Art Benjamin the Mathemagician at the USA Science & Engineering Festival!

we live on the cutting edge of physics material science engineering and nanotechnology because at Lockheed Martin we're engineering a better tomorrow well good afternoon ladies and gentlemen my name is art Benjamin and I am a Mathemagician what that means is I combine my loves of math and magic to do something I call mathematics but before I get started with anything too mathematical I thought I'd begin with a magic trick has nothing to do with math really it's just a really cool trick but for this I'll need a volunteer to assist me someone here I do not know and let's see okay in the Orioles shirt what's your name let's give Harrison a nice round of applause I'm up here Harrison I'm a big fan of the Orioles I went to I went to graduate school at Johns Hopkins so in many a fond memory Harrison have we ever met before no but you've seen me before but I haven't seen you before right you seem proud of that fact but that's good because Harrison I'm going to show you and everyone here a card trick that has never been seen before never been seen before because no one can see the cards Harrison if you would pick a card any card at all from the deck look at the cards show it to everyone but do not let me see it all right now I'll shuffle the cards so you see they're not in any particular order Harrison I'd like you to place the card back inside the deck but just to make it interesting turn the card upside down first upside down just like that good notice all the cards are face up except for Harrison's which is face down now watch carefully is this took me years of practice watch watch watch as I make the deck of cards disappear from my hands hmm reappear inside of this box a box which only moments ago Harrison was empty trust me now I realize Harrison what you were doing a moment ago was just a figment of your imagination but what was the card for that brief second at least that you imagined that you selected Harrison what card did you imagine king of what spade heart diamond door Club king of diamonds that's amazing because you'll notice in this deck that one card and only one card has been turned upside down would you be so kind as to show everyone the upside down card the King of Diamonds and let's give Harrison a nice round of applause Thank You Harrison well done thank you great well while you're trying to figure that one out I have another question for the audience by any chance did anyone happen to bring with them this afternoon a calculator of some sort if you have a calculator perhaps even on your phone and if you're very comfortable using it raise your hand they need a few volunteers to help me out here let's see it will take okay we got 1 & 2 & 3 & 4 with the four of you bring out your calculators join me up here on stage let's give these volunteers a nice round of applause come on up now since I haven't had the chance to work with these calculators I need to make sure that they are all working properly would somebody get us started by giving us a two digit number please how about a two digit number yell it out 27 and another larger two digit number go ahead 36 multiply 27 times 36 make sure you get 972 exactly or the calculators are not working don't get 972 972 give them a round of applause now I notice that took some of us a little time to get the answer I'll give you a shortcut for multiplying even faster there's something called the square of a number which most of you know is taking a number and multiplying it by itself for instance five squared would be 25 six squared would be 36 seventy three squared would be we don't know something bigger right now most of your calculators have little shortcuts for squaring and if you know them you should use them what I'm going to try and do now is to square in my for two-digit numbers faster than they can do on their calculators even using the shortcut method what Alaska's for people here in the in the first row how about one two three four say where you are just yell out at a two-digit number and if you would square the first number the second the third and the fourth one I will try and race you to the answer so quickly a two digit number please sixty-four okay next 76 okay next 84 and one more 74 would you call out your answers please 4096 5-7 7-6 still working on it okay 84 times 84 while he's doing that what did you get 54 76 and finally let's call it 7,000 56 and give him a round of applause now show you the shortcut yeah so do 84 well this one this is a weird one isn't it where do you get try another calculator okay let me try to take this one step further clear that calculator whatever you've got on it I'm going to try to square some three-digit numbers this time I won't even write these down I'll just call them out as they're called out to me anyone I point to call out a three-digit number anyone on our panel verify the answer if I get the answer right give me a thumbs up if I make a mistake let me know and I'll try and fix it a three-digit number starting with you 241 squared is 58 thousand and eighty one five eight zero eight one good great how about another three-digit number sir 222 is 49 thousand two hundred eighty four four nine two eight four correct oh good all right another three-digit number sir 788 is 620 1284 six two one two eight four now let me try that one again 620 1284 no you gave me a hard one I have to get back to that one 788 you said right I see what I did wrong I said in a 620 620 singer 20,000 944 thank you good another three digit number go ahead 578 is three hundred thirty four thousand and eighty four three three four oh eight four good one last three digit number go ahead 999 is 998 thousand and one thank you very much home let me try to take this one step further I'm going to try no guarantees I'm going to try to square a four-digit number this time and I'm not going to beat you to the answer on this one except maybe you yeah but that's okay but I will try to get the answer right to make this a little more random how about we take the second row here if I can get the first four of you to call out a single digit that will be the four digit number that I'll square go ahead starting with a single digit six next four three seven this will take me a little bit of time so bear with me forty-one million four hundred thirty four thousand nine hundred sixty-nine good thank you very much now I would attempt to square a five digit number and I can but unfortunately some calculators cannot what can you do so although I think most of your can these days I'll talk to you later about that but in the meanwhile let me conclude the first part of my show by trying something even trickier let's take the largest number on the board here 7056 would you each enter seven zero five six on the calculator and instead of squaring at this time I want you to take that number and multiply it by any three-digit number that you'd like but don't tell me what you're multiplying by just multiply it by any random three-digit number so you should have as an answer either a six digit or probably a seven digit number how many digits do you have there six or seven you have seven seven seven six seven great is there any possible way that I could know what seven digit numbers they have say no good then I shall attempt the impossible or at least the improbable what I'd like each of you to do is to call out for me any six of your seven digits any six of them in any order you'd like one digit at a time I shall try and determine the digit you've left out so starting with your seven digit number call out any six of them please wait actually I'll repeat them as you say them so they can hear so you started with eight five two five seven two did you leave out the number seven yes that's one you have a seven digit number called any six of yours loud and clear three zero one seven one six I'm having a little bit of trouble with this one let me get back to you don't forget your number you've got a seven digit number called six of your seven in any order four three four five two zero remember the number you left out as well finally you've got a seven digit number any six of yours really scramble them up this time to zero zero two three two you know I asked the three of you to do me a favor at this moment I want you to concentrate on the digit you left out doesn't do any good I know it just looks dramatic here and yet I seem to be getting a lot of nothing which of you left out a zero you both left that that's why I was getting a lot of nothing but you didn't right you didn't leave out a zero I I think if I'm not mistaken can you left out the number nine great and let's give all four of these people a nice round of applause thank you very much well done excellent for my next number I thank you I'd like to present something we Mathemagician x' refer to as magic squares now for those of you don't know these these are kind of like pseudo ku on steroids and you'll see what I mean by that in just a minute now I've done such an extensive study on magic squares that I'd like to create one for all of you right before your very eyes but for this I'll need another assistant someone here I do not know and let's see I do not know okay what's you what's your name what's your name Alex give Alex a nice round of applause come up here Alex oh wait wait was that who you were choosing is that are you Alex okay come on up here outs I was I thought I was picking one of the young ladies there but Alex you're just gonna have to do Alex if you would stand right there Alex I what I'm gonna ask you to do is is are you willing to share with us your birthday including the year I did it for you this morning all right Alex that I'm definitely gonna ask you to step down I'm gonna get somebody else how about why don't I get you I was trying to get you anyway what's your name RIA come on up here let's give real nice round of applause sorry about that fantastic now RIA is that our ia our our hea RIA RIA spelling was not my best subject real let me ask you another question and if it's too personal I can change the question RIA are you willing to share with us your birthday including the year great RIA what is your birthday March 26 what year 2003 now RIA if we were to add the numbers in your birthday together let's see 3 plus 26 is 29 plus 20 is 49 plus 3 is 52 so 52 becomes your magic number just like 52 cards in a deck now real what I'm going to try and do is to fill out this box in such a way as to get your magic number appearing here as much as I possibly can this will take me a couple of seconds so bear with me here I think that works real would you choose for us any row row number 2 3 or 4 which would you like 3 okay class together 4 plus 21 is 25 plus 25 is 50 plus 2 is 50 to the US were 329 49 52 1923 25:52 26 27 32 52 would you choose a column reah 1 2 3 or 4 - ok class 26 plus 4 is 30 plus 21 is 50 1 plus 1 is 50 - the odds word 322 26 would be to 2020 - 47 52 3 30 30 - 50 - how about that now Rhea I am not through with you I decided since this was your Magic Square based on your birthday and no extra charge I would give you these diagonals as well check it out here 26 plus 21 is 47 plus 2 is 49 plus 3 is 52 3 7 32 52 but I didn't stop there either I decided since this was for Rhea wouldn't it be great if we could get these 4 in the center to add up as well check it out here 4 plus 2 is 6 plus 25 is 31 plus 21 is 52 but that I stopped there no really may have noticed I put a little extra attention in that corner I did that so I could get these four squares 3 plus 26 is 29 plus 4 is 33 plus 19 is 52 to add up and I figured heck as long as we got that group of 4 let's have a party we may as well get this script before 2649 foot for 20 23 50 52 four twenty five twenty six twenty to twenty-five thirty seven forty seven fifty two but that I stopped no I said Rio wouldn't be happy unless we got this group before this group before this group before this group before this group before this group before I have to apologize RIA I was not quite able to get this group of fort nor that group before to add up but I had to do it that way if I was going to get these four in the corners I knew that would be important to you 3/6 2652 but wait here's the cool part RIA not only do those four numbers in the corners add to 52 if you look at them closely you'll see we have three 26 2003 I thought you'd like that so please keep this as a souvenir for me and let's all give RIA a nice round of applause Thank You RIA very much whoo hey speaking of birthdays by any chance does anyone here happen to know the day of the week that they were born on if you think you know your actual birthday raise your hand okay starting starting with you sir what year what year was it 2002 and what month October what 19th was that a Saturday mom says yes good how about another another year what year 2002 and the month September what 27 was that a Friday terrific how about yours what year yep mm 1973 and what month October what nineteen was that a Friday wait let me think of this out October 19th I'm pretty sure it is a Friday but I'll tell you what you were there not me but luckily hmm there are apps for everything these days and let's see if I can get you to help me out here for just a second you sir come on come on over either of you would be fine all you have to do is type in the year and the rest is pretty clear so you said go ahead 1973 and you said October press the October button and look at the calendar and the night and the 19th is a Friday your mother lied to you what can I say Google at Google her I'll tell you what as long as you have the app let's try something even trickier the app will go as far into the past as 1600 and as far into the future as the year 9999 let me ask you for a year between 1600 and nineteen nine thousand nine hundred ninety nine what year would you like five four six three okay let me think about that for a moment okay and what month would you like press the September button and September what seventh will will that be a Monday and it'll be cloudy I think thank you very much that's another app thank you now by the way if anyone else wants to find out their birthday see me after the show I will either be at this table right over here or you could find me in booth 34 37 it's right under that storm cloud that you see right there so it's just on the other side of those those booths right under the storm cloud is where my booth is so you'll see me at this table right afterwards and for the rest of the day and all of tomorrow I'll be at that stormy table now folks if I were performing for a different sort of audience I might follow this with other feats of magic and mind but for an audience such as this one I actually prefer to break the magician's rule and explain to you most of what you've seen me do up here and more in fact I'd like to conduct the rest of this program the next 20 minutes or so very informally so feel free at any time to interrupt me with questions even if it has nothing to do with what I'm talking about it's more interesting that way so let me start with I've got hours and hours of stuff I could share with you but I see your hand up first so you can have the first question sir what is your question how did I square numbers so quickly I'm glad you asked let me show you the method I use for squaring two-digit numbers and if you're still interested in following me we can bring it up to three digit numbers and higher give us a small two digit number as our first example 10 is so easy because it ends in zero we all know 10 squared is a hundred give us a number now that doesn't end in zero 28 okay so this time the nearest easy number that does end in zero would be 130 so I'm gonna go up to 230 now whatever comes up must come down if I go up to 230 I have to balance it by going down to 226 so the first part of my calculation is I do 30 times 26 now don't panic that's just three times 26 with a friendly zero attached I like zeros okay let's do three times 26 together and the most important part about doing this is I want you to do it from left to right okay so three times 20 is what 60 three times six is eighteen sixty plus 18 from left to right is what 78 okay so 30 times 26 is 78 with a zero attached 780 almost done all we have to add to this is the square of the number we went up and down we went up and down two who squared is four and there's your answer 784 let's do a couple more examples I want to make sure you all get very good at these how about another how about another two-digit number go ahead 13 now that's one you might even know already right the nearest seesee number would be 10 so we'll go down 3 to 10 so we have to go up to what 16 now 10 well I'm afraid that's me goodbye no it's just kidding okay so where were we 13 squared we go down 3 to 10 we go up 3 to 16 10 times 16 is 160 add to that the square of what 3 which is 9 so the answer is 169 good all right now it's your turn all right when you think you vet got the answer raise your hand all right see who can get this one first I want you to try to square in your head no calculator no paper I want you to try to square the number 97 it looks hard but it's not bad think of what you'll go up to think of what you'll go down to multiply and add I saw some of you have it already I'm very impressed I think I saw in the yellow shirt I thought you and one of the first ones will just shout out your answer what did you get he is absolutely right nine thousand four hundred nine give him a nice round of applause what grade are you in what greater fourth grade give a big round of applause for that now what did you do I hope you went up three to a hundred down three to ninety four ninety four times a hundred is ninety four hundred plus the square of three which is nine to get nine thousand four hundred and nine give him another round of applause very well done yeah so anyway if you want to take this up further if you want to square like a three-digit number let me just show you quickly how I square the three digit numbers let's say and in order to do these you have to be really really fast at the two digit squares for me the two digit squares are practically memorized because I've been doing them for such a large part of my life but I don't have the three digit squares memorized so let's say I was given a number like 213 this time I go up or down to the nearest hundred so the nearest easy number would be two hundred so I go down 13 to 200 up 13 to what to 26 now I'll do two times to 26 and I'll attach the zeros at the end two times 200 is 400 two times 26 is 52 add them together and you have 452 with two zeros is 45202 add is the square of 13 which you all know by now 13 squared is 169 and there's your answer 45,000 369 let's hear it for algebra because that's what this is all based on anyway other questions what else would you like to know about yes sir in the blue shirt how do I do the magic squares oh I don't always explain that one but you asked so nicely I will but I should tell you the reason Jen's don't explain their tricks is we've all made that mistake before and we never get the reaction we want we want people to say wow that's clever you're good but you never do I mean how have you reacted most of the time someone's explained a magic trick to you it's like oh that's dumb I thought you were good but I just wasn't paying attention so I will explain to you the secret of the magic square but just remember how impressed you were before I gave the explanation okay all right that's a deal all right you asked the question we can do your birthday or somebody else's what would you like okay go ahead October 19 set 1979 now he's four years in the 1900s I just used the last two digits like 79 if you were born in the 2000s I'll typically do 20 and whatever the last two digits are there okay but with a first step the most important step is you have to add these four numbers correctly because if you make a mistake there's nothing we can do so 10 plus 2 19 is 29 plus 7 is 36 Plus 9 is 45 so 45 becomes your magic number now because you've seen the trick before you know that the birthday not only shows up in the top row but also in the four corners so what numbers gonna go here 19 and that's the first number I write down and what number is gonna go there 7 and that's the last number that I write down because I like to keep it a surprise but I wrote it there anyway next I go up the diagonal I always go in the same order and the secret is this you take this number and you add 1 to it now if you're born in the 2000s and you have a 20 here that's going to be 21 right there you have a 7 here so I'm just gonna add 1 which makes it 8 and now it becomes like the easiest pseudo coup you've ever tried because what do we know about this diagonal we know that it has to add up to 45 but I have three of the four numbers already 19 plus 8 is 27 plus 9 is 36 so what has to go here to make that 45 9 so that's what goes first next I have next I want to get this group of 4 to add up 997 that adds up to 25 so what has to go here 20 to get 45 then I go to this group before I told you it's like easy sodoku 19 plus 9 plus 7 is 35 so that makes this ah 10 then I've got 10 10 and 19 that's 39 which makes this off 6 now if you remember with rias magic square we were not able to get this group of 4 and that group afford to add up don't even try but the good news is the way the algebra works these two numbers are always the same and these two numbers are always the same so I slide this 10 over and that gives me a 10 and that makes this column add up then I go to the middle 10 9 8 is 27 makes this an 18 10 8 and 19 is 37 makes that an 8 18 8 8 is 34 that makes that 11 your brains getting tired from all the adding and subtracting so I say the easiest parts for last this number is going to be 1 9 and this number comes from the top it's a 7 and that's the secret of the magic square thank you exactly other questions yes what's your question how did I figure out the day of the week that things are that you were born on since we're getting near the end of our hour I'm not going to go into all the details here the short there are two very short answers the one first is I'm using a mathematical formula where I take a number that comes from the month and the date and the year and I add those three numbers together and the total tells me the day of the week a shorter answer is at my table right there near the speaker as well as at my booth I have some DVDs that will explain everything that I do so if you're interested in learning in fact here let me just do a very short commercial and that'll be the end of that if you're interested in learning how to do mental math everything from addition subtraction multiplication division estimation figuring out the birthdays everything I know is is in a DVD course it's got two DVDs and the book they sell it online for $200 I sell it for just $40 it's my mental math course I also have a course on the joy of mathematics that is middle school and high school math algebra geometry trigonometry PI my favorite number Fibonacci numbers my favorite numbers I want you not only to learn the math I want you to love the math that has four DVDs and a book it sells for 69 Mets of games and puzzles blackjack poker backgammon solving a Rubik's Cube any pseudo coup that's 450 and I have a course on discrete mathematics that's the mathematics of computer science that's also for DVDs that's 60 you can get all four of them for $190 and if that was your original total then you really need this course and yes I take cash check and credit card and debit card see me at my table or at my booth today or tomorrow okay uh-oh one other commercial not something I'm selling except for my college for the last 27 years I've been a professor of mathematics at a school in California called Harvey Mudd College we have any any mutters in the audience here we have some mutters how fantastic site hard we're a very small College we only have 800 students but they all major in math or science or engineering so when you have a wonderful event like the science and engineering festival you know that mutters will be out in full force we all one third of our students go on to get PhDs they get some of the highest paying jobs in the country and something I could not have said ten years ago one half of the students at Harvey Mudd College are women and that is a wonderful thing when I started there 27 years ago it was over a three to one ratio of guys to girls actually the guy said it was more like a pie to one ratio the girls said as far as finding a guy was concerned they said the odds were good but the goods were odd that might still be true today but don't tell anyone I said that anyway if you love math or science and I know all of you do because here you are on a weekend celebrating science and engineering that I that I want you to or contact our ill assurance staff again students from Thomas Johnson school please visit any info anyone in a yellow shirt if you're from Thomas Johnson school other questions what else what else would you like to know as I got time for one or two more and then I'll launch into my grand finale what's your question why does the squaring work in well here's the short formula okay if you want to square a number a then what I'm telling you to do is take a and go up some distance D take a and go down the same distance D multiply them together and add what if you were following me what do you add then d squared now is that going to work well those of you algebra pros out there what's a plus D times a minus D a squared minus d squared so when you add the d squared the DS go away and you're left with a squared let's hear it for algebra I love algebra great question other things what else what else would you like to know God oh how did I do the card trick okay if everyone asks me at the same time how'd you do it I did it very well let me take one or two more questions and I'll launch into my grand finale what's your question yeah so question was what came first my mental math skill or my ability to do this algebraically definitely it was the mental math and the playing with numbers I'll even tell you how I came about this and I'll bet many in the audience would find this interesting I remember I was in eighth grade and like many an eighth grader I was thinking about numbers that added up to 20 that was a strange kid and I always thinking in numbers like 10 and 10 9 and 11 8 and 12 and so on and I was wondering if they add up to 20 how big could the product be and I figured that 10 times 10 is a hundred and I figured that was the biggest it could get so we tried other things 9 times 11 was 99 which was almost a hundred but it was shy by one then eight times twelve was 96 which was almost a hundred but it was shy by 4 then 7 times 13 is 91 which was shy by 9 and then I got 84 which was shy by 16 and 75 which was shy by 25 and I noticed something as I pulled the numbers apart the product that's smaller and how far were they from the top 1 4 9 16 25 what are those numbers perfect squares I said that's really cool I wonder if that always works so how do you find out if something always works well algebra yes but even better try another example cuz if it doesn't work then you just got lucky but if it does work then you're probably on to something so I thought about numbers that added up to 26 so here we are with 13 and 13 again which is 169 twelve times fourteen is 168 eleven times 15 is 165 ten times 16 is 160 and so on and I saw the same pattern they were getting small by 1 4 9 16 25 and so on and then I had one of the most creative ideas I've ever had in my life which is unfortunate because it was like you know 50 40 years ago but I said hey you could use this pattern as a way to square numbers because what if you wanted to do 13 times 13 instead of doing it the usual way why not instead do 10 times 16 because that's easier and then add back 1 2 3 squared and 160 plus 9 was 169 and that is exactly how I came up with the formula before I really learned algebra thank you very much all right so now that you know how it works I'm going to end by trying one last thing for you I'm willing to try to square a five digit number which I mentioned earlier so if you have a big calculator feel free to bring it out but to make my job more interesting for you as well as for me I'm going to do this last problem thinking out loud so you can actually honestly hear what's going on in my mind while I do a calculation of this size let's create a five digit number how about we take the second row if I can get five of you to call out a digit that'll be my five digit number starting with you seven two four six seven seventy two thousand four sixty seven squared yuck let me explain to you how I'm going to attempt this problem I'm going to break the problem down into three parts I'll do 72,000 squared plus 467 squared plus 72 thousand times 467 times to add all those numbers together and with any luck arrive at the answer now let me recap thank you while I explain something else while I do this last calculation you will hear some words not just numbers but also some words enter the calculation this is a phonetic code that I use that allows me to convert numbers into words I store them as words later on retrieve them as numbers I know it sounds complicated it's not I just don't want you to think you're seeing anything bizarre up here there's definitely a method to my madness one last instruction for my judges with calculators now who's got an answer raise their hand a bunch of you you should have a ten digit number beginning with five ending with nine in between I don't know yet there's a 50% chance that I'll make a mistake somewhere in the middle if I do don't tell me what the mistake is just say your clothes or something and I'll try and figure it out which can be pretty entertaining in itself if however I am right whatever you do don't keep it to yourselves make sure everybody knows that I got the answer right because this is my Big Finish okay so without any more stalling and I have been a little here we go I'll start the problem in the middle with 72 times 467 that's 9 times 8 I'll take advantage again 9 times 467 is 3600 plus 603 is 4203 multiply that by 8 if you have 33,000 624 double that to get 67,000 248 67,000 248 becomes joke nerve joke nerve is 6 7 2 4 8 that seems right I'll go on joke nerve ok next we do 72 squared which is 5 184 so I can say 5 billion take the 184 add that to joke 184 plus 67 is 251 million nerve nerve ok finally we do 467 squared that's 500 times 434 plus 33 squared is two hundred seventeen thousand plus 1089 is two hundred eighteen thousand and 89 save up if I need it save up take the 218 have that two nerve to get four hundred sixty six thousand and 89 yes good thank you all very much I hope you enjoyed mathemagics I'm Arthur Benjamin thank you

Channel: USA Science & Engineering Festival

Views: 6,425

Rating: 4.8933334 out of 5

Keywords: Art Benjamin, Mathemagician, USASEF, SciFest, #SciFest, USA Science & Engineering Festival, Math games, Math Show, Science Festival, Math Festival, Math Fest

Id: 40obcajXiwU

Length: 43min 58sec (2638 seconds)

Published: Mon Jun 20 2016