A paper published in the January 2010 issue of Computers & Mathematics with Applications which, according to Times Higher Education, “used unspecified computer ‘magnification technology’ to provide the first proof of a Euclidean axiom called the ‘parallel postulate'”, has been withdrawn by the publisher.
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MAA Mathematical Petting Zoo
A figure 8 knot, a Temari ball with cuboctahedral symmetry and a Klein bottle in the MAA's mathematical petting zoo
The MAA recently displayed a mathematical petting zoo at the USA Science & Engineering Festival, along with a slideshow of pictures from their MAA Found Math collection.
The page about the event doesn’t have any pictures on it but it does have lots of links to the artists and their portfolios. The usual suspects are represented — non-orientable manifolds and polyhedra are in abundance — but there are a couple of unfamiliar objects, and they’re all pleasing to look at and think about.
(via MAA Found Math on Flickr)
Follow the timeline of Alan Turing’s life
The Science Museum in London have created a Facebook timeline of Alan Turing’s life and events afterwards. It’s an excellent use of the new Timeline feature – you can scroll up and down the timeline from Turing’s birth to the current day, which contains plenty on his codebreaking and work with early computers as well as more mundane things like his schooling and the invention of the very first chess-playing computer program. Appropriately, his tragic death is a small footnote to a fascinating life, just a couple of lines. Scrolling back up towards the present, you can see how Turing’s reputation was restored and commemorated, leading up to 2012, the Alan Turing Year.
The number line is not an intuitive concept
Some cognitive scientists have done an experiment on some people in Papua New Guinea to test the hypothesis that the number line is based on an in-built intuition that all humans share. They concluded that it isn’t, and that you can use cardinal numbers without placing them mentally on a line.
Math/Maths 95: Massively Multiplayer Online Mathematics
A new episode of the Math/Maths Podcast has been released.
A conversation about mathematics between the UK and USA from Pulse-Project.org. This week Samuel and Peter spoke about: Math Massive Open Online Course (MOOC); A-level sciences ‘lack the maths students need’; School maths should be more practical, say (some) teenagers; College Dropout Became Mathematical Genius After Mugging; Feminine math, science role models do not motivate girls; The Reason that Spies love Math; Rubik’s Challenge 2012; Concorde TSP App; The Traveling Salesman Version of Sam’s Face; Wikipedia adds MathJax display option; IMA YouTube channel; Protection of Freedoms Bill; The Aperiodcast; HUMANS V NATURE: Engineering FTW; and more.
Get this episode: Math/Maths 95: Massively Multiplayer Online Mathematics
Matt Parker’s maths problem page in The Telegraph
Matt’s latest set of puzzles, as part of the Make Britain Count campaign, are online at The Telegraph. This round of puzzles is all about factors, and there have been previous puzzle sets about consecutive numbers and prime numbers.
“Futurama theorem” slightly improved
The “Futurama theorem”, also known as Keeler’s Theorem after its creator, was a bit of maths invented for the Futurama episode The Prisoner of Benda, to solve a problem where the characters get their heads mixed up and need to swap them back without any one pair swapping heads twice. It was enthusiastically reported by the geeky press, and rightly so, because it’s a fun bit of real maths with a wonderful application. Dana Ernst has written some very good slides about the theorem, working from “what is a permutation?” up to the algorithm itself.
Anyway, some students from the University of California, San Diego have extended the result, giving a better algorithm for finding the minimum number of switches to put everyone’s head back in the right places, give optimal solutions for two particular situations, and give necessary and sufficient conditions for it being possible to represent the identity permutation as $m$ distinct transpositions in $S_n$.
Paper: http://arxiv.org/abs/1204.6086
via James Grime