In The Imitation Game, Benedict Cumberbatch plays Alan Turing, the genius British mathematician, logician, cryptologist and computer scientist who led the charge to crack the German Enigma Code that helped the Allies win WWII. Turing went on to assist with the development of computers at the University of Manchester after the war, but was prosecuted by the UK government in 1952 for homosexual acts which the country deemed illegal.
Release date: November 21, 2014 (official trailer)
Unfortunately, the alternating pattern doesn’t continue.
The next term in this sequence is composite again.
Numberphile provides this wicked explanation of boolean circuits (fundamental basic models for computers) with dominoes.—
One of the key characteristics of mathematicians and puzzlers is that they don’t simply give up, they try to prove that it’s impossible.
tjdaviss said: About your post on the quadratic formula. It goes back up in September every year, because that is when students are forced to start to learn about it. Down in the summer because nobody likes what they teach in school.
You’re not exactly right.
For most students, the quadratic formula is indeed a gruesome encounter with some non-trivial mathematics. They don’t know where it comes from, have to learn it by heart, and know how to use it only in straightforward but artificial exercises. No creativity to be found. It can even be disapproved to try something new instead of sticking to the plan.
The source of that problem doesn’t lie with the math itself: it’s the system of education that’s inherently wrong. To make students appreciate mathematics, they should be taught to think, instead of to calculate. Creativity, intuition and interest should be stimulated, by letting students try to solve problems, instead of giving them a magic formula to apply and to learn by heart. Math is not solving quadratics by a formula, it’s understanding why the formula works.
If you’re the lucky student who understands math is about deducing real life truths, and not about calculations with contrived interpretations, you just may be wanting to learn about cool mathematics during summer. I do. But then you wouldn’t need to waste time on looking up the quadratic formula, because you’d know where it comes from.
Don’t blame mathematics for being boring, blame school.
This is the magic hexagon. The numbers add up to 38 along each straight line. It can be called the magic hexagon rather than a magic hexagon because there are no other hexagons numbered 1,2,…,n with this property, no matter how many layers the arrangement has (except for the one which is just one hexagon with 1 written in it, but that’s hardly magical…).
(Source: Mathematical Gems I by Ross Honsberger)
This chart shows how to solve every quartic polynomial.
Notice it also shows how to solve cubics and quadratics, but it can’t be improved to quintics (polynomials of degree five) or higher, because only polynomials with degree less than five can be solved algebraically in general: this is the Abel-Ruffini theorem. Some specific quintics can be solved, but the method is far more tedious. In 2004 Daniel Lazard wrote out a three-page formula for the roots of a general solvable quintic.—