brain teasers in english with answers

Thank you Amanda ok who’s on the lights lets bring the lights down a little so that people can actually see this and can’t see me much better thank you thank you as Amanda told you my name is Tony Barcellos from the math department and I was concerned about the turnout I see the rooms a little crowded i did caution my colleagues from the math department not to create any scenes and at least we can tell they will not be doing the wave so we should be actually matt can do the wave all by itself Brett okay i know where this is going I plan to insult your intelligence quite deeply because the math that’s going to appear on the screen is going to be extremely simple so you will grasp it immediately and you say to yourself I know that why is he telling me this because i know this already well that’s the thing you’re already a math genius in that you know these basics but you may not know what you know in the sense that these things have a lot more significance than you might realize so let’s start off by looking at a particular genius undeniable genius all of you will recognize him immediately right you all recognize him yes everyone recognizes galileo galileo wait that’s wrong Galileo Galilei I i think that’s a lyric from something ok everyone knows about you Galileo everyone knows that he’s famous for some reason if you know about his fame you probably are aware of that when he got his first telescope he didn’t use it to spy on the neighbors he tilted up and looked at the sky and the four Galilean satellites of Jupiter four moons of Jupiter are named the Galilean satellites because he saw them he saw them he could tell from night after night that they were orbiting Jupiter and it messed up the whole plan where everything was supposed to orbit the Earth this is disturbing but Galileo documented his work and published published all kinds of amazing things about the heliocentric theory as opposed to geo centric you know heliocentric centers the earth on geocentric center is very eccentric for the Sun geocentric for the earth and then my college roommate egocentric because he was the center of the universe center of the universe is

Default brain teasers in english with answersuniverse center of the universe is currently living in san diego alright so this was a big deal you know he got in trouble well let’s talk about some of the things he discovered that didn’t have to do would the system of the solar system let’s talk about physics at its basic and let’s start off with one of the simplest things I can think of here is Math you know area of a rectangle is length times width we all know that right got its easy being a math genius and you can even draw picture 04 by three and you can even count them with 12 square units that’s pretty easy everyone knows that a length times with a simple product for area we use simple products for other things distance equals rate times time rate times time is one of the great fun things that you did an algebra remember how much you enjoyed distance rate times time problems and trains leaving chicago for some reason everyone wanted to leave Chicago here’s an example i tell my algebra students or my pre algebra students student that they all know that if they travel at 60 miles an hour if they ever do that for three hours you go a hundred and eighty miles we all understand this kind of map on an intuitive level and it’s kind of unfortunate we don’t understand the process that underlies it because we think it’s all instantly intuitive and there’s nothing fancy going on actually fairly clever so if you started off 60 miles an hour three hours hundred eighty miles where would that get us oh fresno okay well you know these things happen I go to fresno fairly frequently i have family there I keep them where I can find them easily this is the same graph except tonight i did a rectangle thing and now I boot lake the coordinate system into and now its harder well its not harder you got a t axis this is a velocity time graph and 60 miles an hour for three hours you have a hundred eighty so far no one is challenged by any of this you’re all thinking I totally understand this we need it to be more exciting so wow now it’s more except no i don’t know that that’s more exciting but this is a different trip see the velocity its down here at zero and it gradually climbs to 60 over the course of three hours first

1 brain teasers in english with answersover the course of three hours first hour up to 20 second hour up to 40 next 30 and it’s just half the rectangle that we had before do you all agree that one-half base times height is a perfectly good way to find the area of that triangle and that area still represents the distance travelled it still represents distance traveled and now its one half times 60 miles per hour times three hours so so what what’s that blue stuff what distance are we talking about now all of you math geniuses can tell me immediately what it is any math genius present it’s not a hundred and eighty anymore it’s now 90 thank you ok please control yourself alright 90 so where does that get us that we can’t win alright lets move on ok so we’re taking a look at this guy again it’s the same graph I’ve made one tiny little change one tiny little change i added this so be careful not to panic it’s just saying that for every hour you put on another 20 miles per hour so like I said after the first hour you’re going 20 after two hours you’re going 40 after 3 hours are going 60 so we’re just taking this number down here T whatever he is employing it in here and that helped out you’re going does anyone know what it means to talk about gaining 20 miles per hour per hour what’s that all about when you talked about speeding off the word for that is acceleration and everyone knows what acceleration is acceleration is the feeling that you get when you speed up and you’re pressed back in the driver’s seat and your passengers are too alright so we have this nice little formula we put this together and we’re talking about acceleration acceleration is this number right here this 20 which is for all of you people who remember a little bit of algebra it’s basically your slope i also want to point out that this is not a realistic trip this trip to turlock initially you’re so reluctant to get there that you’re going near 0 miles an hour but eventually you’re up to 20 okay this is gonna be really exciting trip on highway 99 right they’re going about 99 after an hour you’re all the way up to 20 miles an hour okay and by this point you might be kind of

brain teasers in english with answers and by this point you might be kind of

2 brain teasers in english with answersand by this point you might be kind of excited because you know you’re looking at the road from under the steering wheel as you speed up and eventually you get up to 40 and then 60 i’m going to make a comment about the earlier trip because i’m making fun of this trip as unrealistic well if we if we go back to this trip 60 miles an hour all the time at the beginning of the trip you’re going 60 miles an hour so I guess you jumped into a speeding car at that point you realize that mathematical models are a little bit artificial and because in reality i realize we have cruise control now so you can walk the speed and never vary but in reality most of the time we speed up and slow down so things get kind of Wiggly and it gets harder and harder to compute this blue area but that didn’t stop Galileo remember him that didn’t stop Galileo from getting some fundamental computations done which we’re going to see in just a minute so let’s go forward again welcome to turlock and there’s that ok so there’s that formula and there with me as we make things abstract years time this entire base right here and after T hours you’re going a times t remember a was the acceleration the slope of this guy and then this blue distance is going to be one-half this height times that base basically multiplying based on height so it’s getting more exciting now one half at square is the distance for constant acceleration if you are speeding up at the constant rate if your acceleration is constant you end up with this triangular distance graph and that blue state that blue mileage or whatever units are using it will tell you that’s how far down you get starting with that constant acceleration this is a lot more complicated than just distance equals rate times time a lot more complicated little more complicated so now that all the math geniuses here are completely excuse me for this i apologize up to speed and no that was really good wasn’t I shouldn’t Telegraph that but so there’s that formula i did it big that’s so I wouldn’t shout who knows what I did this yes sir gravity yeah that’s heavy math alright so now I’m

3 brain teasers in english with answersyeah that’s heavy math alright so now I’m edging back toward galileo galileo was the guy who started figuring out the laws of physics in particular that one-half at square things but that there’s a there’s a teeny little problem i’m going to click one more time and replace G with 32 how come I got 16 what happened oh there’s one-half ok and math geniuses understand it when you take 32 and multiply it by a half you get 16 I I apologize for the unit’s these are British imperial units this is if you’re talking about feet and second because gravitational acceleration on the earth is 32 feet per second per second approximatly and so you may know British imperial units very influential even the British don’t use them anymore they’ve gone metric but it is kind of convenient we have a nice round number here that’s how far something falls under the influence of gravity in freefall you let something go and that’s how fast it travels how fast it travels how far it goes the longer you let something drop the faster it speeds up it accelerates gravity is constant acceleration and for all of you who are really old if you remember the space program when the astronauts went to the moon on atop the saturn for be third stage and they got up to something like 25,000 miles per second they were going really fast seven miles per second i think is what it is i meant to say per hour ok so let’s talk about seven miles per second they have to speed up to get there and while they were speeding up they were pressed back in their acceleration couches and they were experiencing several geez up of acceleration 1g of acceleration you feel like you’re on the earth when you’re experiencing several g’s of acceleration your face want to peel back and you stop being able to take deep breaths so the astronauts all train to get through this they had a lot of acceleration several g’s of acceleration now let’s talk about Galileo and how he figured this out because Galileo was in the era before stopwatches and if you take something and simply drop it it goes kinda of fast it’s difficult to measure you want to do splits on it right like if you have a time-lapse photographs that you could measure things even have any of that he had his pulse and there were indications that it was a problem for him to do his experiments because he kept getting excited watching these things happen and he had to say calm so if you’re a scientist in the fifteen and sixteen hundred and you want to study freefall and if you want to figure out how gravity operate on a freely falling object what do you do to help if you’re a genius perhaps slightly more of a genius than those of us here you slow down gravity what the hell is that that is Galileo’s inclined plane if you’ve never seen this before take a gander at that and appreciate a scientific instrument from a few hundred years ago today they are made out of aluminum and plastic but in those days a young think it’s a nice carpentry work on this by using an inclined plane instead of simply dropping something Galileo figured that he could roll it down an inclined plane and attenuate the gravity retard gravity slow gravity down that’s up pretty clever thing to do here’s a little schematic acceleration it speeds up every second it travels farther and farther and if you had one of these inclined planes were things slow down and instead plunk it hits the ground quickly it slowly rolls down the incline plane yet speeding up but now you can measure things you can mark stuff on the incline plane and notice these intervals then check those out if you go back if you go back to look at Galileo’s instrument there are the markers this is obviously not mark one ok this is not his first version after he worked with it he knew where to put the spacers to indicate when the ball is rolling through by the way have you noticed what on each of these little hoops can you tell little bells you roll the ball down and ding ding ding and he thought that was kind of cool alright and because they’re spaced apart they were supposed to ring at uniform intervals because it’s going faster so they needed to be farther apart so if you listen to the ball going down the incline play you were supposed to hear evenly spaced rings of the bell and he could you know adjust these until he had this lovely spacing which I borrowed this from the University of British Columbia where someone did this graph for his physics class and notice the distance increases much faster because it’s a square well then where do you go from there let’s go back to this guy falling on earth alright if you are from a different planet you’re falling rate may vary but not while you’re on earth let’s talk about what happens if you fall for one second what’s 1 x 1 x 16 you will fall 16 feet ok if you fall for two seconds what’s two times 2 4, 4 x 16 64 ok so you fall 64 feet in two seconds oh oh thank goodness for excel this first unlabeled column okay math geniuses tell me what the first column represents time in seconds yeah and this one represents how far you’ve fallen well at zero you haven’t fallen then you fallen 16 now you falling 64 144 that’s next and it keeps on going and this guy this last column let’s suppose that I got Matt to volunteer for a falling object experiment and I put them up on a cliff 1024 tall okay and then we push him off after one second he fallen 16 feet he’s now at 1,008 feet so basically what’s going on I’m just taking this away from 64 and after 8 seconds kerplunk or splash or some smashing pumpkin sound did you know Galileo liked to drop things from stuff in particular there is the story we don’t know how true it is but about the leaning tower he’s up there he goes with to wait and let them drop and they fall down and they land at the same time because you never saw anything about mass or weight in here things just fall under gravity there are some assumptions assumptions are very simple the assumptions tell you things like well first of all assume there’s no air because it gets in the way ok the other thing is that assume gravity is uniform as if the earth is completely uniform instead of having mass concentrations did you know that gravity is slightly different in different places I check to see where Jenny Craig built her spas ok and the other thing we assume this this is a bit of a problem when you’re going to operate over a wide range you’re assuming the earth is flat fortunately given the internet these days people who believe that have found each other and have been making videos that you can watch on youtube proving the earth is flat but it’s not it’s an approximation who knows the name of David Scott David Scott anyone know who he is any suspicions how about if I mention Apollo 15 David Scott is the commander of the Apollo 15 moon mission who pointing out that the moon has no air one of the assumptions that we have to make about ballistics on earth that we don’t have to make and Galileo used LED weights they have very little air resistance they just pile on through and if they’re heavy or they’re relatively life they still go to the bottom and almost exactly the same time David Scott had a hammer if he had a hammer he could hammer geological samples so that was from his astronaut exploration kit and in his pocket on his own volition he took a souvenir he took a feather and he dropped them at the same time in front of a camera during the transmission to earth and feathers don’t flow in vacuum the feather and of a hammer hit the lunar surface at the same time it was a Galileo experiment done on the moon in the absence of air in vacuum so that was kind of cool really day was going alan shepard one better because on Apollo 14 alan shepard took a golf club in a golf ball and teed off and somewhere on the moon there is a golf ball that Alan Jeffers blew over the horizon best drive ever ok let’s move on from this one the falling object because i have just a few more tiny little interesting things to point out because i’m supposed to be telling you the secrets of the universe in here and all we have so far is a bit of a grasp on gravity here’s a graph this my same table here right and here’s well fall ok so down you go and math geniuses recognize that shape that shape is what’s that called that is called a parabola yeah have you ever noticed how mathematicians keep stealing words from people yeah for example you’ve heard of the word hyperbole when an English professor tells you to avoid hyperbole here she is telling you what dont exaggerate or in particular don’t over-exaggerate exaggerate just the right amount so hyperbole well in math a hyperbola is a geometric shape and in astronomy or celestial mechanics a hyperbolic orbit is an orbit being followed by an object that’s going faster than escape velocity in other words if something goes by the earth in a so called hyperbolic orbit that means going so fast that it can’t be captured by the earth it has more than escape velocity and you may have heard the word perrible perrible is a story about something that’s supposed to make a point well a parabola is one step down from a hyperbola a parabolic orbit you know something that is shaped like this by the way if you take it back and consider it symmetry with the T squared term nice beautiful u-shape if something goes vising by on a parabolic orbit that means it’s traveling at exactly escape velocity just fast enough to was on by and keep on going and never come back and if you were an astronomer an observational astronomer and you see something you say i would like to announce that this object is traveling at parabolic speed and you know what everyone would say how many decimal places because if it’s just a little bit short then it’s on a giant ellipse that sucker is going to come back if it’s a little bit high then it’s not a parabola it’s just a stretched-out hyper bluff that is the exact no room for error and I’ll tell you this much more to date astronomers have never spotted a comma excuse me a comet on a parabolic orbit every time they see a comet it looks like it’s probably an ellipse that goes way back out to the edge of the solar system and back there’s never been a confirmed sighting of something going a hyperbolic speech in other words visiting the solar system and never coming back alright so parabola remember that bit about destroying your enemies ok a lot of mathematics is devoted to this objective and here are some parabolas look at that nice parabolas huh if you throw an object in the air it comes to earth and we kind of know where because when you throw an object ballistically words again what does it mean when you say oh he went ballistic when you say someone but went ballistic you’re saying that crazy here’s the thing it means they lost control they were out of control when you throw a rock or a baseball or most anything in algebra book you don’t control the flight the moment you let go it is in ballistic motion and it’s going to make up a parabola going to make a parabola shape so you have yourself a nice cannon and a convenient little backyard howitzer whatever you may have when you fire it at the moment the moment the projectile leaves the barrel it’s in ballistic motion and it is making a parabola if you go online and Google ballistics or ballistic tables you will discover an incredible list specific to various sorts of weaponry saying that here’s the inclination you used to get this distance downrange it’s really quite awesome this one I like because the artist did two things he drew parabolas but he drew them in pairs look at this guy 15 degrees kind of shallow whats this one oh 75 degrees what we call few degrees that add up to 90 compliments yeah it turns out that if you’re firing at an enemy whose right here there’s someone you don’t like who’s right here well you can loft it high and bring it down right on top of your enemy it gives them quite a bit time to prepare but you know if he has some kind of rampart in front of him if he’s dug in in straight down surprise or if you simply want to get him pretty straight on and he’s just standing there you can fire low oh and by the waiting because of the symmetry of this whatever the muzzle velocity is right here when it hits the target at the other end it’s going to have essentially that same velocity back think about the one that goes way up high gravity gravity time fighting gravity gravity slowly stopping it and right up here okay and if your coyote you would stop for a while and look around before you realize something went terribly wrong but if you’re just a projectile you immediately start back and you’re speeding up speeding up speeding up and by the time you get here your speed is just about the same as it was at the moment of firing so I like that one while i was looking I also grabbed this one and now you can see a whole collection of ranges and meters so this is a small sort of pocket sized piece of weaponry because you can only get a few thousand meters down range but this one is also working out the altitude the maximum height every bit of this can be computed with algebra basic algebra can do all of these things they can’t however take into account air resistance and that take you to a whole nother realm of mathematics you start doing differential equations and figure out stuff like that we’re not going to go there and as long as were talking about weaponry I I had to do this I can’t help myself my senior year when I was going to school in pasadena the people in fleming house I was affiliated with Fleming house went to south west academy in san marino Southwest Academy was one of these military-type boarding schools where all the kids were dressed as cadets and they have this 1812 war of 1812 canon in their front yard on a pedestal and my classmates went and stole it and brought it on campus and it was plugged with concrete and the spokes were nearly rotten so some of the carpentry skills students in fleming house went to the Southwest Academy in san marino in the middle of the night and repaired the spoakes they were working repairing the cannon for a few nights and after it was ready to go several dozen students there were over a hundred members at fleming house a few dozen students or several dozen students went and took ropes and towed that through the streets of Pasadena and put it in front of fleming house where the next morning the people in the other student houses got up and realize that fleming house ruled and there was just no question about that they removed the concrete they fired that sucker they put it back in working condition and there was an disarmament a series of disarmament talks with the administration behold the administration building there’s we have a yearbook photo a class of 73 Fleming house put in its section of the yearbook a photograph of Throop Hall half destroyed in the background at the end of the olive walk and in front there’s a picture of the cannon pointing at the admin building and my classmates are standing around looking like militants and it wasn’t in the yearbook but it was occasionally set on campus suck at this berkeley because our administration building has been destroyed to tell the truth I i probably should make a full disclosure guys know about the Northridge earthquake yeah it destroyed or damaged some of the buildings on the Caltech campus in 1970 and our admin building was condemned and during my senior year they tore it down and during my senior year my classmates stole the cannon and it was irresistible to set up a photo up ok well let’s turn away from that I need to up the ante just a bit Newton’s cannon the little zoom dance a little bit fuzzy but Newton imagined the cannon on top of a mountain and firing it and firing it and firing it until eventually it would miss the horizon because it goes farther and farther until at some point it’s going fast enough to where it just goes all the way around and hits you in the back oh wait a minute he allowed himself a little clearance that was wise you ever seen this illustration before Newton is famous for his law of gravitation Newton’s law of gravity which involves the acceleration of gravity in the attraction between two objects and by the way there are lots of squares in it it’s an inverse-square law you saw a square figuring very importantly in the whole business of a falling object well it figures in this too and so Newton was talking about orbital mechanics and let’s bring him onstage areas and there’s the picture this is a spread from his Principia Mathematica which is apparently an important book that most people havent read it was all about his theory of gravitation his theory of the solar system anyone know what he stuck on at the end as just sort of a little post grip he invented calculus and he tucked it at the end of the book just in case anyone was interested in how he has done this stuff someone once said would Newton have been able to do all of this if he hadn’t been smart I think the answer to that is no and we aren’t math geniuses at his level but let’s appreciate this calculus students here and also those taking AP calculus in high school they are learning stuff that Newton invented back in the 1600 so they can do stuff that It used to take the greatest minds on the earth to do but we have advanced to such a point that we have a grasp on some of this and to sort of bring this to a close look at that sucker do you see the parabola this dish is a parabolic dish antenna and you have seen parabolic dishes all over the place for things like anyone have an idea satellite TV those dishes that you see sprouting off or microwave relay towers parabolic dishes we don’t see those because a lot of them that they’re enclosed from the element but inside there’s a parabolic dish antenna and this is the very large array anyone ever seen this you know where it is it’s in New Mexico ok it’s in socorro and in the desert south part of the state and years ago I got to climb around inside one of these this is like 82 feet across or 25 meters for those who have gone metric and you see this guy here’s a guy about 6 feet tall right here and remember he’s closer if he was back here he’d be a little bit smaller and he’d be on this staircase so that you can climb up and get inside if you’re a maintenance guy the parabolic dish antenna does what it uses the power of the parabola the same shape for falling objects the same shape for falling objects will also gather and focus electromagnetic wave like radio waves right there they come in they bounce off and they collect there and they watched the skies I just had watch the skies again I said that earlier what was not earlier context Galileo now looking up is apparently a good thing ok and i wish more of my students would do that so they wouldn’t be texting so much but this is where i’m going to stop it The Very Large Array accepts visitors if you’re ever traveling in New Mexico and you’re cutting across the desert take a detour go see The Very Large Array it’s hard to grasp it from a single photograph even when you get the scale of it there are 27 of these radio telescope antennas they’re on a three-spoke array with railroad tracks and it turns out that see all these guys here’s one here’s one here’s one here’s one here’s one here’s one fading off into the distance and the radio astrounomers when they want to focus it they don’t do it but their staff goes out and remount the antennas closer together or farther apart it’s not you don’t little knob and focus this guy it takes a couple of days of this mounting and remounting these guys and secrets of the universe come into those dishes if you have any comments about the secrets of the universe you can email me I am an instructor here on campus so you can email me at and a year ago I got as my own personal website which has some of the secrets of the universe on it does this work it does i spoke too soon probably should wait several add-ons are ready for use don’t enable don’t enable go away that’s the end of it folks if you want to get in touch with me because you have brilliant questions from your genius minds i will appreciate the opportunity to respond to them I thank you for your attention and I hope you had a reasonably good time being math geniuses for 40 minutes thank you

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