Perfect Number Proof - Numberphile

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  • čas přidán 5. 01. 2015
  • This video follows on from: • Perfect Numbers and Me...
    More links & stuff in full description below ↓↓↓
    Objectivity: / objectivityvideos
    Mersenne Primes and Perfect Numbers, featuring Matt Parker.
    Matt is the author of Things to Make and Do in the Fourth Dimension. On Amazon US: bit.ly/Matt_4D_US Amazon UK: bit.ly/Matt_4D_UK Signed: bit.ly/Matt_Signed
    Support us on Patreon: / numberphile
    NUMBERPHILE
    Website: www.numberphile.com/
    Numberphile on Facebook: / numberphile
    Numberphile tweets: / numberphile
    Subscribe: bit.ly/Numberphile_Sub
    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
    Videos by Brady Haran
    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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Komentáře • 631

  • @TrackpadProductions
    @TrackpadProductions Před 5 lety +359

    Is putting the lid on a pen the maths equivalent of dropping a mic, then?

  • @MrDannyg77
    @MrDannyg77 Před 8 lety +58

    Matt is great. I love his sense of humor. He's one of very few people who can take the subject of this video and make in entertaining to non-math nerds.

  • @andrewxc1335
    @andrewxc1335 Před 8 lety +125

    I differentiate between groups of operations not with inflection, but with pauses:
    "Two to the... n minus one," versus "two to the n... minus one."

    • @andrewxc1335
      @andrewxc1335 Před 8 lety +14

      It's not dramatic, or anything, just a quick stop / catch-breath type pause. Half a beat, so everyone knows what I'm doing.

    • @toasticide816
      @toasticide816 Před 8 lety +13

      i havent had much of this experience but i generally say "one less than 2 to the n" and "2 to one less than n" rather than having "minus one" in suitable place. others find it annoying for obvious reasons but i like it. :)

    • @precumming
      @precumming Před 6 lety +4

      2 to the n ·*camera zooms in* minus one

    • @helloiamenergyman
      @helloiamenergyman Před 5 lety +1

      me 2

    • @helloiamenergyman
      @helloiamenergyman Před 5 lety +1

      to the n minus 1

  • @isaacechols2483
    @isaacechols2483 Před 7 lety +117

    Matt becomes the child he talks about at 3:43, at 13:37

  • @AdamBomb5794
    @AdamBomb5794 Před 7 lety +31

    Classic Mathematician:
    "Let us assume that we know the total"

  • @numberphile
    @numberphile  Před 9 lety +97

    Matt is the author of Things to Make and Do in the Fourth Dimension. You can support him by checking out his book...
    On Amazon US: bit.ly/Matt_4D_US Amazon UK: bit.ly/Matt_4D_UK Signed: bit.ly/Matt_Signed

    • @alexroberts8755
      @alexroberts8755 Před 9 lety +5

      I got it for Christmas, it's brilliant!

    • @KasabianFan44
      @KasabianFan44 Před 9 lety +2

      Same, it was one of the best Christmas presents I ever got!

    • @AndresRodriguezGuapacha
      @AndresRodriguezGuapacha Před 9 lety +2

      You make me want to go back to university! Why can't all teachers be like Matt?

    • @guanche011
      @guanche011 Před 9 lety

      Hey Brady, the videos in my subscription feed listed this one before (thus older) the previous one, which made it really hard to watch.. Just something to look out for. Really great videos nonetheless!

    • @adithijagannadhan7174
      @adithijagannadhan7174 Před 9 lety

      It's a really good read!

  • @BenTheBikerBoy
    @BenTheBikerBoy Před 9 lety +200

    13:39 Literally the smuggest face ever :')

    • @hankroest6836
      @hankroest6836 Před 5 lety +10

      And admittedly: "...so pleased I'm going to put the caps back on both pens." ! ;-)

  • @LilAnnThrax
    @LilAnnThrax Před 8 lety +318

    It's 2am. I've become addicted to watching Numberphile before bed. I'm watching towards the beginning where we are looking at the pattern of the 2, 4, 16, 64... And I think to myself, those are powers of 2. Then I see they are the prime -1. I figure Matt will say "this is obviously just 2 to the power of the prime minus one." When he says he tortures kids with it and it's not obvious at all I feel so happy that I finally understood a non obvious Numberphile concept. I finally feel like I belong. Loved this video!

    • @Reydriel
      @Reydriel Před 8 lety +8

      +Ann Beckman
      He tortures KIDS with it, not adults, whom I believe will see the pattern pretty much immediately :P

    • @Cloiss_
      @Cloiss_ Před 8 lety +11

      +Reydriel I'm 12 years old and I saw the pattern immediately... I'm also taking Geometry so I'm familiar with formal proofs already too.

    • @mikikiki
      @mikikiki Před 8 lety +7

      +EpikCloiss37 12 year olds were doing geometry in the late 1800s, too. ☺️

    • @Cloiss_
      @Cloiss_ Před 8 lety +9

      Then what happened to our education system? Now you have to be in super special programs for that... (which are based on IQ of all things... Not a true measure in my opinion...)

    • @TheRedstoneTaco
      @TheRedstoneTaco Před 7 lety +1

      I NOTICED THAT TOO WOW! :D
      I USED A CALCULATOR TO DETERMINE THAT 8191 is multiplied by 4096 to get 33,550,336!

  • @jz5738
    @jz5738 Před 9 lety +179

    Oh that was beautiful; math truly is the music of logic!

    • @tggt00
      @tggt00 Před 9 lety +24

      Usually I hear people say the opposite, music is the math of art.

    • @jz5738
      @jz5738 Před 9 lety +1

      I agree!

    • @maxischmidt1299
      @maxischmidt1299 Před 9 lety

      Very well said... cool^^

    • @oz_jones
      @oz_jones Před 8 lety +4

      +tggt00 Music is a massles body with a mathematical heart :)

    • @noahjames9457
      @noahjames9457 Před 6 lety +1

      Jasko Z Math is the science of the art of the music of logic.

  • @zacktobar13
    @zacktobar13 Před 9 lety +12

    It blows my mind how similar of a feeling this video gives me to watching my calc 2 professor do proofs for certain series tests...

  • @Formulka
    @Formulka Před 9 lety +208

    "I use this to torment young people" :)

    • @quinn7894
      @quinn7894 Před 3 lety +1

      3:27 Did he just call high school students "young"?

    • @wittlewill6839
      @wittlewill6839 Před 3 lety

      nice

    • @ru2225
      @ru2225 Před 3 lety

      @@quinn7894 secondary (high) schoolers start at around age 10/11 in Australia and UK (where he's from and where he lives respectively), which is young :)

  • @golux-57
    @golux-57 Před 5 lety +12

    Matt Parker, I would have loved to have you as a math professor in school.
    I've always loved math, and even majored in it as college. It was teachers like you who made it even more interesting.

  • @dragan176
    @dragan176 Před 9 lety +28

    You should do more of these proof videos, this was really great!

  • @GLRaema
    @GLRaema Před 9 lety +17

    Matt looks so happy at the end of this video :D

  • @olanmills64
    @olanmills64 Před 2 lety +2

    For some reason, I find Brady's incredulity at the beginning to be hilarious."You've already shown a link!"

  • @nathanielmcclaflin1374
    @nathanielmcclaflin1374 Před 7 lety +13

    I love this channel! Matt has told me everything I needed to know about perfect numbers and mersenne primes in this video and his one that came right before it that I can teach it to my classmates that know nothing about it.

  • @traktortarik8224
    @traktortarik8224 Před 6 lety +10

    I just pronounce superscripts more quickly when they're together, like parentheses

  • @jacobbaer785
    @jacobbaer785 Před 7 lety +43

    Haha.. "that's why Australians are so good at math" 4:54

    • @nathanielmcclaflin1374
      @nathanielmcclaflin1374 Před 7 lety +3

      Matt is so funny

    • @TruthNerds
      @TruthNerds Před 5 lety +2

      "Ethan, count to ten!"
      "Yes, ma'am. One alligator, two alligator…"
      (Yes, I know there are no alligators in the wild in Australia.)

  • @marouaneh175
    @marouaneh175 Před 9 lety +7

    I would have loved to see a proof of the other way around, that is every even perfect number has a Mersenne prime factor.

  • @dembro27
    @dembro27 Před 10 měsíci +1

    I think I would've gotten stuck at the geometric series step, but everything else was explained well and clicked for me. Cool!

  • @rocqua
    @rocqua Před 9 lety +3

    So what about the proof that all (even) perfect numbers are of this form?

  • @fahrenheit2101
    @fahrenheit2101 Před 2 lety +3

    Yay! For once in my life I did the whole thing myself before watching the video. The only difference with my method was to prove the sum of that particular geometric series by induction, because I already knew what the answer was by inspection, so it seemed like the best proof to use, especially given that I didn't even notice it was a geometric series...

  • @NUGGet-3562
    @NUGGet-3562 Před 5 lety +2

    Holy frick I am blown away, this is one of the coolest things ever

  • @niansenx
    @niansenx Před 9 lety +8

    Love it! I may need to watch it again! Any plans for a Numberphile book?

  • @isaac10231
    @isaac10231 Před 9 lety +5

    I saw you on tv! Outrageous acts of science!
    Haha that's awesome.

  • @hmv678
    @hmv678 Před 6 lety +1

    Fabulous proof. Thank you for a great video.

  • @SpiderwebRob
    @SpiderwebRob Před 9 lety

    Last two vids were really good. Keep it up Brady.

  • @stevefrandsen7897
    @stevefrandsen7897 Před 8 lety

    Happy 2016 Matt. I enjoy your videos.

  • @juandesalgado
    @juandesalgado Před 5 lety +2

    Lovely video, thanks. This link was known to the ancient Greeks... but the converse (that all perfect numbers are of this form) had to wait until Euler. I wish you could dedicate one more video to this other side of the proof.

  • @Dombowerphoto
    @Dombowerphoto Před 9 lety +19

    Rising inflection,,, good work

  • @kostal1991
    @kostal1991 Před 9 lety

    I like this proof! Helped me to understand what was shown on the previous video.

  • @BritishBeachcomber
    @BritishBeachcomber Před 2 lety +1

    13:34 turns to camera, looking very smug, "but now we've managed to prove it"...

  • @jopaki
    @jopaki Před 8 lety +9

    "torment young people" LOL keep that up!

  • @Melthornal
    @Melthornal Před 9 lety +7

    I haven't done math in ages, but I'm proud to say not only did I follow along with the video, but I was a step or two ahead.

  • @KarlFFF
    @KarlFFF Před 9 lety

    Can't wait for objectivity! The onscreen links didn't work though, but the description wasn't far away :)

  • @stiveturtle530
    @stiveturtle530 Před 7 lety +2

    I saw the pattern, I've never felt so accomplished

  • @Bo2gLiTcHmAsTeRtRoLl
    @Bo2gLiTcHmAsTeRtRoLl Před 9 lety +1

    I love these videos!

  • @WillFast140
    @WillFast140 Před 9 lety

    A new year, a new Matt Parker video. What a great start to 2015! (Although I'm sure Matt would argue that a year is a meaningless or at least arbitrary measure of time)

  • @OmegaCraftable
    @OmegaCraftable Před 9 lety +5

    Oh my goodness Brady is making a mausoleum channel.

  • @GothicKin
    @GothicKin Před 8 lety +11

    If you've ever worked with binary you know that the sum of all the powers of 2 up to n - 1 equals 2^n - 1

    • @TheRedstoneTaco
      @TheRedstoneTaco Před 7 lety

      I havent even worked with binary I just learned that concept from a Khan Academy video showing how to count to 31 with your fingers xD. I feel like a special snowflake xD

    • @GothicKin
      @GothicKin Před 7 lety

      TheRedstoneTaco
      Or the binary number with only the nth digit =1 is exactly 2^n, 10000000.... -1 = n-1 ones, which is 2^ (n-1)

    • @htmlguy88
      @htmlguy88 Před 7 lety

      technically if you use both hands you could count up to over 1000 lol

    • @htmlguy88
      @htmlguy88 Před 7 lety

      and if you can do it with your thumbs they have 2 segments each ( some may say three including the connection to the wrist) and you get up past 1 million then.

    • @taysem321
      @taysem321 Před 4 lety

      Yes! I thought exactly that, the sum of powers up to n-1 is 1111111... with n-1 digits, and if you add 1, it becomes 1000... with a 1 and n-1 zeros, which is 2^n

  • @tigerbalmks
    @tigerbalmks Před 9 lety

    love you, matt and brady

  • @user26912
    @user26912 Před 7 lety +16

    Isn't the pattern more clear in binary? Aren't we obscuring the pattern by thinking in decimal?

    • @Shadowmere29
      @Shadowmere29 Před 7 lety +6

      But to prove that about binary, you must still use geometric series, so in the end you get the same result either way.

    • @JM-us3fr
      @JM-us3fr Před 6 lety +2

      Yes of course. This is far more easily understood in binary, so some of the algebra could be skipped, but the proof would still be necessary

    • @harry_page
      @harry_page Před 4 lety

      6 -> 110
      28 -> 11100
      496 -> 111110000
      8128 -> 1111111000000
      The amount of 1s is n, the amount of 0s is n-1

  • @TorgieMadison
    @TorgieMadison Před 9 lety +1

    "I'm so pleased I'm going to put the lids back onto both of the pens" Hahahaha! You're good on camera! Well proof'd :)

  • @williamsaraiva4562
    @williamsaraiva4562 Před 3 lety

    Beautiful ❤️. Congratulations!!!

  • @ripperbelgium
    @ripperbelgium Před 9 lety +5

    An interesting property of even perfect numbers that follows this theorem (although the proof is not as exiting) is that all even perfect numbers end with the digits 6 or 28.
    Another interesting fact as that the proof in this video was proven in one way by Euclides and by Euler in the other, two of the greatest mathematicians of all time. Euler also did some work on odd perfect numbers.

    • @leadnitrate2194
      @leadnitrate2194 Před 5 lety

      Actually, Euclid proved this theorem and Euler proved its coverse (that all perfect numbers are of this form.)

    • @KasabianFan44
      @KasabianFan44 Před rokem

      @@leadnitrate2194
      That’s… literally what he said…

    • @leadnitrate2194
      @leadnitrate2194 Před rokem

      @@KasabianFan44 I thought "one way by Euclid and by Euler in the other" meant that he was saying they proved the same thing two different ways, which isn't true.
      Now that you're pointing it out though, I can see how I was probably wrong.

    • @KasabianFan44
      @KasabianFan44 Před rokem

      @@leadnitrate2194
      Ahhhhh I see, my bad

  • @LineGrinder01
    @LineGrinder01 Před 9 lety +7

    Matt has got to be the best teacher ever.

    • @mkj1887
      @mkj1887 Před 3 lety

      Stand and deliver?

  • @cbhowmick
    @cbhowmick Před 9 lety

    thank you guys!!!!!!!

  • @KWGTech
    @KWGTech Před 9 lety +14

    Why math > science: You dont have idiots claiming satanism in the comments.
    (and just to be clear im not saying everyone is like this)

    • @eNSWE
      @eNSWE Před 9 lety +3

      ***** lolwat. quantum mechanics is one of the most well empirically tested fields of physics there is. it has been thoroughly tested again and again and again during the entire 20th century. also, you'd be hard pressed to find any physicist at all who doesn't acknowledge it's validity.

    • @the0dued
      @the0dued Před 9 lety

      ***** are you taking about things like particle physics, super symmetry, super gravity, m-theory, super fluid vacuum theory, and loop quantum gravity. because they are not all subsets of quantum theory thought they use ideas from quantum mechanics they would be more accurately described as parts of theoretical physics.

  • @lvalentino6325
    @lvalentino6325 Před 4 lety +2

    I wish to be at one of his classes🤓

  • @ilirllukaci5345
    @ilirllukaci5345 Před rokem

    Superb video.

  • @dominicpancella3012
    @dominicpancella3012 Před 2 lety +1

    The perfect numbers are the triangular numbers of the Mersenne primes, or the factors that you multiply by are half the prime plus 1

  • @Emerson_Bass
    @Emerson_Bass Před 7 lety

    Matt has a book. It's called " Things to Make and Do in the Fourth Dimension Parker Square". Check it out

  • @Tangobaldy
    @Tangobaldy Před 9 lety

    Totally above my intelligence! Looking forward to next video

  • @notoriouswhitemoth
    @notoriouswhitemoth Před 9 lety

    To avoid confusion it might help to be a bit more rigorous - and a bit more formal - with the syntax, differentiating the product of 2^n minus one from two to the power of the difference of n-1. It's a litte harder to follow, but if you understand it, it makes it clearer which is which.

  • @burgers8
    @burgers8 Před 9 lety

    I've seen Matt Parker in countless numbers of these videos and I just realized he reminds me of The Doctor.

  • @JM-us3fr
    @JM-us3fr Před 8 lety +15

    You proved each Mersenne prime makes a perfect number of that form. You should prove the converse too: every even perfect number has that specific form.

    • @Leyrann
      @Leyrann Před 4 lety

      Is that proven, or have we just not disproven it?

    • @shambosaha9727
      @shambosaha9727 Před 4 lety +3

      @@Leyrann Euler proved it

    • @coc235
      @coc235 Před 3 lety

      An odd number can't be written in that form, and we don't know if there are any odd perfect numbers, therefore this isnt proven

    • @Mmmm1ch43l
      @Mmmm1ch43l Před 2 lety

      @@coc235 they specified "even perfect number" so yes, it was proven

  • @billstevens3796
    @billstevens3796 Před 4 lety +1

    And I'm screaming 256 without thinking it through, I guess I subconsciously realized it was powers of two.

  • @josnardstorm
    @josnardstorm Před 8 lety +60

    ..."negative one plus two to the n"...ambiguity gone

    • @stickmandaninacan
      @stickmandaninacan Před 8 lety +21

      technically that could still mean (-1+2)^n, but i don't think any one normal would actually think that

    • @josnardstorm
      @josnardstorm Před 8 lety +3

      +stickmandaninacan oh, yah. That hadn't occurred to me.

    • @ferko28
      @ferko28 Před 7 lety +1

      minus 1 plus the nth power of two is the only case that there's no ambiguity at all, i guess.

    • @Shadowmere29
      @Shadowmere29 Před 7 lety +3

      +stickmandaninacan No. (-1+2)^n is 1^n, which is 1. The order that you put the base and exponent matter with this operation.

    • @ffggddss
      @ffggddss Před 6 lety +1

      Best IMHO is, "two to the n power minus one" vs "two to the n minus one power."
      Completely unambiguous.
      "to the" and "power" act like left and right parentheses there.

  • @LordMarcus
    @LordMarcus Před 9 lety +22

    Is it just me, or does anyone else get a real self-satisfied kick out of people who insist it's not possible to solve infinite sums in the manner described starting at 11:00?

    • @steffahn
      @steffahn Před 9 lety +20

      The sum in the video is not even infinite.

    • @Wout12345
      @Wout12345 Před 9 lety +3

      Yeah, stuff can get a bit vague when you get to infinite sums. But this one's finite, so there's no real ambiguity to the result. The dots are not necessary, you could as well write the entire sum out and that way it's obvious all of the middle cancels out.

    • @screw0dog
      @screw0dog Před 9 lety +7

      This method only works for infinite sequences whose sum converges. (Unless you're a physicist who doesn't care about rigour).

    • @vernement4752
      @vernement4752 Před 9 lety +15

      Wrong, infinity is a concept, not a number.

    • @BlueCosmology
      @BlueCosmology Před 9 lety +3

      Well, you shouldn't because they're the ones that are right. That is a perfectly valid method for solving a finite sum, however it is COMPLETELY invalid for an infinite sum other than the small subset that completely converge. Using that method you can get literally any value answer you want. Look up the Riemann series theorem. It is well known that if you manipulate an infinite sum in this way you can arise at any solution you want. For instance 1+2+3+4+... can be shown using this method to equal -50, 2, 17, 99992, 1/6 and absolutely any other value (or also equally be shown not to equal anything).

  • @LordNethesis
    @LordNethesis Před 9 lety

    More of this on numberphile would be appreciated :) this is maths

  • @twilightknight123
    @twilightknight123 Před 9 lety +1

    In a previous video about the mandelbrot set and the numbers 63 and -7/4, Dr. Krieger stated that every Mersenne number (other than 63) would have a new prime divisor. Is there any way you could show a video of a proof of that?
    She also said that 63 being the 6th element in the sequence was the cause of it not having a new prime divisor. Is that because it is a perfect number? In that case, would the 28th element not have a new prime divisor as well?
    I've been struggle to find anything online proving her statement and I haven't been able to prove it myself either so if a video could be made (or at least if I could be given a link to an article) that would be fantastic.

  • @NickiRusin
    @NickiRusin Před 9 lety

    Beautiful.

  • @clickrick
    @clickrick Před 5 lety +9

    3:35 "professional jerk".
    I'd love to see that as your profession on official documents.

  • @Schlynn
    @Schlynn Před 6 lety

    Fun proof. Similar to a lot of the proofs I did when studying polygonal numbers.

  • @ronakpol1580
    @ronakpol1580 Před 9 lety

    1st few souls to see this one!!
    XD don't know if it indicates how responsive my cellphones notifications are.. or how interesting these videos are that it makes me watch them even when i have a test the following day XD

  • @daalfredLP
    @daalfredLP Před 8 lety +1

    Yeah! I found the Pattern for the Factors :D

  • @shush1329
    @shush1329 Před 2 lety +1

    I demand a Parker prime!

  • @agnesjeffery850
    @agnesjeffery850 Před 7 lety

    I don't change my tone when differentiating between 2^(n-1) and 2^n-1. I use pauses. There's 2 to the…n minus one vs 2 to the n…minus 1.

  • @hegebaggethun5650
    @hegebaggethun5650 Před 4 lety

    Hi Numberphile, thanks for this lovely video. At time 10:10 I look at the workings and can't understand why the first line of the calculation (on top) is multiplied by (2^n) - 1, this is not included on the second line up from the bottom, did I misunderstand somewhere?

  • @TIMS3O
    @TIMS3O Před 9 lety

    Another way to see that the geometric sum of 2:s at the end is equal 2^n-1 is to see the sum as a strip of n-1 1:s in binary which is the same 2^n-1

  • @BlaiseIgirubuntu
    @BlaiseIgirubuntu Před 9 lety +1

    That was beautiful

  • @maxnullifidian
    @maxnullifidian Před 5 lety

    Watching people do math is like watching people dance - I can't do either, but it's fun to watch someone who does it well.

  • @WildStar2002
    @WildStar2002 Před 9 lety +10

    I knew that 6 was a perfect number from my childhood, but on a lonely day with nothing to do (and before the internet) I worked out that 28 was the next one and that 496 the third one when I noticed the pattern in the factors and stumbled onto Mersenne primes by accident as I tried to work out more perfect numbers. I was so excited! Alas, that I was not the first (by millennia) - but it was still fun to discover on my own!
    Awesome video and explanation of why it works out this way. Thanks!

    • @JM-us3fr
      @JM-us3fr Před 6 lety

      Mathematics at its best

    • @theblackwidower
      @theblackwidower Před 5 lety

      That's always fun. I remember being bored one day and trying to write a proof for the the quadratic equasion, I think it was nearly a decade before I found out what proofs were. So satisfying.

  • @starponys0740
    @starponys0740 Před 5 lety

    At 9:16, I start seeing two sequences multiplied by the Mersenne prime -- instead of just one.

  • @nov51947
    @nov51947 Před 9 lety

    I have been a fan of both Perfect Numbers and Mersenne Primes since high school (~50+ yrs ago!!), but I have never seen this proof! In the immortal words of Mr. Spock..."Fascinating!"

  • @sadieandbean
    @sadieandbean Před 9 lety +3

    I'm in high school and I got the pattern before you said it. I do feel smug :)

  • @vileguile4
    @vileguile4 Před 9 lety +2

    What's à perfekt Numbers?
    Lol Swedish spelling correction when typing English :)
    What's a perfect number - the perfect question to answer at the start of this video!

  • @dcs_0
    @dcs_0 Před 7 lety

    What I would give to have Matt Parker as my maths teacher...

  • @danphillips8530
    @danphillips8530 Před 4 lety +1

    The largest known perfect number, which is the 51st perfect number known, is (2^82589932)(2^82589933 - 1)

  • @benhbr
    @benhbr Před 9 lety +3

    @9:09 a wrong factor (2^n-1) appears in the first line

  • @magicalpencil
    @magicalpencil Před 9 lety

    that hit me right in the maths

  • @lexinaut
    @lexinaut Před 8 lety

    Knocks me Mersennesless! Two-per duper! Foundational number theory I would think. And by the way, who do you think WILL win the geometric series this year? The Common Ratios are favored.
    Thanks! Like this a lot!

  • @TakeWalker
    @TakeWalker Před 9 lety +3

    I am in severe awe of this man's mathematical prowess.

  • @Fjollmongo
    @Fjollmongo Před 9 lety

    About loking smug. Matt's look at the end.. :)

  • @xxxromant
    @xxxromant Před rokem +1

    3:36 oh wow damn, im not sure if maybe i once already watched this video and forgot or already watched a video about it and forgot but i actually managed to figure out the pattern first try, kinda happy about that uwu

  • @fakjbf
    @fakjbf Před 9 lety

    I realized the pattern had something to do with powers of two, it was actually the first thing I saw. I just hadn't worked out what they all were before he showed it, so I didn't get the chance to see the connection to the first column.

  • @NoahtheEpicGuy
    @NoahtheEpicGuy Před 3 lety

    I immediately saw that pattern as 2^(n-1) because binary, 2^n (because of programming, binary is something I use on the daily), and because it related to the equation (2^n)-1, also related to binary.
    It's funny when you think about it, math and programming are so similar yet so different, or at least in my mind they are.

  • @badcalculon
    @badcalculon Před 9 lety +161

    As a CS grad, the first thing I saw was the pattern

    • @matobozo666
      @matobozo666 Před 9 lety

      im sorry, but what's a CS grad?

    • @Slithy
      @Slithy Před 9 lety +3

      Matej božič Computer sciences graduate, i guess.

    • @matobozo666
      @matobozo666 Před 9 lety +3

      Slithereenn oh yeah.. probably, thanks!

    • @Slithy
      @Slithy Před 9 lety

      Matej božič You're always welcome :)

    • @physjim
      @physjim Před 9 lety +16

      congrats i saw it in less than 5 sec and i'm still an undergrad, anyone with a basic understanding of powers can see it stop gloating, in fact if a student can't see the pattern he should be worried

  • @kidbuu8025
    @kidbuu8025 Před 8 lety

    you dont need geometric series to solve that, just add 1 to the 1+2+4+..., you can see that the 1 you add merge the 1, equal 2, then 2 merge 2 equal 4 and so on until it is 2 to the n, and finally minus 1 which you added earlier.

  • @SWhite-hp5xq
    @SWhite-hp5xq Před 8 lety

    I went through another day not having to use these calculations, again.

  • @AkiSan0
    @AkiSan0 Před 9 lety +1

    That smug face at the end! :D

  • @dimitris5267
    @dimitris5267 Před 6 lety

    If we use the equation (2^n -1)(2^n-1) I noticed that the number of divisors(including the number itself) of a perfect number is always equal 2n. Does someone know why is that?

  • @darreljones8645
    @darreljones8645 Před 9 lety

    A little-known fact is the converse of the theorem proved here is also true: If an even number is perfect, it must be of the form described here (i.e, 2 ^ (n - 1) * ((2 ^ n) - 1) ). This was proved by either Euler or Fermat, I'm not sure which. The proof is also longer than this one.

  • @sethv5273
    @sethv5273 Před 17 dny

    I found the 2,4,16,64 incredibly quickly. I’m not a genius, I just had already read the top comment

  • @dr.rahulgupta7573
    @dr.rahulgupta7573 Před 3 lety +1

    Excellent presentation of the topics. Many many thanks. DrRahul Rohtak India

  • @ND62511
    @ND62511 Před rokem

    Interestingly enough, one way to tackle the 1 + 2^1 + 2^2 + … 2^(n-2) + 2^(n-1) summation is to write it in binary. What happens when you do that is you get a binary number that’s a series of 1s that’s n-1 digits long, so if you’re familiar with how binary numbers work it becomes immediately obvious what the sum is.

  • @Natalie-cx3cp
    @Natalie-cx3cp Před 9 lety

    Matt,
    When I go to university I want to be in your class! What university do you teach at? I got your signed book for Christmas with shapes of constant width 2d and 3d, utilities mug, and the heart keyring! (I can't remember what it was called) they were the best presents ever!

  • @Danicker
    @Danicker Před 7 lety

    Pattern at the start seemed obvious to me, but a interesting video none the less

  • @WorldOfDeepThought
    @WorldOfDeepThought Před 9 lety +16

    There's a mistake at 10:00.
    It should be: (1+2+...+2^(n-1)) + (2^n -1) + .........
    You wrote: (1+2+...+2^(n-1))*(2^n -1) + (2^n -1) + .........

    • @chevizz
      @chevizz Před 9 lety +17

      9+10=21

    • @hshdhdbnd
      @hshdhdbnd Před 9 lety +4

      Agreed, same mistake at 9:19

    • @Nicegeist
      @Nicegeist Před 9 lety

      I think that was originally supposed to be a reminder, that the sum in that line adds up to (2^n)-1 ... but using commentary with round brackets in equations is not a smart thing to do.

    • @CYXXYC
      @CYXXYC Před 9 lety +1

      ***** or 9+4=30

    • @some1rational
      @some1rational Před 9 lety +1

      yes, plz correct, i try to follow along but mistakes like these can literally throw the video out of wack

  • @ThatOldGuyYouKnow
    @ThatOldGuyYouKnow Před 8 lety +1

    Can you prove this problem via Induction of the series?