉᴾᶫᵃʸ Thank you, random stranger on youtube, have a great Christmas as well!

@MrRoboticWarfare 7 жыл бұрын

Cyan? I didn't take you for the kind of person to write these comments... that's disappointing.

@Neueregel 7 жыл бұрын

the main celebration was 4 days ago and it was called Winter Solstice!!

@kat_stuff 7 жыл бұрын

David -flamingsword1 did you just assume that those jokes were still funny in 2017?

@DanDart 7 жыл бұрын

Wow, that e one. That was so beautiful.

@fastr1337 7 жыл бұрын

I wish i was as passionate about anything like this man is passionate about math. LOVE the videos, keep it up!

@PandaBlubber 7 жыл бұрын

this just blew my mind, thank you Dr. Grime

@ambidexter2017 7 жыл бұрын

My favorite thing about this formula is that it contains the number 42. I think all formulas for fundamental mathematical constants should.

@Brianww777 7 жыл бұрын

Wow! That's incredible! You guys make mathematics so interesting! Your fun, lightheaded approach to the subject makes it accessable to the layperson (me) without the feelings of intimidation that math usually conjures. P.S. I love the paper used in your videos...

@MrGrumbleguts 2 жыл бұрын

This isn't maths though, it's arithmetic.

@SpeedStar76 7 жыл бұрын

Thanks to another of your videos, I recognised e before you said it! You have taught me more than 5 years of 1980s comprehensive school... thank you :)

@gabrieleranucci6425 5 жыл бұрын

Actually this was the first numberphile video I saw. I found it by chance on an app called Curiosity and since them I've been in love with this channel!!

@astherphoenix9648 7 жыл бұрын

i love Dr Grime on numberphile

@AnteP-dx4my 7 жыл бұрын

I LOVE THIS GUY , HE IS GREAT GUY !

@TomatoBreadOrgasm 7 жыл бұрын

HE'S ALSO A SINGINGBANANA. THAT IS HIS KZfaq USERNAME. CHECK IT OUT.

@preddy09 7 жыл бұрын

BUT IS HE AMAZIN GUY?

@AnteP-dx4my 7 жыл бұрын

Geebz YEEEE

@AnteP-dx4my 7 жыл бұрын

TomatoBreadOrgasm tnx

@DrKaii 4 жыл бұрын

NO HE IS PURE EVIL. Don't let that charming smile charm you. His agenda is global domination.

@lisalisa9706 7 жыл бұрын

Another awesome fact about e: the line that is tangent to log_b (x) (log of x of base b) that also passes through the origin (0,0), for ANY positive b different than 1, touches the curve at x=e. That's a nice relation between the inverse function of e^x and the number e.

@jaidenboucher0 7 жыл бұрын

That is such a nice, satisfying formula I'm so happy.

@michaelbauers8800 7 жыл бұрын

woah, that is amazingly cool. It was not obvious to me he was just writing an elaborate version of the limit formula until he showed his work, heh

@trobin 7 жыл бұрын

Looks incredible

@denvernaicker8250 7 жыл бұрын

its great to see james again

@dermaniac5205 7 жыл бұрын

Thanks for this awesome christmas present!

@LeiosLabs 7 жыл бұрын

Holy Cow! My mind has literal-e been blown!

@jimothyjimothy1 6 жыл бұрын

LeiosOS Sorry! Thought this was Google

@parthiancapitalist2733 6 жыл бұрын

I think you mean /lɪtɹ̩əli/

@ryanlira7194 6 жыл бұрын

LeiosOS *stares dissaprovingly*

@nazishahmad1337 5 жыл бұрын

leios Os here what u was doing

@Kitulous 5 жыл бұрын

Julius The Reformer no he meant /lɪɾɚɹəli/

@SebastianLopez-nh1rr 7 жыл бұрын

I got a pandigital formula for 2... 10 there you go

@ianwubby6271 7 жыл бұрын

Well, first you have to specify that it's in binary, but it does work. How about 1+(23456789^0)?

@chickeyy1792 7 жыл бұрын

Ianwubby Smart and tricky in the same way because you used the 0 as well, but ironically to be the power of all the digits other than 1 to make it a 1 itself, of course summed with the 1 before the brackets to make it a 2

@F17A 7 жыл бұрын

Berniksus dude the answer is 1

@richardweiss5217 7 жыл бұрын

Why? We're talking about approximation here. 2 = 10 with an error of 8.

@biodrengen 7 жыл бұрын

Richard Weiss 2 number system

@x9_modulator236 7 жыл бұрын

Hey Numberphile! I love ur videos! Can u do one on decimal factorals

@Deafingblow 7 жыл бұрын

These kinds of videos are why I love math.

@acorn1014 7 жыл бұрын

My favorite is the golden ratio. (1 + 5^(4/8))/2 + 7(9 - 6 - 3)

@AdrenalineL1fe 7 жыл бұрын

oh shi...

@gammaknife167 7 жыл бұрын

to be fair, the golden ratio is an algebraic number, making its pandigital formula rather simple...

@ImaginaryHuman072889 7 жыл бұрын

agreed with rohan. since the golden ration is exactly equal to (1+sqrt(5))/2, you can pretty easily create a pandigital formula equal to that. here's a few more just off the top of my head: (1+5^(4/8))/2+(63/9)-7 (1+5^(3/6))/(8/4)+9-7-2

@Kino-Imsureq 6 жыл бұрын

seh (1+5^(4/8))/2 + 7(9-6-3) (1+sqrt(5))/2 + 7(0) (1+sqrt(5))/2

@43labontepetty 6 жыл бұрын

You missed a pair of parentheses. Lol. Its technically not exactly the golden ratio anymore.

@AbiJaay 7 жыл бұрын

I find these videos weirdly relaxing even though I have absolutely no idea what's going on. XD

@CalvinThomasMusicGO 7 жыл бұрын

Mind blown! How can that number be so accurate to e? I'm so glad I watched this video!

@Svm777 7 жыл бұрын

I love James Grime videos!

@aday07271996 7 жыл бұрын

What's a mathematician's favorite dessert? Pi-e

@SLAMgamer11 5 жыл бұрын

ARE YOU FOR REAL

@jazzybank 5 жыл бұрын

No. Numberphile told me that it's cak(e).

@bip901 5 жыл бұрын

0.42331

@agar0285 4 жыл бұрын

1+2+3+4+5+6+7...=?

@FplusETVChannel 4 жыл бұрын

agarRoyale 2002 infinity

@Akhi11eus 7 жыл бұрын

Damn, Grime throwing some shade on the Pi formula!

@popcornpretzel6720 7 жыл бұрын

I'm so glad james is back

@vagabond7199 6 жыл бұрын

This is pretty cool! Numberphile never disappoints me.

@zallen05 7 жыл бұрын

This is really ingenious stuff, I wonder if the other participants used the properties of powers to achieve pan-digital formulas in their submissions. Such an insightful approach to the challenge 👏👏👏

@senc1971 7 жыл бұрын

Thanks for showing us this. This has got to be one of the most impressive things in mathematics, at least amongst the set of results in maths that's not too difficult for me to understand, ha. First of all just to approximate e to 10^25 decimal places is pretty cool, but to do it with a pandigital formula--quite clever indeed! Great idea for a numberphile video.

@nicolasfpauly 7 жыл бұрын

I'm a 27 graphic designer, and I don't know that much in mathematics. I can't explain why I've been so much fascinated by your videos @numberphile, but this has become a serious addiction. Loving your stuff!

@nicolasfpauly 7 жыл бұрын

And yes, I also think there are too much "points" in pi formula.

@meet1639 7 жыл бұрын

Thanks for that, I will be using that in competitive coding!!

@pavphone2616 7 жыл бұрын

Yo James you should make videos for your own channel!

@N3KLAZ 7 жыл бұрын

Is there any mentionable reason for the "6*7" in the formula and why it's not just 42?

@numberphile 7 жыл бұрын

+N3KLAZ so it's pandigital

@gauravcheema 7 жыл бұрын

N3KLAZ to make it pandigital.. other wise the digit would repeat and that wouldnt be cool

@Trias805 7 жыл бұрын

The same reason as for the formula itself. Otherwise you can just come up with any huge number and place it in the formula (1+1/N)^N

@Paretozen 7 жыл бұрын

oh them trolls :) nice one

@StGroovy 7 жыл бұрын

Because 42 is the answer to the meaning of life, so... I don't know. Help me out.

@chorthithian 6 жыл бұрын

I love this guy a thorough amount

@luisrosano3510 7 жыл бұрын

You are amazing guys! Cheers from Uruguay!

@ArchDennam 7 жыл бұрын

Oh yes. This really tickles my fancy.

@AnonYmous-xs8nx 7 жыл бұрын

In (fairly) simple terms, how did Sabey decide on that value for *N*?

@nh-a6713 7 жыл бұрын

its a big number and it uses the remaining digits from 1-10, the bigger the number is, the closer it will approximate e regardless of any properties the number has

@Szibenwaro 7 жыл бұрын

He needed a formula, which is the reciprocal of another formula that uses the digits he didn't already use. (excluding 1 of course)

@norielsylvire4097 7 жыл бұрын

The way our mind works with numbers and logic is simply beautiful

@gremlinn7 7 жыл бұрын

I find the one for Pi, at the end, to be much MORE impressive than the video's main one for E. After all, the one for E is just piggybacking on the large-x limit of (1 + 1/x)^x and only relied on finding a way of divvying up {2,3,4,5,6,7,8,9} to write a power-tower number in two different ways. (Still a bit clever!)

@ownage3523 7 жыл бұрын

But how did he figure to use 3^(2^85) to start?

@connorhamilton5707 7 жыл бұрын

Justin Marinelli It could have been any number as long as he used an equivalent number with the other digits he needed to make it a pandigital equation. I'm sure he never actually calculated the number, and he probably played around with other combinations before finding that one.

@mikedonovan9033 7 жыл бұрын

The formula for e calls for taking n to infinity, aka a really big number. When he was making the pandigital formula for e, he thought "I have to create a formula that puts in a 'really big number' for n, however that number must also satisfy the pandigitalness of the formula". So, he chose 3^(2^85) because: 1.) It is really big 2.) It has the characters he needs to make the formula pandigital.

@ownage3523 7 жыл бұрын

Thanks

@chadtindale2095 7 жыл бұрын

Brady, We love you, We love your videos. It's Christmas time. Stop editing videos and spend it with your wife and dogs.

@ExCoSeH 7 жыл бұрын

I love Dr James so much

@conexant51 5 жыл бұрын

That's simply amazing!.. I love it!

@Hecatonicosachoron 7 жыл бұрын

e is the best constant.

@chickeyy1792 7 жыл бұрын

Jason93609 Nope I'm a π person myself

@SuntzuDragon 7 жыл бұрын

I will be i, let us join together and be one. Shoutout to all who get that joke.

@masamainio4052 7 жыл бұрын

Harnoor Lal nice meme

@chickeyy1792 7 жыл бұрын

Harnoor Lal Did you mean; get one and be zero? ;)

@Hecatonicosachoron 7 жыл бұрын

Minus one. And all odd integers can join in.

@AveImperatorProductions 7 жыл бұрын

Why do english speakers outside of America call both parenthesis and brackets "brackets?" Doesn't that get confusing when you end up with equations containing both? Is there a slight inflection difference I'm missing?

@klaxoncow 7 жыл бұрын

Nah, there's no inflection difference. It's just colloquial laziness. It could potentially be confusing. But, well, if there's a chance of ambiguity then you should just use the correct terminology (or the variants of "square brackets" and "curly brackets" to be explicit about their shapes). It's not that the terminology is actually different. It's just a colloquial thing not to be too bothered by it.

@AveImperatorProductions 7 жыл бұрын

Ah okay, in case you couldn't tell I'm much more of a linguist than a mathematician, this had always been something I've wondered about. Thanks!

@joshuarosen6242 7 жыл бұрын

I'm genuinely amazed. That is very cool.

@rosiefay7283 7 жыл бұрын

Thank you for highlighting this little mathematical curiosity. IMO a nicer expression for e is the one seen at 4:04 that uses the digits 1 to 8. It isn't as accurate, but it uses an additional finesse. 1/ln (1+x) = 1/x + 1/2 + o(1) (1/x + 1/2 + o(1)) ln (1+x) = 1 (N + 1/2 + o(1)) ln (1 + 1/N) = 1 (1 + 1/N)^(N+.5) ~~ e For a given N, the expression is more accurate with that .5 in the exponent than without. In case you didn't spot that expression, it's (1 + 2^-76)^(4^38 + .5)

@Replay260 7 жыл бұрын

I identify as pandigital.

@Roescoe 7 жыл бұрын

Is counting your digits considered sexist?

@Requiem100500 7 жыл бұрын

I am trans-cendental.

@HandreyAlex 7 жыл бұрын

Go back to Numblr.

@poznyakpoznyak 6 жыл бұрын

Ugh, sick of your non-binary BS. There are only two digits, 1 and 0.

@britishman5300 6 жыл бұрын

Support the BDDP community Binary duodecimal decimal pandigital

@GetMeThere1 7 жыл бұрын

So...this prompts a question: what is the biggest number you could write using just the ten digits? I'm ashamed to say this is not immediately obvious to me. Might it be 91 raised to the 80, raised to the 7, 6, 5, 4, 3, 2 (or the reverse?)? I'd like to know -- and I'd like to know whether one can give a simple explanation of a "proof." Maybe I'm just tired, but the answer isn't obvious to me right now...

@Daniel-dc5mr 7 жыл бұрын

GetMeThere1 I think it is the reverse

@Daniel-dc5mr 7 жыл бұрын

GetMeThere1 Maybe 90^81^72^63^54

@DanteDeRuwe 7 жыл бұрын

Would using factorials be considered cheating? Because that's a way of generating huge numbers...

@Daniel-dc5mr 7 жыл бұрын

54^63^72^81^90

@anticorncob6 7 жыл бұрын

2^3^4^5^6^8^91 You want as many exponents as possible and you order them from smallest to biggest (2^100 is much bigger than 100^2 for example)

@patrykmazurkiewicz3866 6 жыл бұрын

This guy must be a quite happy/lucky chap doing what he so much loves (talks maths so passionately) with such a great success (having >2M subscriptions)!

@TyDreacon 7 жыл бұрын

On one hand, I love it. On the other hand, I so badly want to know if that's the most accurate pandigital formula for e, or if there's another pandigital formula that's even more accurate than that.

@hitchikerspie 7 жыл бұрын

This is really e-erie!

@downstream0114 7 жыл бұрын

I identify as a pandigital number.

@maxchatterji5866 7 жыл бұрын

Hilarious

@Mohamedbloo 7 жыл бұрын

Not hilarious

@lkjhfdszxcvbnm 7 жыл бұрын

Downstream01 Now it's an official sexual orientation

@4.0.4 7 жыл бұрын

Downstream01 What would be the gender pronoun of a pandigital number?

@ordermind 7 жыл бұрын

The pronoun is 123456789.

@doyowan 7 жыл бұрын

I first thought the formula would equal a new pandigital number... that was even cooler! :)

@ziadhossam5862 7 жыл бұрын

Here before 20 views love numberphile

@tropicalnofruit1419 4 жыл бұрын

When I heard 18 trillion trillion digits my eyes opened up so much😂 I love maths

@goutamboppana961 2 жыл бұрын

18 Septillion

@spencertaylor6910 6 жыл бұрын

Simply brilliant.

@RealClassixX 7 жыл бұрын

How wonderfully creative.

@IAmBrownThunderOfficial 7 жыл бұрын

1:20 Aaaannnd I need a new pair of underwear.

@dramawind 7 жыл бұрын

I need a new pair of pants as well.

@Kalumbatsch 7 жыл бұрын

And then he lets all the air out of it by explaining the pathetic little trick but you've already gone to the trouble of shitting your pants.

@gordongorgy9148 6 жыл бұрын

😉 TIHS TNSAW TAHT

@protonix07gaming8 5 жыл бұрын

@@Kalumbatsch but how you'll start to something that can take all the digits from 1-9 in all the transformations. It's still something one has to figure out by his brains.

@salmjak 7 жыл бұрын

"It's really cute." "...It's approximately e."

@astitvasharma6887 6 жыл бұрын

The most beautiful formula after e^iπ=-1

@JockzillaTheSniper 7 жыл бұрын

I was just expecting a pandigital formula to equal a pandigital number from the beginning of the video. But this was much better!

@armandstefan635 7 жыл бұрын

Who else besides me loves this channel? :)

@L3ON360Z 7 жыл бұрын

we all love it!

@masterofstorms1886 6 жыл бұрын

Armand Stefan you and 2248653 other individuals

@EpicB 7 жыл бұрын

((1+9^-4)^6*7)^3^2^85 = e, therefore Half-Life e confirmed.

@stumbling 7 жыл бұрын

Still follows the rule that Valve can't count to 3. :)

@gui18bif 6 жыл бұрын

2011 called

@tanaypandey1771 3 жыл бұрын

@@stumbling we have HL alyx , waiting for 3 :)

@seanwilliams7968 5 жыл бұрын

this is so incredibly awesome!

@Schenkel101 6 жыл бұрын

What makes the e formula so much more impressive than pi is that it links back to the definition of the number

@p11111 5 жыл бұрын

Include 0 by adding +0 to any pandigital formula

@thereelburke4634 7 жыл бұрын

What paper do they use ?

@Dadik2580 7 жыл бұрын

Brown paper.

@chickeyy1792 7 жыл бұрын

Unbleached paper

@MegaMGstudios 7 жыл бұрын

TheReel Burke le brown paper

@parthiancapitalist2733 6 жыл бұрын

Non GMO paper

@43labontepetty 6 жыл бұрын

Jeff paper

@bluebyrd1300 2 жыл бұрын

That’s a *lovely little formula* Gonna use this tomorrow for my maths unit test (unit test is on 3D geometry )

@gaganvs4090 7 жыл бұрын

Please make a video of all the greek (or non-english) alphabets or symbols used in maths and their uses, please

@keithplayzstuff2424 7 жыл бұрын

6 hours ago better say something... golden ratio = (4-3+5^(1/2))/(7+9-6-8)

@NZAnimeManga 7 жыл бұрын

^ now that's truly beautiful ;)

@keithplayzstuff2424 7 жыл бұрын

Wow, thanks for replying. Of course, it took 5 minutes but it was an "early" comment anyway.