ABOUT THE SPEAKER
Arthur Benjamin - Mathemagician
Using 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").

More profile about the speaker
Arthur Benjamin | Speaker | TED.com
TED2005

Arthur Benjamin: A performance of "Mathemagic"

Arthur Benjamin face "Matemagie"

Filmed:
9,599,588 views

Într-o prezentare vioaie, matemagicianul Arthur Benjamin se întrece cu un grup de calculatoare pentru a găsi rădăcinile unor numere din 3 cifre, rezolva o dificilă ecuație mentală și ghicește câteva zile de naștere. Cum face toate astea? Vă va spune chiar el.
- Mathemagician
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 morningdimineaţă ladiesdoamnelor and gentlemendomnilor.
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Bună ziua doamnelor și domnilor.
00:14
My nameNume is ArtArta BenjaminBenjamin, and I am a "mathemagicianmathemagician."
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Ma numesc Art Benjamin si sunt un "matemagician"
00:18
What that meansmijloace is, I combinecombina my lovesiubește of mathmatematica and magicmagie
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Asta inseamna ca eu combin doua pasiuni - matematica si magia,
00:21
to do something I call "mathemagicsmathemagics."
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pentru a realiza ceea ce eu numesc "matemagie"
00:24
But before I get starteda început, I have a quickrapid questionîntrebare for the audiencepublic.
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Inainte sa incepem, am o intrebare scurta pentru public.
00:27
By any chanceşansă, did anyoneoricine happenîntâmpla
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Din intamplare,
00:29
to bringaduce with them this morningdimineaţă a calculatorcalculator?
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a adus cineva in aceasta dimineata un calculator?
00:33
SeriouslySerios, if you have a calculatorcalculator with you, raisea ridica your handmână, raisea ridica your handmână.
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Serios, daca aveti un calculator la voi, ridicati mana, ridicati mana.
00:37
I -- was -- your handmână go up?
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Ma -- gandeam -- mana ta e sus?
00:39
Now bringaduce it out, bringaduce it out. AnybodyOricine elsealtfel?
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Adu-l aici, adu-l aici. Altcineva?
00:41
I see, I see one way in the back.
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Vad ... vad o mana ridicata departe in spate.
00:43
You sirdomn, that's threeTrei,
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Dumneavoastra domnule, acum avem trei,
00:45
And anybodycineva on this sidelatură here?
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Si cineva din partea aceasta?
00:48
OK, you over there on the aisleculoar. Would the fourpatru of you with calculatorscalculatoare
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Da, tu cel de la margine. As vrea ca voi patru cu calculatoare
00:50
please bringaduce out your calculatorscalculatoare, then joina adera me up on stageetapă.
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va rog, aduceti-va calculatoarele, apoi veniti langa mine pe scena.
00:53
And let's give these volunteersvoluntari a nicefrumos roundrundă of applauseaplauze.
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Sa le oferim voluntarilor un rand generos de aplauze.
00:55
(ApplauseAplauze)
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(Aplauze)
00:58
That's right. Now, sincede cand I haven'tnu au had the chanceşansă
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Asa. Acum, pentru ca nu am avut ocazia
01:01
to work with these calculatorscalculatoare, I need to make sure
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sa lucrez cu aceste calculatoare, trebuie sa ma asigur
01:04
that they are all workinglucru properlycum se cuvine.
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ca toate functioneaza corect.
01:06
Would somebodycineva get us starteda început by givingoferindu- us a
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Pentru inceput ar putea cineva sa ne dea
01:08
two-digitdouă cifre numbernumăr please?
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un numar din doua cifre, va rog?
01:11
How about a two-digitdouă cifre numbernumăr?
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Cine are un numar de doua cifre?
01:13
AudiencePublicul: 22.
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Audienta: 22.
01:14
ArthurArthur BenjaminBenjamin: 22. And anothero alta two-digitdouă cifre numbernumăr, SirDomnule?
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Arthur Benjamin: 22. Si inca un numar de doua cifre, domnule?
01:16
AudiencePublicul: 47.
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Audienta: 47.
01:17
ABAB: MultiplyMultiplica 22 timesori 47, make sure you get 1,034,
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AB: Inmultiti 22 cu 47 si verificati sa va dea 1,034,
01:21
or the calculatorscalculatoare are not workinglucru. Do all of you get 1,034? 1,034?
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sau calculatoarele nu functioneaza. Aveti toti 1,034? 1,034?
01:26
WomanFemeie: No.
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Femeia: Nu.
01:27
ABAB: 594. Let's give threeTrei of them a nicefrumos roundrundă of applauseaplauze there.
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AB: 594. Sa le oferim celor trei un rand de aplauze.
01:31
(ApplauseAplauze)
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(Aplauze)
01:33
Would you like to try a more standardstandard calculatorcalculator, just in casecaz?
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Vreti sa incercati cu un calculator standard, in orice caz?
01:35
OK, great.
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Bine, perfect.
01:37
What I'm going to try and do then --
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Ce urmeaza sa fac --
01:39
I noticeînștiințare that tooka luat some of you a little bitpic of time to get your answerRăspuns.
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Am observat ca v-a luat ceva timp pentru a ajunge la rezultat.
01:42
That's OK. I'll give you a shortcutscurtătură for multiplyingînmulțirea
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Dar este in regula. Am sa va dau o scurtatura pentru
01:45
even fastermai repede on the calculatorcalculator.
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inmultirea mai rapida pe calculator.
01:47
There is something calleddenumit the squarepătrat of a numbernumăr,
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Exista radacina la patrat a unui numar,
01:49
whichcare mostcel mai of you know is takingluare a numbernumăr
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ceea ce inseamna, dupa cum stiti, numarul
01:51
and multiplyingînmulțirea it by itselfîn sine.
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imnultit cu el insusi.
01:53
For instanceinstanță, fivecinci squaredpătrat would be?
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De exemplu, cinci la patrat ar fi?
01:55
AudiencePublicul: 25.
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Audienta: 25.
01:56
ABAB: 25. Now, the way we can squarepătrat on mostcel mai calculatorscalculatoare --
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AB: 25. Acum, felul in care ridicam la patrat cu majoritatea calculatoarelor --
01:58
let me demonstratedemonstra with this one --
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am sa va arat cu acesta --
02:00
is by takingluare the numbernumăr, suchastfel de as fivecinci,
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este tastarea numarului, adica cinci,
02:02
hittinglovind "timesori" and then "equalseste egală,"
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apasand "inmultit" si apoi "egal",
02:05
and on mostcel mai calculatorscalculatoare that will give you the squarepătrat.
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iar pe multe calculatoare ar trebui sa va dea radacina.
02:08
On some of these ancientvechi RPNRPN calculatorscalculatoare,
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Pe unele calculatoare mai vechi,
02:10
you've got an "x squaredpătrat" buttonbuton on it,
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aveti un buton "x la patrat" pe el,
02:12
will allowpermite you to do the calculationcalcul even fastermai repede.
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va va permite sa calculati chiar mai repede.
02:15
What I'm going to try and do now is to squarepătrat, in my headcap,
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Ceea ce voi incerca acum, este sa ridic la patrat, in cap,
02:18
fourpatru two-digitdouă cifre numbersnumerele
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patru numere de doua cifre
02:20
fastermai repede than they can do on theiral lor calculatorscalculatoare, even usingutilizând the shortcutscurtătură methodmetodă.
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mai rapid decat pot ei calcula, chiar folosind metoda rapida.
02:24
What I'll use is the secondal doilea rowrând this time, and I'll get fourpatru of you --
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Voi folosi al doilea rand de aceasta data, si as dori de la voi --
02:26
one, two, threeTrei, fourpatru -- to eachfiecare yellstrigăt out a two-digitdouă cifre numbernumăr,
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unu, doi, trei, patru -- sa strigati cate un numar de doua cifre,
02:29
and if you would squarepătrat the first numbernumăr,
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si as vrea ca tu sa ridici la patrat primul numar,
02:33
and if you would squarepătrat the secondal doilea, the thirdal treilea and the fourthAl patrulea,
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tu al doilea, al treilea si al patrulea,
02:35
I will try and racerasă you to the answerRăspuns. OK?
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iar eu voi incerca sa va intrec. In regula?
02:38
So quicklyrepede, a two-digitdouă cifre numbernumăr please.
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Deci repede -- un numar de doua cifre, va rog.
02:41
AudiencePublicul: 37.
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Audienta: 37.
02:42
ABAB: 37 squaredpătrat, OK.
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AB: 37 la patrat, da.
02:44
AudiencePublicul: 23.
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Audienta: 23.
02:45
ABAB: 23 squaredpătrat, OK.
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AB: 23 la patrat, da.
02:47
AudiencePublicul: 59.
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Audienta: 59.
02:48
ABAB: 59 squaredpătrat, OK, and finallyin sfarsit?
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AB: 59 la patrat, da, iar ultimul?
02:49
AudiencePublicul: 93.
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Audienta: 93.
02:51
ABAB: 93 squaredpătrat. Would you call out your answersrăspunsuri, please?
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AB: 93 la patrat. Imi puteti spune raspunsurile, va rog?
02:54
WomanFemeie: 1369. ABAB: 1369.
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Femeia: 1369. AB: 1369.
02:56
WomanFemeie: 529.
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Femeia: 529.
02:57
ABAB: 529.
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AB: 529.
02:58
Man: 3481.
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Barbatul: 3481.
02:59
ABAB: 3481.
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AB: 3481.
03:00
Man: 8649.
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Barbatul: 8649.
03:01
ABAB: Thank you very much.
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AB: Va multumesc foarte mult.
03:02
(ApplauseAplauze)
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(Aplauze)
03:07
Let me try to take this one stepEtapa furthermai departe.
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Haideti sa mergem un pas mai departe.
03:10
I'm going to try to squarepătrat some three-digittrei cifre numbersnumerele this time.
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Am sa ridic la patrat niste numere de trei cifre acum.
03:13
I won'tnu va even writescrie these down --
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Nici nu o sa le mai scriu --
03:15
I'll just call them out as they're calleddenumit out to me.
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o sa le scriu direct cand mi se spun.
03:17
AnyoneOricine I pointpunct to, call out a three-digittrei cifre numbernumăr.
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Cel spre care arat cu degetul, striga un numar de trei cifre.
03:20
AnyoneOricine on our panelpanou, verifyverifica the answerRăspuns.
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Oricine din juriu, verifica raspunsul.
03:22
Just give some indicationindicaţie if it's right.
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Doar spuneti-mi daca e bine.
03:24
A three-digittrei cifre numbernumăr, sirdomn, yes?
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Un numar din trei cifre, doumnule?
03:27
AudiencePublicul: 987.
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Audienta: 987.
03:28
ABAB: 987 squaredpătrat is 974,169.
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AB: 987 ridicat la patrat e 974,169.
03:31
(LaughterRâs)
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(Rasete)
03:33
Yes? Good.
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Da? Bun.
03:35
AnotherUn alt, anothero alta three-digittrei cifre --
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Inca un numar de trei cifre --
03:37
(ApplauseAplauze)
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(Aplauze)
03:38
-- anothero alta three-digittrei cifre numbernumăr, sirdomn?
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-- inca un numar de trei cifre, domnule?
03:41
AudiencePublicul: 457.
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Audienta: 457.
03:42
ABAB: 457 squaredpătrat is 205,849.
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AB: 457 ridicat la patrat este 205,849.
03:45
205,849?
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205,849?
03:47
Yes?
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Da?
03:49
OK, anothero alta, anothero alta three-digittrei cifre numbernumăr, sirdomn?
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Bun, inca, inca un numar de trei cifre, domnule?
03:52
AudiencePublicul: 321.
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Audienta: 321.
03:53
ABAB: 321 is 103,041. 103,041.
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AB: 321 este 103,041. 103, 041.
03:56
Yes? One more three-digittrei cifre numbernumăr please.
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Da? Inca un numar de trei cifre, va rog.
03:59
AudiencePublicul: Oh, 722.
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Audienta: umm, 722.
04:01
ABAB: 722 is 500 -- oohooh, that's a harderMai tare one.
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AB: 722 este 500 -- uf, acesta e mai greu.
04:04
Is that 513,284?
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raspunsul este 513,284?
04:07
WomanFemeie: Yes.
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Femeia: Da.
04:08
ABAB: Yes? Oh, one more, one more three-digittrei cifre numbernumăr please.
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AB: Da? Inca unul, inca un numar de trei cifre, va rog.
04:11
AudiencePublicul: 162.
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Audienta: 162.
04:12
162 squaredpătrat is 26,244.
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162 ridicat la patrat este 26,244.
04:16
Thank you very much.
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Va multumesc foarte mult.
04:18
(ApplauseAplauze)
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(Aplauze)
04:25
Let me try to take this one stepEtapa furthermai departe.
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Hai sa incercam un pas mai departe.
04:28
(LaughterRâs)
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(Rasete)
04:30
I'm going to try to squarepătrat a four-digitpatru cifre numbernumăr this time.
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Am sa ridic la patrat un numar de patru cifre, acum.
04:33
Now you can all take your time on this; I will not beatbate you to the answerRăspuns on this one,
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Puteti sa calculati linistiti; nu va voi da raspunsul mai rapid,
04:36
but I will try to get the answerRăspuns right.
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dar am sa incerc sa va dau raspunsul corect.
04:38
To make this a little bitpic more randomîntâmplător, let's take the fourthAl patrulea rowrând this time,
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Pentru a face mai aleatorie alegerea, am sa iau al patrulea rand acum,
04:41
let's say, one, two, threeTrei, fourpatru.
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sa spunem, unu, doi, trei, patru.
04:44
If eachfiecare of you would call out a singlesingur digitcifre betweenîntre zerozero and ninenouă,
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Spuneti va rog cate un singur numar de la zero la noua,
04:46
that will be the four-digitpatru cifre numbernumăr that I'll squarepătrat.
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acesta va fi numarul nostru din patru cifre pe care il voi ridica la patrat.
04:49
AudiencePublicul: NineNouă.
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Audienta: Noua.
04:50
ABAB: NineNouă.
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AB: Noua.
04:51
AudiencePublicul: SevenŞapte. ABAB: SevenŞapte.
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Audienta: Sapte. AB: Sapte.
04:52
AudiencePublicul: FiveCinci. ABAB: FiveCinci.
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Audienta: Cinci. AB: Cinci.
04:53
AudiencePublicul: EightOpt. ABAB: EightOpt.
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Audienta: Opt. AB: Opt.
04:55
9,758, this will take me a little bitpic of time, so bearurs with me.
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9,758, imi va lua ceva timp, asteptati putin.
04:58
95,218,564?
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95,218,564?
05:07
WomanFemeie: Yes.
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Femeia: Da.
05:08
ABAB: Thank you very much.
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AB: Va multumesc foarte mult.
05:10
(ApplauseAplauze)
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(Aplauze)
05:18
Now, I would attemptatentat, încercare to squarepătrat a five-digit5 cifre numbernumăr --
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Acum, as incerca sa ridic la patrat un numar din cinci cifre --
05:21
and I can --
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si pot --
05:23
but unfortunatelydin pacate mostcel mai calculatorscalculatoare cannotnu poti.
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dar din pacate multe calculatoare nu pot.
05:25
(LaughterRâs)
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(Rasete)
05:27
Eight-digitOpt cifre capacitycapacitate -- don't you hateură that?
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Spatiu pe opt biti -- nu urati asta?
05:30
So, sincede cand we'vene-am reachedatins the limitslimite of our calculatorscalculatoare --
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Deci, cum am ajuns la limita calculatoarelor noastre --
05:33
what's that? Does yoursa ta go --
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poftim? Al tau merge --
05:36
WomanFemeie: I don't know.
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Femeia: Nu stiu.
05:37
ABAB: Does yoursa ta go highersuperior?
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AB: Al tau merge mai sus?
05:39
Oh -- yoursa ta does?
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Ah -- al tau?
05:41
Man: I can probablyprobabil do it.
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Barbatul: Cel mai probabil pot.
05:42
ABAB: I'll talk to you latermai tarziu.
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AB: O sa vorbim noi mai tarziu.
05:44
In the meanwhileîntre timp, let me concludeîncheia
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Intre timp, as termina
05:46
the first partparte of my showspectacol by doing something a little trickiermai complicat.
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prima parte a spectacolului meu prin a face ceva mai greu.
05:49
Let's take the largestcea mai mare numbernumăr on the boardbord here, 8649.
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Hai sa luam cel mai mare numar de pe plansa, 8649.
05:52
Would you eachfiecare enterintroduce that on your calculatorcalculator?
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Puteti introduce fiecare asta in calculator?
05:55
And insteadin schimb of squaringCuadratura it this time,
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Dar in loc sa ridicati la patrat acum,
05:57
I want you to take that numbernumăr and multiplymultiplica it
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As vrea sa luati numarul si sa il inmultiti
05:59
by any three-digittrei cifre numbernumăr that you want,
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cu orice numar din trei cifre doriti,
06:02
but don't tell me what you're multiplyingînmulțirea by --
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dar nu imi spuneti cu ce numar il inmultiti --
06:04
just multiplymultiplica it by any randomîntâmplător three-digittrei cifre numbernumăr.
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doar inmultiti-l cu orice numar aleatoriu de trei cifre.
06:07
So you should have as an answerRăspuns eitherfie
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Ar trebui sa aveti ca raspuns fie
06:09
a six-digitșase cifre or probablyprobabil a seven-digitSir numbernumăr.
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un numar format din 6 cifre, sau poate 7.
06:13
How manymulți digitscifre do you have, sixşase or sevenȘapte?
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Cate cifre are al tau, sase sau sapte?
06:14
SevenŞapte, and yoursa ta? WomanFemeie: SevenŞapte.
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Sapte, iar al tau? Femeia: Sapte.
06:16
ABAB: SevenŞapte? SevenŞapte?
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AB: Sapte? Sapte?
06:19
And, uncertainincert.
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Deci, nesigur.
06:21
Man: Yeah.
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Barbatul: Da.
06:22
ABAB: SevenŞapte. Is there any possibleposibil way that I could know
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AB: Sapte. Ar fi cumva posibil sa stiu
06:24
what sevenȘapte digitcifre numbersnumerele you have? Say "No."
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ce numar de sapte cifre aveti? Spuneti "Nu."
06:27
(LaughterRâs)
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(Rasete)
06:29
Good. Then I shalltrebuie attemptatentat, încercare the impossibleimposibil --
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Bun. Atunci am sa incerc imposibilul --
06:31
or at leastcel mai puţin the improbableimprobabil.
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sau cel putitn improbabilul.
06:33
What I'd like eachfiecare of you to do is to call out for me
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Ce as dori ca fiecare sa imi spuna
06:35
any sixşase of your sevenȘapte digitscifre, any sixşase of them,
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oricare sase dintre cele sapte cifre, oricare sase,
06:38
in any orderOrdin you'dte-ai like.
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in ce ordine doriti.
06:40
(LaughterRâs)
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(Rasete)
06:41
One digitcifre at a time, I shalltrebuie try and determinea determina the digitcifre you've left out.
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Cate o cifra pe rand, iar eu am sa incerc sa gasesc ultima cifra.
06:46
So, startingpornire with your seven-digitSir numbernumăr,
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Deci, incepand cu numarul de sapte cifre,
06:48
call out any sixşase of them please.
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spune-mi oricare sase cifre, te rog.
06:50
WomanFemeie: One, OK, 197042.
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Femeia: Unu, da, 197042
06:56
ABAB: Did you leavepărăsi out the numbernumăr 6?
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Ai omis cumva cifra 6?
06:57
WomanFemeie: Yes, ABAB: Good, OK, that's one.
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Femeia: Da, AB: Bun, primul.
06:59
You have a seven-digitSir numbernumăr, call out any sixşase of them please.
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Tu ai un numar de sapte cifre, spune-mi oricare sase te rog.
07:01
WomanFemeie: 44875.
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Femeia: 44875.
07:04
ABAB: I think I only heardauzit fivecinci numbersnumerele. I -- wait -- 44875 --
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AB: Cred ca am auzit doar cinci numere. 44875...
07:09
did you leavepărăsi out the numbernumăr 6?
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ai omis numarul sase?
07:11
WomanFemeie: Yes. ABAB: SameAcelaşi as she did, OK. You've got a seven-digitSir numbernumăr --
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Femeia: Da. AB: La fel ca ea, bun. Tu ai un numar de sapte cifre --
07:13
call out any sixşase of them loudtare and clearclar.
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spune-mi oricare sase tare si clar.
07:16
Man: 079044.
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Barbatul: 079044.
07:20
ABAB: I think you left out the numbernumăr 3?
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AB: Cred ca ai omis numarul 3?
07:22
That's threeTrei. The oddsșanse of me gettingobtinerea all fourpatru of these right by randomîntâmplător guessingghicitul
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Asta-l al treilea. Sansele ca eu sa ghicesc toate patru numerele corect
07:26
would be one in 10,000: 10 to the fourthAl patrulea powerputere.
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ar fi una din 10,000: 10 la puterea a patra.
07:29
OK, any sixşase of them.
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Bun, oricare sase dintre ele.
07:32
Really scrambleîncăierare them up this time, please.
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Amesteca-le bine de data aceasta, te rog.
07:34
Man: 263972.
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Barbatul: 263972.
07:38
ABAB: Did you leavepărăsi out the numbernumăr 7?
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AB: Ai omis numarul 7?
07:40
And let's give all fourpatru of these people a nicefrumos roundrundă of applauseaplauze.
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Haideti sa le acordam acestor oameni un rand de aplauze.
07:42
Thank you very much. (ApplauseAplauze)
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Va multumesc foarte mult.
07:52
For my nextUrmător → numbernumăr --
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Pentru numarul urmator --
07:54
(LaughterRâs)
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(Rasete)
07:57
while I mentallymental rechargereîncărcare my batteriesbaterii,
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pana imi incarc bateriile,
07:59
I have one more questionîntrebare for the audiencepublic.
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am o intrebare pentru audienta,
08:02
By any chanceşansă, does anybodycineva here happenîntâmpla to know
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Din intamplare, isi cunoaste cineva
08:07
the day of the weeksăptămână that they were bornnăscut on?
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ziua saptamanii in care s-a nascut?
08:10
If you think you know your birthnaștere day, raisea ridica your handmână.
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Daca va cunoasteti ziua de nastere, ridicati mana.
08:14
Let's see, startingpornire with -- let's startstart with a gentlemandomn first,
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Hai sa vedem, incepem cu -- hai sa incepem cu un domn,
08:17
OK sirdomn, what yearan was it, first of all? That's why I startstart with a gentlemandomn first.
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Bun domnule, ce an a fost, in primul rand? De asta incep cu un domn.
08:20
What yearan?
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Ce an?
08:21
AudiencePublicul: 1953.
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Audienta: 1953.
08:22
ABAB: 1953, and the monthlună?
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AB: 1953, si luna?
08:24
AudiencePublicul: NovemberNoiembrie. ABAB: NovemberNoiembrie what?
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Audienta: Noiembrie. AB: Noiembrie cat?
08:25
AudiencePublicul: 23rdRd.
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Audienta: 23.
08:26
ABAB: 23rdRd -- was that a MondayLuni? AudiencePublicul: Yes.
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AB: 23 -- a fost cumva o zi de Luni? Audienta: Da.
08:28
Yes, good. SomebodyCineva elsealtfel? Who elsealtfel would like --
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Da, bun. altcineva? Cine mai vrea --
08:30
see I don't -- haven'tnu au seenvăzut any women'sFemei handsmâini up.
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nu am vazut nicio doamna ridicand mana.
08:32
OK, it's -- how about you, what yearan?
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Bun, este -- dar tu, ce an?
08:34
AudiencePublicul: 1949. ABAB: 1949, and the monthlună?
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Audienta: 1949. AB: 1949, iar luna?
08:36
AudiencePublicul: OctoberOctombrie. ABAB: OctoberOctombrie what?
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Audienta: Octombrie. AB: Octombrie cat?
08:37
AudiencePublicul: FifthA cincea.
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Audienta: Cinci.
08:38
ABAB: FifthA cincea -- was that a WednesdayMiercuri?
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AB: Cinci -- a fost o zi de Miercuri?
08:40
Yes, my -- I'll go way to the back right now, how about you?
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Da, -- hai sa mergem mult in spate, tu?
08:42
YellTipa it out, what yearan? AudiencePublicul: 1959.
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Striga mai tare, ce an? Audienta: 1959.
08:44
ABAB: 1959, OK -- and the monthlună?
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AB: 1959, bun -- iar luna?
08:46
AudiencePublicul: FebruaryFebruarie.
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Audienta: Februarie.
08:48
ABAB: FebruaryFebruarie what? AudiencePublicul: SixthA şasea.
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AB: Februarie cat? Audienta: Sase.
08:50
ABAB: SixthA şasea -- was that a FridayVineri? AudiencePublicul: Yes.
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AB: Sase -- a fost o zi de Vineri? Audienta: Da.
08:52
Good, how about the personpersoană behindin spate her?
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Bun, ia sa vedem, persoana din spatele ei?
08:54
Call -- call -- what yearan was it?
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Spune -- spune -- in ce an?
08:56
AudiencePublicul: 1947. ABAB: 1947, and the monthlună?
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Audienta: 1947. AB: 1947, iar luna?
08:58
AudiencePublicul: MayPoate. ABAB: MayPoate what?
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Audienta: Mai. AB: Mai cat?
09:00
AudiencePublicul: SeventhA şaptea. ABAB: SeventhA şaptea -- would that be a WednesdayMiercuri?
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Audienta: Sapte. AB: Sapte -- a fost cumva o zi de Miercuri?
09:02
AudiencePublicul: Yes.
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Audienta: Da.
09:03
ABAB: Thank you very much.
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AB: Va multumesc foarte mult.
09:05
(ApplauseAplauze)
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(Aplauze)
09:09
AnybodyOricine here who'dcare ar like to know the day of the weeksăptămână they were bornnăscut?
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Este cineva care ar dori sa stie ziua din saptamana cand s-a nascut?
09:12
We can do it that way.
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Putem face si asa.
09:14
Of coursecurs, I could just make up an answerRăspuns and you wouldn'tnu ar fi know,
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Bineinteles ca as putea inventa o zi, iar voi nu ati sti,
09:16
so I come preparedpregătit for that.
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asa ca am venit pregatit pentru asta.
09:18
I broughtadus with me a bookcarte of calendarscalendare.
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Am adus cu mine un almanah al calendarelor.
09:21
It goesmerge as fardeparte back into the pasttrecut as 1800, 'causepentru ca you never know.
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Merge pana in anii 1800, pentru ca nu stii niciodata.
09:25
(LaughterRâs)
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(Rasete)
09:27
I didn't mean to look at you, sirdomn --
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Nu am vrut sa ma uit la tine, domnule --
09:29
you were just sittingședință there.
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doar stateai acolo.
09:31
AnywayOricum, ChrisChris, you can help me out here, if you wouldn'tnu ar fi mindminte.
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Oricum, Chris, ai putea sa ma ajuti putin aici?
09:34
This is a bookcarte of calendarscalendare, and I'll askcere --
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Acesta e un almanah al calendarelor, si am sa intreb --
09:36
who was it that wanted to know theiral lor birthnaștere day? You sirdomn? OK.
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cine voia sa isi cunoasca ziua de nastere? Tu, domnule? Bun.
09:38
What yearan was it, first of all?
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Ce an a fost, in primul rand?
09:40
AudiencePublicul: 1966.
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Audienta: 1966.
09:41
ABAB: '66 -- turnviraj to the calendarcalendar with 1966 --
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AB: '66 -- da pagina la 1966 --
09:43
and what monthlună?
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si ce luna?
09:45
AudiencePublicul: AprilAprilie. ABAB: AprilAprilie what?
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Audienta: Aprilie. AB: Aprilie cat?
09:47
AudiencePublicul: 17thlea. ABAB: 17thlea -- I believe that was a SundayDuminica.
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Audienta: 17. AB: 17 -- cred ca a fost o Duminica.
09:50
Can you confirma confirma, ChrisChris?
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Poti sa ne confirmi, Chris?
09:52
ChrisChris AndersonAnderson: Yes. ABAB: Yeah, OK. I'll tell you what, ChrisChris:
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Chris Anderson: Da. AB: Da, bun. Hai sa vedem, Chris,
09:54
as long as you have that bookcarte in frontfață of you,
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daca tot esti cu almanahul in fata,
09:57
do me a favorfavoare, turnviraj to a yearan outsidein afara of the 1900s,
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ajuta-ma, da pagina la un an in afara 1900'
10:01
eitherfie into the 1800s or way into the 2000s --
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ori printre anii 1800 ori mult inspre 2000' --
10:04
that'llcare va be a much greatermai mare challengeprovocare for me.
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ar fi o provocare mai mare pentru mine.
10:06
What yearan, ChrisChris, would you like?
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Ce an, Chris?
10:07
CACA: 1824.
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CA: 1824.
10:08
ABAB: 1824, OK.
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AB: 1824, bun.
10:11
And what monthlună? CACA: JuneIunie.
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Si ce luna? CA: Iunie.
10:13
ABAB: JuneIunie what? CACA: SixthA şasea.
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AB: Iunie cat? CA: Sase.
10:15
ABAB: SixthA şasea -- was that a SundayDuminica?
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AB: Sase -- era o zi de Duminica?
10:17
CACA: It was. ABAB: And it was cloudynoros.
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CA: Da. AB: Si a fost innorat.
10:20
Good, thank you very much.
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Bun, va multumesc foarte mult.
10:22
(ApplauseAplauze)
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(Aplauze)
10:28
But I'd like to wrapîmpacheta things up now
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Dar as dori sa terminam
10:30
by alludingaluzie to something
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prin a reveni la ceva
10:33
from earliermai devreme in the presentationprezentare.
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ce am discutat mai devreme.
10:35
There was a gentlemandomn up here who had a 10-digit-cifre calculatorcalculator.
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Era un domn care avea un calculator pe 10-biti?
10:38
Where is he, would you standstand up,
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Unde este, poate sa se ridice,
10:42
10-digit-cifre guy?
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tipul cu 10-biti?
10:44
OK, well standstand up for me just for a secondal doilea,
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Bun, stai in picioare pentru o secunda,
10:47
so I can see where you are.
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sa pot vedea unde esti.
10:49
OK, oh, OK -- you have a 10-digit-cifre calculatorcalculator, sirdomn, as well?
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Ah, bun -- si dumneavoastra aveti un calculator pe 10-biti, domnule?
10:52
OK, what I'm going to try and do, is to squarepătrat in my headcap
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Bun, ceea ce am sa incerc acum, este sa ridic la patrat in minte
10:56
a five-digit5 cifre numbernumăr requiringcare necesită a 10-digit-cifre calculatorcalculator.
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un numar de cinci cifre, necesitand un calculator pe 10-biti.
10:59
But to make my jobloc de munca more interestinginteresant for you, as well as for me,
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Dar pentru a face totul mai interesant pentru voi, cat si pentru mine,
11:04
I'm going to do this problemproblemă
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Am sa rezolv aceasta problema
11:06
thinkinggândire out loudtare.
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gandind cu voce tare.
11:08
So you can actuallyde fapt, honestlysincer hearauzi
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Iar voi veti auzi, serios,
11:11
what's going on in my mindminte
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ceea ce imi trece mie prin cap
11:13
while I do a calculationcalcul of this sizemărimea.
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in timp ce fac calcule de marimea aceasta.
11:15
Now, I have to apologizescuza to our magicianMagicianul friendprieten LennartLennart GreenVerde.
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Acum, as dori sa ii cer scuze magicianului nostru Lennart Green.
11:18
I know as a magicianMagicianul we're not supposedpresupus to revealdezvălui our secretssecrete,
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Stiu ca un magician nu ar trebui sa isi arate secretele,
11:22
but I'm not too afraidsperiat that people are going
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dar nu cred ca oamenii vor incepe
11:24
to startstart doing my showspectacol nextUrmător → weeksăptămână, so --
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sa reproduca spectacolul meu intr-o saptamana, asadar --
11:26
I think we're OK.
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cred ca suntem in regula.
11:30
So, let's see, let's take a --
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Asadar, haideti sa vedem, sa luam un --
11:33
let's take a differentdiferit rowrând of people, startingpornire with you.
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haideti sa luam un alt rand, incepand de la tine.
11:35
I'll get fivecinci digitscifre: one, two, threeTrei, fourpatru --
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Am nevoie de cinci cifre: una, doua, trei, patru --
11:38
oh, I did this rowrând alreadydeja. Let's do the rowrând before you,
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ah, am incercat deja pe randul asta. Hai sa luam randul din fata voastra,
11:40
startingpornire with you sirdomn: one, two, threeTrei, fourpatru, fivecinci.
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incepand cu tine: unu, doi, trei, patru, cinci.
11:43
Call out a singlesingur digitcifre -- that will be the five-digit5 cifre numbernumăr
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Strigati cate o singura cifra -- acesta va fi numarul nostru de cinci cifre
11:46
that I will try to squarepătrat. Go aheadînainte.
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pe care il voi ridica la patrat. Haideti.
11:48
AudiencePublicul: FiveCinci. ABAB: FiveCinci.
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Audienta: Cinci. AB: Cinci
11:50
AudiencePublicul: SevenŞapte. ABAB: SevenŞapte.
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Audienta: Sapte: AB: Sapte.
11:51
AudiencePublicul: SixŞase. ABAB: SixŞase.
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Audienta: Sase. AB: Sase.
11:52
AudiencePublicul: EightOpt. ABAB: EightOpt.
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Audienta: Opt. AB: Opt.
11:54
AudiencePublicul: ThreeTrei. ABAB: ThreeTrei.
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Audienta: Trei. AB: Trei.
11:56
57,683
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57,683
12:01
squaredpătrat. YuckLa naiba.
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la patrat. Bleah.
12:03
Let me explainexplica to you how
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Am sa incerc sa va explic
12:05
I'm going to attemptatentat, încercare this problemproblemă.
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cum am sa abordez aceasta problema.
12:08
I'm going to breakpauză the problemproblemă down into threeTrei partspărți.
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Am sa incep prin a imparti problema in trei parti.
12:11
I'll do 57,000 squaredpătrat,
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Am sa fac 57,000 la patrat,
12:13
plusla care se adauga 683 squaredpătrat,
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plus 683 la patrat,
12:17
plusla care se adauga 57,000 timesori
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plus 57,000 inmultit cu
12:20
683 timesori two.
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683 inmultit cu doi.
12:22
AddAdauga all those numbersnumerele togetherîmpreună,
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Adun toate aceste numere,
12:24
and with any lucknoroc, arriveajunge at the answerRăspuns.
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si cu putin noroc, voi ajunge la rezultat.
12:28
Now, let me recaprecapitulare.
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Acum, hai sa recapitulam.
12:31
Thank you.
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Multumesc.
12:34
While I explainexplica something elsealtfel --
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Intre timp am sa explic altceva --
12:37
-- I know, that you can use, right?
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-- stiu ca poti folosi, nu?
12:40
While I do these calculationcalcul[s],
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Cat timp fac aceste calcule,
12:42
you mightar putea hearauzi certainanumit wordscuvinte,
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veti auzi niste cuvinte cheie,
12:44
as opposedopus to numbersnumerele, creepfluaj into the calculationcalcul.
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care pe langa numere, vor aparea in calcule.
12:48
Let me explainexplica what that is.
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Hai sa va explic ce inseamna.
12:49
This is a phoneticfonetic codecod,
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Reprezinta un cod fonetic,
12:51
a mnemonicmnemonic devicedispozitiv that I use,
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un dispozitiv mnemotic pe care il folosesc,
12:53
that allowspermite me to convertconvertit numbersnumerele into wordscuvinte.
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care imi permite sa transform numere in cuvinte.
12:56
I storemagazin them as wordscuvinte, and latermai tarziu on retrieveprelua them as numbersnumerele.
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Le memorez ca si cuvinte, iar apoi le transform in numere.
12:59
I know it soundssunete complicatedcomplicat; it's not --
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Stiu ca suna complicat; dar nu e --
13:01
I just don't want you to think you're seeingvedere something out of "RainPloaie Man" here.
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Vreau doar sa stiti ca nu vedeti o scena din "Rain Man" acum.
13:04
(LaughterRâs)
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(Rasete)
13:06
There's definitelycategoric a methodmetodă to my madnessnebunie --
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Sigur exista o metoda in nebunia mea --
13:08
definitelycategoric, definitelycategoric. Sorry.
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sigur, sigur. Scuze.
13:10
(LaughterRâs)
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(Rasete)
13:14
If you want to talk to me about ADHDADHD afterwardsdupă aceea,
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Daca doriti sa discutam despre sindromul ADHD dupa aceea,
13:16
you can talk to me then. All right --
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putem vorbi atunci. Asadar --
13:18
by the way, one last instructioninstrucție,
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chiar, o ultima rugaminte,
13:20
for my judgesjudecători with the calculatorscalculatoare -- OK, you know who you are --
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pentru cei din juriu, cu calculatoarele -- bun, stiti cine suntet --
13:23
there is at leastcel mai puţin a 50 percentla sută chanceşansă
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exista cel putin 50 la suta sansa
13:26
that I will make a mistakegreşeală here.
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ca eu sa gresesc.
13:29
If I do, don't tell me what the mistakegreşeală is;
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Daca gresesc, nu imi spuneti ce gresala am facut;
13:32
just say, "you're closeînchide," or something like that, and I'll try and figurefigura out the answerRăspuns --
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doar spuneti "pe aproape", sau ceva de genul acesta, iar eu am sa incerc sa rezolv --
13:35
whichcare could be prettyfrumos entertainingdistractiv in itselfîn sine.
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ceea ce ar putea fi interesant.
13:39
If, howeverin orice caz, I am right,
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807000
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Daca, totusi, am dreptate,
13:41
whateverindiferent de you do, don't keep it to yourselftu, OK?
327
809000
3000
orice ati face, nu tineti doar pentru voie, da?
13:44
(LaughterRâs)
328
812000
1000
(Rasete)
13:45
Make sure everybodytoata lumea knowsștie that I got the answerRăspuns right,
329
813000
2000
Fiti siguri ca toata lumea stie ca am gasit raspunsul corect,
13:47
because this is my bigmare finishfinalizarea, OK.
330
815000
3000
pentru ca este marele meu final. Bun.
13:50
So, withoutfără any more stallingîn scădere,
331
818000
3000
Asadar, fara a mai trage de timp,
13:53
here we go.
332
821000
3000
sa incepem.
13:56
I'll startstart the problemproblemă in the middlemijloc, with 57 timesori 683.
333
824000
2000
Am sa incep cu problema din mijloc, cu 57 inmultit cu 683.
13:58
Now, 57 timesori 68 is 3,400, plusla care se adauga 476 is 3876,
334
826000
3000
Acum, 57 inmultit cu 68 este 3,400, plus 476 da 3876,
14:01
that's 38,760 plusla care se adauga 171,
335
829000
3000
adica 38,760 plus 171,
14:04
38,760 plusla care se adauga 171 is 38,931.
336
832000
3000
38,760 plus 171 este 38,931.
14:07
38,931; doubledubla that to get 77,862.
337
835000
4000
38,931; dublam asta si obtinem 77,862.
14:11
77,862 becomesdevine cookiecookie-ul fissionfisiune,
338
839000
2000
77,862 devine "cookie fission",
14:13
cookiecookie-ul fissionfisiune is 77,822.
339
841000
4000
"cookie fission" este 77,822.
14:17
That seemspare right, I'll go on. CookieCookie-ul fissionfisiune, OK.
340
845000
2000
Pare in regula, sa continuam. "Cookie fission", bun.
14:19
NextUrmătoarea, I do 57 squaredpătrat, whichcare is 3,249, so I can say,
341
847000
4000
Apoi, calculez 57 la patrat, care este 3,249, deci pot spune,
14:23
threeTrei billionmiliard. Take the 249, addadăuga that to cookiecookie-ul, 249,
342
851000
5000
3 miliarde. Iau 249 si il adaug la "cookie", 249,
14:28
oopsOops, but I see a carrytransporta comingvenire --
343
856000
2000
ups, dar vad un posibil rest --
14:30
249 --
344
858000
2000
249 --
14:32
addadăuga that to cookiecookie-ul, 250 plusla care se adauga 77,
345
860000
2000
adaug asta la "cookie", 250 plus 77,
14:34
is 327 millionmilion --
346
862000
4000
este 327 de milioane --
14:38
fissionfisiune, fissionfisiune, OK, finallyin sfarsit, we do 683 squaredpătrat,
347
866000
2000
"fission", "fission", bun, in sfarsit, facem 683 la patrat,
14:41
that's 700 timesori 666, plusla care se adauga 17 squaredpătrat
348
869000
2000
adica 700 inmultit cu 666 plus 17 la patrat,
14:43
is 466,489, revRev up if I need it,
349
871000
3000
adica 466,489, rotesc daca am nevoie,
14:46
revRev up, take the 466,
350
874000
2000
rotesc, iau 466,
14:48
addadăuga that to fissionfisiune, to get,
351
876000
2000
adaug asta la "fission" si obtin,
14:50
oh geeGee --
352
878000
2000
of, vai --
14:54
328,489.
353
882000
4000
328,489.
14:58
AudiencePublicul: Yeah!
354
886000
1000
Audienta: Daa!
14:59
ABAB: Good.
355
887000
1000
AB: Bun.
15:00
(ApplauseAplauze)
356
888000
1000
(Aplauze)
15:01
Thank you very much.
357
889000
2000
Va multumesc foarte mult.
15:03
I hopesperanţă you enjoyedsa bucurat mathemagicsmathemagics. Thank you.
358
891000
2000
Sper ca v-a placut "matemagia". Va multumesc
15:05
(ApplauseAplauze)
359
893000
4000
(Aplauze)
Translated by Gabriel Mirea
Reviewed by Alex Ghioiu

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ABOUT THE SPEAKER
Arthur Benjamin - Mathemagician
Using 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").

More profile about the speaker
Arthur Benjamin | Speaker | TED.com