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Spiders and Fly
Posted: February 2012Another pursuit puzzle: Three crazed, robotic professors (or, if you prefer, “spiders”) try to chase down a psychic, but slightly slower student (the “fly”) along the edges of a tetrahedron. It’s easier, perhaps, to draw it out in the view at right below.
Is there a strategy that allows the professors to catch their prey?
An audio podcast in MP3 format.Strange Suitor
Posted: January 2012We’ll have some pursuit puzzles over the next couple of weeks; this segment’s puzzle has a simple and elegant solution, but it might take a while to work it out! In the meanwhile, here’s a little discussion about the glass of water problem. Each time we add or subtract 50%, we are multiplying the quantity of water by 1/2 or 3/2. If we began with 1 glass’ worth, at each stage, we’ll have a quantity of the form 3m/2n with m,n>0 Of course that can never equal 1, but we can get very close if m/n is very close to log3 2 = 0.63092975357145743710… Unfortunately, there’s a serious problem: m/n has to hit the mark pretty closely in order for 3m/2n to get really close to 1, and to get within “one molecule”s worth, m and n have to be huge indeed. How huge? Well, let’s see: an 8 oz. glass of water contains about 1025 molecules; to get within 1/1025 of 1, we need m=31150961018190238869556, n=49373105075258054570781 !! One immediate problem is that if you make a switch about 100,000 times a second, this takes about as long as the universe is old! But there’s a more serious issue. In a glass of water, there’s a real, specific number of molecules. Each time we add or subtract 50%, we are knocking out a factor of 2 from this number. Once we’re out of factors of 2, we can’t truly play the game any more, because we’d have to be taking fractions of water molecules. (For example, if we begin with, say, 100 molecules, after just two steps we’d be out of 2′s since 100=2*2*some other stuff. But even though there are a huge number of water molecules in a glass of water, even if we arrange it so that there are as many 2′s as possible in that number, there just can’t be that many: 283 is about as good as we can do (of course, we won’t have precisely 8 ounces any more, but still.) If we are only allowed 83 or so steps, the best we can do is only m= 53, n = 84 (Let’s just make the glass twice as big to accommodate that), and, as Byon noted, 3^53/2^84 is about 1.0021– not that close, really!
An audio podcast in MP3 format.Hi! Getting Closer
Posted: January 2012So how close, and how quickly, can we get back to exactly one glass of water, adding and subtracting 50% of the total at each step. And what is happening with the “reverse of the square is the square of the reverse” property of 2012, 2011 and 2010?
An audio podcast in MP3 format.Corpuscle Candies
Posted: January 2012In which we continue our contest for SOME interesting fact about the number 2012, describe Newton’s Law of Cooling, and ask another puzzle on the mixing liquids.
An audio podcast in MP3 format.Two Love
Posted: January 2012In which we confess further delight in arithmetic… 1) Send us your candidates for an interesting fact about the number 2012; the winner will receive a handsome Math Prize! As mentioned on the podcast, already its larger prime factor, 503, has a neat connection to the primes 2,3,5, and 7. 2) So what is it about the tetrahedral numbers, and choosing things? In particular, why is the Nth tetrahedral number (aka the total number of gifts on the Nth day of Christmas) is exactly the same as the number of ways of choosing 3 objects out of (N+2)? Not hard, really, to prove, but can you find a simple or intuitive explanation? 3) Finally, about those M&M’s. Maybe I exaggerated a little bit when I claimed this problem holds all the secrets of the thermodynamics of the universe, but I don’t see how! Many classic equations, such as Newton’s Law of Cooling or the Heat Equation, the laws of thermodynamics, and fancier things as well, can all be illustrated by shuffling red and blue M&M’s around. What I don’t understand is how anything got done before M&M’s were invented!
An audio podcast in MP3 format.True Love
Posted: December 2011How much does my True Love love me truly? Kyle and Chaim ponder the question…
An audio podcast in MP3 format.On Cake and Coffee
Posted: December 2011Harry Kaplan joins us for discussion of cake and coffee– and leaves us with a counter-intuitive puzzle…
An audio podcast in MP3 format.The Math Factor Returns!
Posted: December 2011A quick hello from Chaim and Kyle as the Math Factor returns! We’ll be the first to say our Coffee Pot Question isn’t our deepest puzzle ever, but it sure did make a difference in Chaim’s life!
An audio podcast in MP3 format.Strongly Connected Components
Posted: July 2011Samuel Hansen’s Strongly Connected Components podcast features interviews with all kinds of mathematical luminaries (that sounds familiar!) If you’ve been missing the Math Factor, be sure to check it out! Here, we discuss, well, Chaim Goodman-Strauss—the tables are turned!
An audio podcast in MP3 format.Puzzlers Pegg and Stephens!
Posted: April 2011By an amazing coincidence, world-class puzzle creators Ed Pegg (mathpuzzle.com) and James Stephens (puzzlebeast.com) were in Fayetteville Ark. on the very same day! We sit down and discuss the art of puzzle making, their own wonderful puzzles, and their personal favourites.
An audio podcast in MP3 format.HA! Conway on Gardner
Posted: June 2010In this special segment, John H. Conway reminisces on his long friendship and collaboration with Martin Gardner.
An audio podcast in MP3 format.Chaitin on the Ubiquity of Undecidability
Posted: May 2010Greg Chaitin, author most recently of MetaMath!, discusses the ubiquity of undecidability: incredibly all kinds of mathematical and physical systems exhibit utterly unpredictable, baffling behavior– and it’s possible to prove we can never fully understand why!
An audio podcast in MP3 format.
Links
Review the full list of podcast channels in our sciences category of the directory, covering astronomy, anatomy and physiology, biology, chemistry, environmental sciences, physics and mathematics.
Whilst all the podcasts listed in this directory are selected in line with our criteria, we do strongly recommend educators that the contents of all podcasts, podcast feeds and channels are regularly auditioned to ensure that they are suitable and appropriate for the age range of the children and young people.
Friday, 10th February 2012
