The Math Factor podcasts are brought to you by The Math Factor Podcast is a weekly podcast brought to you by C Goodman-Strauss, Professor of Mathematics, the University of Arkansas.
CardColm
Posted: April 2012Colm Mulcahy joins us to share his ice cream trick from his mathematical card trick column on the MAA website! We also discuss the Gathering for Gardner. Colm also shares a quick puzzle, tweeted on his What Would Martin Gardner Tweet feed @WWMGT. And we finally get around to answering our quiz from a few weeks ago. There are indeed two solutions for correctly filling in the blanks in: The number of 1′s in this paragraph is ___; the number of 2′s is ___; the number of 3′s is ____; and the number of 4′s is ___.
An audio podcast in MP3 format.Newton v Leibnitz
Posted: March 2012A break from puzzling to discuss the history of the great Newton-Liebnitz dispute over the invention of Calculus, with the playwright Todd Taylor.
An audio podcast in MP3 format.Happy Root 10 Day!
Posted: March 2012For procrastinators only, we celebrate √10 day! And we pose a new puzzle: The number of 1′s in this quiz is ____ The number of 2′s in this quiz is ____ The number of 3′s in this quiz is ____ The number of 4′s in this quiz is ____ There are actually two solutions to this one, but more generally, what happens with more lines in the quiz? Finally, here’s the link to the special issue of Nature with essays on the great Alan Turing.
An audio podcast in MP3 format.Crazies on the Plane
Posted: March 2012We all know this feeling: someone’s in your seat, and now you’re the nutcase who’s going to take someone else’s seat. After all that what’s the probability the last person on the plane will be able to sit in the correct seat? The three number trick is just a simple version of this one (but here it is quicker and simpler).
An audio podcast in MP3 format.Five Cards
Posted: February 2012Let’s see: First, the “Big News“, a discussion of Carlos May, and another puzzle (a pretty easy one) And still more 2012 facts! From Primepuzzles.net, we learn that 2012 = (1+2-3+4)*(5-6+7*8*9) and there’s still more amazing stuff there that we didn’t try to read on the air.
An audio podcast in MP3 format.Bear Hunt
Posted: February 2012Happy Palindrome Day! (For some of us) Many listeners will have heard about the hunter who walks one mile south, one mile east, then one mile north—and is right back where he started. But in fact there are infinitely many places on the Earth where he could be, and in at least a couple of different ways! And what is the deal with Carlos May?
An audio podcast in MP3 format.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.
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Thursday, 17th May 2012
