TED2005
Arthur Benjamin: A performance of "Mathemagic"
Artur Bendžamin - matemagičar!
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U ovom živahnom nastupu matematičar Artur Bendžamin pokušava da bude brži od digitrona u računanju kvadrata trocifrenih brojeva, napamet rešava izuzetno tešku jednačinu i pogađa rođendane. Kako to radi? Reći će vam.
Arthur Benjamin - Mathemagician
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio
Double-click the English transcript below to play the video.
00:13
Well, good morning ladies and gentlemen.
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Dobro jutro, dame i gospodo.
00:14
My name is Art Benjamin, and I am a "mathemagician."
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Zovem se Artur Bendžamin i ja sam "matemagičar".
00:18
What that means is, I combine my loves of math and magic
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To znači da kombinujem svoju ljubav za matematikom sa magijom
00:21
to do something I call "mathemagics."
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u nešto što zovem "matemagijom".
00:24
But before I get started, I have a quick question for the audience.
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Ali pre nego što počnem, imam kratko pitanje za publiku.
00:27
By any chance, did anyone happen
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Da li je neko slučajno
00:29
to bring with them this morning a calculator?
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poneo ovog jutra sa sobom digitron?
00:33
Seriously, if you have a calculator with you, raise your hand, raise your hand.
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Ozbiljno, ako imate digitron kod sebe, podignite ruku, podignite ruku.
00:37
I -- was -- your hand go up?
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Ja - sam - vi ste digli ruku?
00:39
Now bring it out, bring it out. Anybody else?
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Izvadite ga, izvadite ga. Još neko?
00:41
I see, I see one way in the back.
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Vidim, vidim jednu skroz iza.
00:43
You sir, that's three,
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Vi gospodine, to je 3.
00:45
And anybody on this side here?
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Neko na ovoj strani ovde?
00:48
OK, you over there on the aisle. Would the four of you with calculators
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Ok, vi tamo pored prolaza. Možete li vas četvoro sa digitronima
00:50
please bring out your calculators, then join me up on stage.
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da ih donesete i pridružite mi se na pozornici?
00:53
And let's give these volunteers a nice round of applause.
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I dajmo ovim dobrovoljcima lep aplauz.
00:55
(Applause)
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(Aplauz)
00:58
That's right. Now, since I haven't had the chance
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U redu. Sada, pošto nisam imao priliku
01:01
to work with these calculators, I need to make sure
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da radim s ovim digitronima, moram da se uverim
01:04
that they are all working properly.
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da rade ispravno.
01:06
Would somebody get us started by giving us a
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Može li neko da počne dajući nam
01:08
two-digit number please?
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dvocifreni broj, molim?
01:11
How about a two-digit number?
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Može jedan dvocifreni broj?
01:13
Audience: 22.
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Publika: 22.
01:14
Arthur Benjamin: 22. And another two-digit number, Sir?
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Arthur Benjamin: 22. I još jedan dvocifreni broj, gospodine?
01:16
Audience: 47.
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Publika: 47.
01:17
AB: Multiply 22 times 47, make sure you get 1,034,
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Pomnožite 22 sa 47, proverite da li ste dobili 1034,
01:21
or the calculators are not working. Do all of you get 1,034? 1,034?
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ili digitroni ne rade. Da li ste svi dobili 1034? 1034?
01:26
Woman: No.
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Žena: Ne.
01:27
AB: 594. Let's give three of them a nice round of applause there.
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594. Dajmo za ovo troje jedan lepi aplauz?
01:31
(Applause)
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(Aplauz)
01:33
Would you like to try a more standard calculator, just in case?
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Želite li možda neki običniji digitron za svaki slučaj?
01:35
OK, great.
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Ok, super?
01:37
What I'm going to try and do then --
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Ono što ću pokušati i uraditi je -
01:39
I notice that took some of you a little bit of time to get your answer.
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Primećujem da je nekima od vas trebalo vremena da dođete do rešenja.
01:42
That's OK. I'll give you a shortcut for multiplying
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To je ok. Daću vam prečicu za množenje
01:45
even faster on the calculator.
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na digitronima koje će biti brže.
01:47
There is something called the square of a number,
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Postoji nešto što se zove kvadrat broja,
01:49
which most of you know is taking a number
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za šta većina od vas zna da je to množenje broja
01:51
and multiplying it by itself.
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sa samim sobom.
01:53
For instance, five squared would be?
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Na primer, 5 na kvadrat je?
01:55
Audience: 25.
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Publika: 25
01:56
AB: 25. Now, the way we can square on most calculators --
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25. Sada, način na koji možemo da kvadriramo brojeve na većini digitrona--
01:58
let me demonstrate with this one --
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pokazaću na ovom --
02:00
is by taking the number, such as five,
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je da upišemo broj, na primer 5,
02:02
hitting "times" and then "equals,"
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pritisnemo "puta" i onda "jednako",
02:05
and on most calculators that will give you the square.
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i većina digitrona će vam dati kvadrat.
02:08
On some of these ancient RPN calculators,
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Na nekim starim RPN digitronima,
02:10
you've got an "x squared" button on it,
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postoji naredba "x na kvadrat",
02:12
will allow you to do the calculation even faster.
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koja vam omogućuje da izračunate ovo još brže.
02:15
What I'm going to try and do now is to square, in my head,
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Ono što ću sada pokušati je da kvadriram, napamet
02:18
four two-digit numbers
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4 dvocifrena broja
02:20
faster than they can do on their calculators, even using the shortcut method.
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brže nego što oni mogu na svojim digitronima, čak i sa ovom bržom metodom.
02:24
What I'll use is the second row this time, and I'll get four of you --
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Sada ću koristiti drugi red i vas četvoro -
02:26
one, two, three, four -- to each yell out a two-digit number,
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jedan, dva, tri, četiri -- doviknite mi dvocifreni broj,
02:29
and if you would square the first number,
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a vi kvadrirajte prvi broj,
02:33
and if you would square the second, the third and the fourth,
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a vi drugi, pa treći i četvrti,
02:35
I will try and race you to the answer. OK?
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a ja ću se utrkivati sa vama ko će brže do rešenja. Ok?
02:38
So quickly, a two-digit number please.
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Pa brzo -- molim jedan dvocifreni broj.
02:41
Audience: 37.
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Publika: 37.
02:42
AB: 37 squared, OK.
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37 na kvadrat, ok.
02:44
Audience: 23.
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Publika: 23.
02:45
AB: 23 squared, OK.
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23 na kvadrat, ok.
02:47
Audience: 59.
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Publika: 59.
02:48
AB: 59 squared, OK, and finally?
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59 na kvadrat, ok i konačno?
02:49
Audience: 93.
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Publika: 93.
02:51
AB: 93 squared. Would you call out your answers, please?
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93 na kvadrat. Hoćete li mi reći vaša rešenja, molim?
02:54
Woman: 1369. AB: 1369.
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Žena: 1369. AB: 1369.
02:56
Woman: 529.
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Žena: 529.
02:57
AB: 529.
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AB: 529.
02:58
Man: 3481.
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Muškarac: 3481.
02:59
AB: 3481.
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AB: 3481.
03:00
Man: 8649.
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Muškarac: 8649.
03:01
AB: Thank you very much.
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AB: Hvala vam mnogo.
03:02
(Applause)
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(Aplauz)
03:07
Let me try to take this one step further.
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Dopustite mi da pomerim ovo za jedan korak dalje.
03:10
I'm going to try to square some three-digit numbers this time.
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Ovaj put ću pokušati da kvadriram trocifrene brojeve.
03:13
I won't even write these down --
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I neću ih ni zapisati.
03:15
I'll just call them out as they're called out to me.
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Samo ću viknuti rezultate kada čujem brojeve.
03:17
Anyone I point to, call out a three-digit number.
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Oni na koje pokažem, doviknite trocifreni broj.
03:20
Anyone on our panel, verify the answer.
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Neka sa ove strane neko to potvrdi.
03:22
Just give some indication if it's right.
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Samo dajte naznaku ako je tačno.
03:24
A three-digit number, sir, yes?
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Trocifreni broj, gospodine, da?
03:27
Audience: 987.
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Publika: 987.
03:28
AB: 987 squared is 974,169.
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987 na kvadrat je 974169.
03:31
(Laughter)
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(Smeh)
03:33
Yes? Good.
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Da? Dobro.
03:35
Another, another three-digit --
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Drugi, sledeći trocifreni broj --
03:37
(Applause)
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(Aplauz)
03:38
-- another three-digit number, sir?
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-- još jedan trocifreni broj, gospodine?
03:41
Audience: 457.
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Publika: 457.
03:42
AB: 457 squared is 205,849.
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457 na kvadrat je 205849.
03:45
205,849?
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205849?
03:47
Yes?
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Da?
03:49
OK, another, another three-digit number, sir?
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Ok, sledeći, sledeći trocifreni broj, gospodine?
03:52
Audience: 321.
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Publika: 321.
03:53
AB: 321 is 103,041. 103,041.
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321 je 103041. 103041.
03:56
Yes? One more three-digit number please.
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Da? Još jedan trocifreni broj molim.
03:59
Audience: Oh, 722.
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Publika: Oh, 722.
04:01
AB: 722 is 500 -- ooh, that's a harder one.
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722 je 500 -- ooh, ovo je teže.
04:04
Is that 513,284?
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Je li 513284?
04:07
Woman: Yes.
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Žena: Da?
04:08
AB: Yes? Oh, one more, one more three-digit number please.
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AB: Da? Oh, još jedan, još jedan trocifreni broj molim.
04:11
Audience: 162.
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Publika: 162.
04:12
162 squared is 26,244.
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162 na kvadrat je 26244.
04:16
Thank you very much.
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Hvala vam mnogo.
04:18
(Applause)
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(Aplauz)
04:25
Let me try to take this one step further.
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Dopustite da odem još dalje s ovim.
04:28
(Laughter)
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(Smeh)
04:30
I'm going to try to square a four-digit number this time.
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Pokušaću da kvadriram četvorocifreni broj ovoga puta.
04:33
Now you can all take your time on this; I will not beat you to the answer on this one,
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Ne morate da žurite s ovim; ne mogu da budem brži od vas,
04:36
but I will try to get the answer right.
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ali pokušaću da pogodim tačan odgovor.
04:38
To make this a little bit more random, let's take the fourth row this time,
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Da uvedemo još malo slučajnosti, sada ćemo uzeti 4. red publike,
04:41
let's say, one, two, three, four.
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recimo jedan, dva, tri, četiri.
04:44
If each of you would call out a single digit between zero and nine,
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Ako svako od vas vikne jednu cifru od nula do devet,
04:46
that will be the four-digit number that I'll square.
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to bi bio četvorocifreni broj koji ću da kvadriram.
04:49
Audience: Nine.
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Publika: 9.
04:50
AB: Nine.
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9.
04:51
Audience: Seven. AB: Seven.
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Publika: 7. AB: 7.
04:52
Audience: Five. AB: Five.
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Publika: 5. AB: 5.
04:53
Audience: Eight. AB: Eight.
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Publika: 8. AB: 8.
04:55
9,758, this will take me a little bit of time, so bear with me.
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9758, ovo će malo duže da potraje, tako da budite sa mnom.
04:58
95,218,564?
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95 218 564?
05:07
Woman: Yes.
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Žena: Da.
05:08
AB: Thank you very much.
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Hvala vam mnogo.
05:10
(Applause)
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(Aplauz)
05:18
Now, I would attempt to square a five-digit number --
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Sada bih pokušao da kvadriram petocifreni broj --
05:21
and I can --
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i mogu --
05:23
but unfortunately most calculators cannot.
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ali nažalost mnogi digitroni ne mogu.
05:25
(Laughter)
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(Smeh)
05:27
Eight-digit capacity -- don't you hate that?
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Kapacitet od 8 cifrara -- zar ne mrzite to?
05:30
So, since we've reached the limits of our calculators --
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Pa kako smo došli do granica naših digitrona --
05:33
what's that? Does yours go --
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molim? Da li vaš ide do --
05:36
Woman: I don't know.
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Žena: Ne znam.
05:37
AB: Does yours go higher?
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Da li vaš ide više?
05:39
Oh -- yours does?
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Oh -- ide?
05:41
Man: I can probably do it.
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Muškarac: Verovatno mogu to da uradim.
05:42
AB: I'll talk to you later.
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Pričaću sa vama kasnije.
05:44
In the meanwhile, let me conclude
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U međuvremenu, završio bih
05:46
the first part of my show by doing something a little trickier.
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prvi deo mog nastupa sa nečim malo težim.
05:49
Let's take the largest number on the board here, 8649.
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Uzmimo najveći broj na ovoj ploči, 8649.
05:52
Would you each enter that on your calculator?
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Hoćete li molim vas da ga ukucate u digitrone?
05:55
And instead of squaring it this time,
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I sada umesto da ga kvadrirate,
05:57
I want you to take that number and multiply it
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hoću da ga pomnožite
05:59
by any three-digit number that you want,
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sa bilo kojim trocifrenim brojem,
06:02
but don't tell me what you're multiplying by --
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ali nemojte da mi kažete s kojim--
06:04
just multiply it by any random three-digit number.
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samo pomnožite sa bilo kojim trocifrenim brojem.
06:07
So you should have as an answer either
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Rezultat je ili
06:09
a six-digit or probably a seven-digit number.
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šestocifreni ili sedmocifreni broj.
06:13
How many digits do you have, six or seven?
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Koliko cifara imate, 6 ili 7?
06:14
Seven, and yours? Woman: Seven.
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7, a vi? Žena: 7.
06:16
AB: Seven? Seven?
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7? 7?
06:19
And, uncertain.
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I možda.
06:21
Man: Yeah.
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Muškarac: Da.
06:22
AB: Seven. Is there any possible way that I could know
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7. Postoji li mogućnost da bih mogao da znam
06:24
what seven digit numbers you have? Say "No."
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kojih 7 brojeva imate? Recite "Ne".
06:27
(Laughter)
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(Smeh)
06:29
Good. Then I shall attempt the impossible --
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Dobro. Onda ću da probam nemoguće--
06:31
or at least the improbable.
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ili bar neverovatno.
06:33
What I'd like each of you to do is to call out for me
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Želim da mi svako od vas dovikne
06:35
any six of your seven digits, any six of them,
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bilo kojih 6 od 7 cifara koje imate, bilo kojih 6,
06:38
in any order you'd like.
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u bilo kom redosledu.
06:40
(Laughter)
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(Smeh)
06:41
One digit at a time, I shall try and determine the digit you've left out.
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Jednu po jednu cifru, a ja ću pokušati da pogodim koju ste cifru izostavili.
06:46
So, starting with your seven-digit number,
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Pa, počevši sa vašim sedmocifrenim brojem,
06:48
call out any six of them please.
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molim recite bilo kojih 6.
06:50
Woman: One, OK, 197042.
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Žena: 1, ok, 197042.
06:56
AB: Did you leave out the number 6?
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Da li ste izostavili broj 6?
06:57
Woman: Yes, AB: Good, OK, that's one.
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Žena: Da. AB: Dobro, ok, to je jedan.
06:59
You have a seven-digit number, call out any six of them please.
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Vi imate sedmocifreni broj, viknite bilo kojih 6 od 7?
07:01
Woman: 44875.
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Žena: 44875.
07:04
AB: I think I only heard five numbers. I -- wait -- 44875 --
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Mislim da sam čuo samo 5 brojeva. Ja - čekajte - 44875 -
07:09
did you leave out the number 6?
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da li ste izostavili broj 6?
07:11
Woman: Yes. AB: Same as she did, OK. You've got a seven-digit number --
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Žena: Da. AB: Isto kao ona, ok. Vi imate sedmocifreni broj -
07:13
call out any six of them loud and clear.
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viknite bilo kojih 6 jasno i glasno.
07:16
Man: 079044.
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Muškarac: 079044.
07:20
AB: I think you left out the number 3?
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Mislim da ste izostavili broj 3?
07:22
That's three. The odds of me getting all four of these right by random guessing
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To je 3. Verovatnoća da sam slučajno pogađao ove 4 cifre
07:26
would be one in 10,000: 10 to the fourth power.
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bi bila 1:10 000 tj 10 na 4. stepen.
07:29
OK, any six of them.
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Ok, bilo kojih 6.
07:32
Really scramble them up this time, please.
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Molim da ih stvarno izmešate sada.
07:34
Man: 263972.
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Muškarac: 263972.
07:38
AB: Did you leave out the number 7?
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Da li ste izostavili broj 7?
07:40
And let's give all four of these people a nice round of applause.
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I dajmo svima jedan lep aplauz.
07:42
Thank you very much. (Applause)
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Hvala vam mnogo.
07:52
For my next number --
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Za sledeću tačku -
07:54
(Laughter)
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(Smeh)
07:57
while I mentally recharge my batteries,
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dok mentalno napunim baterije,
07:59
I have one more question for the audience.
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imam jedno pitanje za publiku.
08:02
By any chance, does anybody here happen to know
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Da li neko ovde slučajno zna
08:07
the day of the week that they were born on?
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kog dana u nedelji je rođen?
08:10
If you think you know your birth day, raise your hand.
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Ako mislite da znate dan rođenja, podignite ruku.
08:14
Let's see, starting with -- let's start with a gentleman first,
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Da vidimo, počnimo sa - počnimo prvo sa gospodinom,
08:17
OK sir, what year was it, first of all? That's why I start with a gentleman first.
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Ok gospodine, prvo koja je to godina bila? Zato prvo počinjem sa gospodinom.
08:20
What year?
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Koja godina?
08:21
Audience: 1953.
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Publika: 1953.
08:22
AB: 1953, and the month?
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1953. i koji mesec?
08:24
Audience: November. AB: November what?
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Publika: Novembar. AB: Koji novembar?
08:25
Audience: 23rd.
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Publika: 23.
08:26
AB: 23rd -- was that a Monday? Audience: Yes.
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23. - da li je to bio ponedeljak? Publika: Da.
08:28
Yes, good. Somebody else? Who else would like --
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Da, dobro, neko drugi? Ko bi hteo -
08:30
see I don't -- haven't seen any women's hands up.
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vidite ja ne - nisam još video da žene dižu ruke.
08:32
OK, it's -- how about you, what year?
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Ok, to je - možete li vi, koja godina?
08:34
Audience: 1949. AB: 1949, and the month?
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Publika: 1949. AB: 1949. i koji mesec?
08:36
Audience: October. AB: October what?
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Publika: Oktobar. AB: Koji oktobar?
08:37
Audience: Fifth.
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Publika: Peti.
08:38
AB: Fifth -- was that a Wednesday?
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Peti - da li je to bila sreda?
08:40
Yes, my -- I'll go way to the back right now, how about you?
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Da - otići ću malo iza, vi?
08:42
Yell it out, what year? Audience: 1959.
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Viknite, koja godina? Publika: 1959.
08:44
AB: 1959, OK -- and the month?
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1959. ok - i mesec?
08:46
Audience: February.
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Publika: Februar.
08:48
AB: February what? Audience: Sixth.
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Koji februar? Publika: Šesti.
08:50
AB: Sixth -- was that a Friday? Audience: Yes.
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Šesti - da li je to bio petak? Publika: Da.
08:52
Good, how about the person behind her?
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Dobro, a osoba iza nje?
08:54
Call -- call -- what year was it?
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Recite, recite - koja godina?
08:56
Audience: 1947. AB: 1947, and the month?
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Publika: 1947. AB: 1947. i mesec?
08:58
Audience: May. AB: May what?
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Publika: Maj. AB: Koji maj?
09:00
Audience: Seventh. AB: Seventh -- would that be a Wednesday?
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Publika: Sedmi. AB: Sedmi - da li je to bila sreda?
09:02
Audience: Yes.
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Publika: Da.
09:03
AB: Thank you very much.
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Hvala vam mnogo.
09:05
(Applause)
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(Aplauz)
09:09
Anybody here who'd like to know the day of the week they were born?
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Želi li neko ovde da zna kojeg dana u nedelji je rođen?
09:12
We can do it that way.
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Možemo i tako.
09:14
Of course, I could just make up an answer and you wouldn't know,
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Naravno, mogu da izmislim odgovor i ne biste znali,
09:16
so I come prepared for that.
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pa sam se pripremio za to.
09:18
I brought with me a book of calendars.
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Poneo sam sa sobom knjigu kalendara.
09:21
It goes as far back into the past as 1800, 'cause you never know.
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Ide i do 1800. godine, jer nikad ne znate.
09:25
(Laughter)
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(Smeh)
09:27
I didn't mean to look at you, sir --
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Nisam hteo da gledam u vas, gospodine -
09:29
you were just sitting there.
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samo ste slučajno sedeli tu.
09:31
Anyway, Chris, you can help me out here, if you wouldn't mind.
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Kris, možes li da mi pomogneš, ako ti nije teško.
09:34
This is a book of calendars, and I'll ask --
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Ovo je knjiga kalendara i pitaću -
09:36
who was it that wanted to know their birth day? You sir? OK.
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ko je hteo da zna svoj dan rođenja? Vi gospodine. Ok.
09:38
What year was it, first of all?
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Prvo, koja godina?
09:40
Audience: 1966.
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Publika: 1966.
09:41
AB: '66 -- turn to the calendar with 1966 --
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'66. - okreni kalendar sa 1966. -
09:43
and what month?
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i koji mesec?
09:45
Audience: April. AB: April what?
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Publika: April. AB: Koji april?
09:47
Audience: 17th. AB: 17th -- I believe that was a Sunday.
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Publika: 17. AB : 17. - Verujem da je bila nedelja.
09:50
Can you confirm, Chris?
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Možeš li da potvrdiš, Krise?
09:52
Chris Anderson: Yes. AB: Yeah, OK. I'll tell you what, Chris:
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Kris: Da. AB: Da, ok. Reći ću ti nešto, Kris:
09:54
as long as you have that book in front of you,
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kad već imaš tu knjigu ispred sebe,
09:57
do me a favor, turn to a year outside of the 1900s,
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otvori godine pre 1900-ih
10:01
either into the 1800s or way into the 2000s --
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ili u 1800. ili u 2000.
10:04
that'll be a much greater challenge for me.
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to će biti veći izazov za mene
10:06
What year, Chris, would you like?
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Koju godinu, Kris, želiš?
10:07
CA: 1824.
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Kris: 1824.
10:08
AB: 1824, OK.
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1824, ok.
10:11
And what month? CA: June.
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I mesec? Kris: Jun.
10:13
AB: June what? CA: Sixth.
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Koji jun? Kris: 6.
10:15
AB: Sixth -- was that a Sunday?
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Šesti - da li je bila nedelja?
10:17
CA: It was. AB: And it was cloudy.
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Da. AB: I bilo je oblačno.
10:20
Good, thank you very much.
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Dobro, hvala vam mnogo.
10:22
(Applause)
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(Aplauz)
10:28
But I'd like to wrap things up now
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Hteo bih sada da završim
10:30
by alluding to something
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pozivajući se na nešto
10:33
from earlier in the presentation.
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ranije u mojoj prezentaciji.
10:35
There was a gentleman up here who had a 10-digit calculator.
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Bio je gospodin sa digitronom sa 10 cifara.
10:38
Where is he, would you stand up,
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Gde je, možete li da ustanete -
10:42
10-digit guy?
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momak sa 10 cifara?
10:44
OK, well stand up for me just for a second,
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Ok, ustanite na sekund
10:47
so I can see where you are.
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da vidim gde ste.
10:49
OK, oh, OK -- you have a 10-digit calculator, sir, as well?
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Ok, oh, ok - i vi imate desetocifreni digitron?
10:52
OK, what I'm going to try and do, is to square in my head
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Ok, pokušaću da kvadriram u svojoj glavi
10:56
a five-digit number requiring a 10-digit calculator.
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petocifreni broj za šta je potreban digitron od 10 cifara.
10:59
But to make my job more interesting for you, as well as for me,
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Ali da učinim još interesantijim za vas i za sebe,
11:04
I'm going to do this problem
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rešiću ovaj problem
11:06
thinking out loud.
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na glas.
11:08
So you can actually, honestly hear
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Tako da stvarno možete da čujete
11:11
what's going on in my mind
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šta se dešava u mojoj glavi
11:13
while I do a calculation of this size.
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dok ovo računam.
11:15
Now, I have to apologize to our magician friend Lennart Green.
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Sada, moram da se izvinim našem mađioničaru i prijatelju Lenartu Grinu.
11:18
I know as a magician we're not supposed to reveal our secrets,
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Znam kao mađioničar da ne smemo da otkrivamo naše tajne,
11:22
but I'm not too afraid that people are going
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ali ja se baš i ne plašim da će ljudi početi
11:24
to start doing my show next week, so --
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da izvode moju tačku sledeće nedelje, pa -
11:26
I think we're OK.
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Mislim da smo ok.
11:30
So, let's see, let's take a --
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Pa, da vidimo, uzmimo -
11:33
let's take a different row of people, starting with you.
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neki drugi red ljudi, počevši sa vama.
11:35
I'll get five digits: one, two, three, four --
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dobiću 5 cifara: 1, 2, 3, 4 -
11:38
oh, I did this row already. Let's do the row before you,
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oh, već sam prošao ovaj red. Hajdemo red pre vas,
11:40
starting with you sir: one, two, three, four, five.
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počevši od vas gospodine: 1, 2, 3, 4, 5.
11:43
Call out a single digit -- that will be the five-digit number
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Viknite po jednu cifru - i to će biti petocifreni broj
11:46
that I will try to square. Go ahead.
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koji ću da kvadriram. Krenite.
11:48
Audience: Five. AB: Five.
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Publika: 5. AB: 5.
11:50
Audience: Seven. AB: Seven.
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Publika: 7.AB: 7.
11:51
Audience: Six. AB: Six.
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Publika: 6. AB: 6.
11:52
Audience: Eight. AB: Eight.
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Publika: 8. AB: 8.
11:54
Audience: Three. AB: Three.
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Publika: 3. AB: 3.
11:56
57,683
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57 683
12:01
squared. Yuck.
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na kvadrat. Jao.
12:03
Let me explain to you how
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Objasniću vam kako
12:05
I'm going to attempt this problem.
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ću da pokušam da rešim ovaj problem.
12:08
I'm going to break the problem down into three parts.
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Razbiću problem na 3 dela.
12:11
I'll do 57,000 squared,
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uradiću 57 000 na kvadrat,
12:13
plus 683 squared,
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plus 683 na kvadrat,
12:17
plus 57,000 times
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plus 57 000 puta
12:20
683 times two.
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683 puta 2.
12:22
Add all those numbers together,
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Saberem sve te brojeve,
12:24
and with any luck, arrive at the answer.
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i uz malo sreće, dobiću rešenje.
12:28
Now, let me recap.
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Sada, ponovimo.
12:31
Thank you.
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Hvala vam.
12:34
While I explain something else --
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Dok objasnim nešto drugo -
12:37
-- I know, that you can use, right?
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- znam, to možete da iskoristite, zar ne?
12:40
While I do these calculation[s],
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Dok računam
12:42
you might hear certain words,
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možda čujete neke reči,
12:44
as opposed to numbers, creep into the calculation.
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nasuprot brojevima, kako dolaze usled računanja.
12:48
Let me explain what that is.
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Objasniću.
12:49
This is a phonetic code,
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To je fonetički kod,
12:51
a mnemonic device that I use,
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mnemonički način pamćenja koji koristim,
12:53
that allows me to convert numbers into words.
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koji pretvara brojeve u reči.
12:56
I store them as words, and later on retrieve them as numbers.
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Pamtim ih kao reči i posle vraćam kao brojeve.
12:59
I know it sounds complicated; it's not --
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Znam da zvuči komplikovano, nije -
13:01
I just don't want you to think you're seeing something out of "Rain Man" here.
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Samo ne želim da mislite da gledate nešto iz "Kišnog čoveka".
13:04
(Laughter)
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(Smeh)
13:06
There's definitely a method to my madness --
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Postoji metoda za moje ludilo -
13:08
definitely, definitely. Sorry.
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definitivno, definitivno. Izvinite.
13:10
(Laughter)
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(Smeh)
13:14
If you want to talk to me about ADHD afterwards,
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Ako hoćete da pričate sa mnom o ADHD-u
13:16
you can talk to me then. All right --
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možemo kasnije. U redu -
13:18
by the way, one last instruction,
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usput, poslednja instrukcija,
13:20
for my judges with the calculators -- OK, you know who you are --
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za moje sudije sa digitronima - ok, znate ko ste -
13:23
there is at least a 50 percent chance
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ima bar 50 posto šanse
13:26
that I will make a mistake here.
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da ću da napravim grešku ovde.
13:29
If I do, don't tell me what the mistake is;
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Ako napravim, ne recite koja je greška
13:32
just say, "you're close," or something like that, and I'll try and figure out the answer --
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već "blizu si" ili tako nešto i probaću da nađem rešenje -
13:35
which could be pretty entertaining in itself.
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što bi bilo i samo po sebi zanimljivo.
13:39
If, however, I am right,
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Ako međutim, pogodim,
13:41
whatever you do, don't keep it to yourself, OK?
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šta god da radite, ne ćutite, ok?
13:44
(Laughter)
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(Smeh)
13:45
Make sure everybody knows that I got the answer right,
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Neka svi znaju da sam pogodio tačan odgovor,
13:47
because this is my big finish, OK.
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jer to je moj veliki završetak, ok.
13:50
So, without any more stalling,
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I bez daljeg odlaganja,
13:53
here we go.
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krećemo.
13:56
I'll start the problem in the middle, with 57 times 683.
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Počeću sa problemom u sredini, 57 puta 683.
13:58
Now, 57 times 68 is 3,400, plus 476 is 3876,
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Sada, 57 puta 68 je 3400 plus 476 je 3876,
14:01
that's 38,760 plus 171,
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to je 38760 plus 171,
14:04
38,760 plus 171 is 38,931.
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38760 plus 171 je 38931.
14:07
38,931; double that to get 77,862.
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38931; dupliram to je 77862.
14:11
77,862 becomes cookie fission,
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77862 postaje "cookie fission",
14:13
cookie fission is 77,822.
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"cookie fission" je 77822.
14:17
That seems right, I'll go on. Cookie fission, OK.
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To izgleda dobro, idem dalje. "Cookie fission", ok.
14:19
Next, I do 57 squared, which is 3,249, so I can say,
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Sledeće, 57 na kvadrat je 3249, pa mogu da kažem
14:23
three billion. Take the 249, add that to cookie, 249,
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3 milijarde. Uzmem 249 dodam "cookie", 249,
14:28
oops, but I see a carry coming --
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oops, vidim preliv -
14:30
249 --
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249 -
14:32
add that to cookie, 250 plus 77,
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dodam na cookie, 250 plus 77
14:34
is 327 million --
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je 327 miliona -
14:38
fission, fission, OK, finally, we do 683 squared,
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"fission", "fission", ok, konačno, 683 na kvadrat,
14:41
that's 700 times 666, plus 17 squared
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to je 700 puta 666, plus 17 na kvadrat
14:43
is 466,489, rev up if I need it,
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je 466489, brže ako treba
14:46
rev up, take the 466,
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brže, uzmem 466,
14:48
add that to fission, to get,
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dodam na "fission", da dobijem
14:50
oh gee --
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o Bože -
14:54
328,489.
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328489.
14:58
Audience: Yeah!
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Publika: Da!
14:59
AB: Good.
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AB: Dobro.
15:00
(Applause)
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(Aplauz)
15:01
Thank you very much.
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Hvala vam mnogo.
15:03
I hope you enjoyed mathemagics. Thank you.
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Nadam se da ste uživali u matemagiji. Hvala vam.
15:05
(Applause)
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(Aplauz)
ABOUT THE SPEAKER
Arthur Benjamin - MathemagicianUsing daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty.
Why you should listen
Arthur Benjamin makes numbers dance. In his day job, he's a professor of math at Harvey Mudd College; in his other day job, he's a "Mathemagician," taking the stage in his tuxedo to perform high-speed mental calculations, memorizations and other astounding math stunts. It's part of his drive to teach math and mental agility in interesting ways, following in the footsteps of such heroes as Martin Gardner.
Benjamin is the co-author, with Michael Shermer, of Secrets of Mental Math (which shares his secrets for rapid mental calculation), as well as the co-author of the MAA award-winning Proofs That Really Count: The Art of Combinatorial Proof. For a glimpse of his broad approach to math, see the list of research talks on his website, which seesaws between high-level math (such as his "Vandermonde's Determinant and Fibonacci SAWs," presented at MIT in 2004) and engaging math talks for the rest of us ("An Amazing Mathematical Card Trick").
Arthur Benjamin | Speaker | TED.com