80th Carnival of Mathematics
Welcome to the heavily delayed 80th Carnival of Mathematics. Apparently, 80 is the smallest number with exactly 7 representations as a sum of three distinct primes. Head over to Wolfram Alpha to find them. 80 is also the smallest number that is diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, …) – EIGHTY = 5+9+7+8+20+25 = 74 (Thanks Number Gossip).
Over at The Endeavour, John Cook discusses the principle of the single big jump (complete with SAGE notebooks) where he demonstrates that ‘your total progress is about as good as the progress on your best shot’…but only if the distribution is right.
Denise asks “What was it really like to work and think in Roman numerals, and then to suddenly learn the new way of calculating? Find out with these new books about math history.” in Fibonacci Puzzle. She is also running a competition which will be ending very soon so you’ll need to hurry if you want to enter.
Guillermo Bautista discusses origami in Paper Folding: Locating the square root of a number on the number line while Gianluigi Filippelli explains how some researchers found a solution to a computational problem using a biological network.
David R. Wetzel gives us Saving the Sports Complex Algebra Project in an effort to better engage math students while Alexander Bogomolny brings us a whole host of engaging math activities for the summer break and Pat Ballew introduces a Sweet Geometry Challenge.
I came across a couple of interesting articles about Markov Chain Monte Carlo (MCMC) simulations this month. The first is from John Cook, Markov Chains don’t converge while the second is by Danny Tarlow, Testing Intuitions about Markov Chain Monte Carlo: Do I have a bug?
Matt Springer brings us Spherical Waves and the Hairy Ball Theorem (below)
Peter Rowlett of Travels in a Mathematical World fame recently had a paper published in Nature about the Unplanned Impact of Mathematics where he talks about how it can take decades, or even centuries, before research in pure mathematics can find applications in science and technology. For example, quaternions, a 19th century discovery which seemed to have no practical value, have turned out to be invaluable to the 21st century computer games industry! Something for the bean-counters to bear in mind when they obsess over short term impact factors of research.
Over at Futility Closet, we have a fun problem called School Reform.
Terence Tao gives us a geometric proof of the impossibility of angle trisection by straightedge and compass while the Geometry and the imagination blog discusses Rotation numbers and the Jankins-Neumann ziggurat.
Several people have been discussing recent changes in EPSRC (The UK’s main UK government agency for funding research and training in engineering and the physical sciences) including Timothy Gowers (A message from our sponsors), Burt Totaro (EPSRC dirigisme) and Paul Glendinning (Responding to EPSRC’s Shaping Capability Agenda).
Finally, one of my favourite mathematical websites is MathPuzzle.com. Written by Ed Pegg Jr, it is possibly the best online resource for recreational mathematics you can find. Go and take a look, you’ll be very glad you did.
That’s it for this month. The next Carnival of Math will be over at Wild About Math on 2nd September and you can submit articles using the carnival submission form. If you can’t wait until then, head over to I Hope This Old Train Breaks Down for the Math Teachers at Play carnival on August 19th. If you are new to the math carnivals and are wondering what’s going on then take a look at my introduction to mathematics carnivals.
Follow the Carnival of Math on Twitter: @Carnivalofmath This is also the best way of reaching me if you’d like to be a future host for the carnival.