Another cool watch, illustrating the prime numbers.

Another cool watch, illustrating the prime numbers.

(Source: ioanaiuliana21)

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)

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)

  • 91 is composite
  • 9901 is prime
  • 999001is composite
  • 99990001 is prime
  • 9999900001 is composite
  • 999999000001 is prime
  • 99999990000001 is composite
  • 9999999900000001 is prime
  • 999999999000000001 is composite

Unfortunately, the alternating pattern doesn’t continue.
The next term in this sequence is composite again.

A Mario parody on the famous Möbius strip by M.C. Escher.

A Mario parody on the famous Möbius strip by M.C. Escher.

(Source: ioanaiuliana21)

ε-Red Riding Hood and the Big Bad Bolzano-Weierstrass Theorem

A bedtime store for you and your mathematically inclined children.

(via mathlover1530)

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.
A knitted tangle by Emily Autumn Goddard.

A knitted tangle by Emily Autumn Goddard.

(Source: notanicedragon, via celticknotdaily)

Framed formulas (joint project)

When I saw this post of likeaphysicist, with formulas that elegant they deserve to be framed in, I decided I needed to make some myself. We’re about to move in a couple of weeks, and I would like to actually have some real framed formulas on my new bedroom wall :D

So, I’ve set up this project on writeLaTeX! Anybody who thinks of a great mathematical formula (not too physical please, preferably pure math), can easily add it in this project. The syntax should be self-explanatory, just add a line \formula{\$…a…\$}{…b…}{…c…}, with being the formula, b the title, and a one-line caption; LaTeX handles the rest.

Have fun LaTeXing! It would be wonderful if we could make it up to, say 100 formulas. As a side note, please be responsible: don’t delete other submissions or edit preamble code without good reason.

PS: of course you may add your name to the source code, if you want so.

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 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)

(Source: twocubes, via mathhombre)

Some formulas are plainly beautiful, aren’t they?

(Source: likeaphysicist, via geometricloci)

The Galton board: a cool statistical device illustrating the central limit theorem by the correspondence between the discrete binomial distribution and the continuous normal distribution.

The Galton board: a cool statistical device illustrating the central limit theorem by the correspondence between the discrete binomial distribution and the continuous normal distribution.

(Source: ibmblr)

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.

(Source: plus.google.com, via allofmymaths)

(Source: ioanaiuliana21)

A collection of beautiful mathematics: attractive pictures and fun results