# maths

Cousin E pointed out something odd about the International Mathematical Olympiad. It's an annual competition for high school students. And girls do super poorly in it. We ran some stats on the data for 2015 and 2016, and found that a national team with more than one female member gets less than half the median points per capita of an all-male team. With one female member, it's 59-78%.
The question I want to address is not whether women are in empirical fact worse at maths than men. Nor do I, if this is the case, want to discuss whether it's because of nature or nurture. I want to understand…

tab clearing:
A collection of maths GIFs posted purely for aesthetic reasons.
Simple Fractals
Minimalist Posters of MathematicalObjects...

Inquires Timmy. But its a stupid question. Indeed, a curiously illiberal anti-business not-really-thought-through question. The premiss is the usual one: the degrees aren't useful, they are a hangover from the old days, they aren't value-for-money, and they don't teach people what business wants them taught.
But of course what they do give you, even if you believe all that, is a piece of paper that allows employers to value you.
One solution is just to say, aha, universities are just convenient traps for the initiativeless, whilst those with va-voom get on with making their way in biznis. In…

In the latest issue of Significance, the journal of the Royal Statistical Society & American Statistical Association, economists Barry Reilly, Neil Rickman and Robert Witt take a look at the surprisingly mediocre returns that bank robbers can expect. The Fiscal Times has the story:
In the U.S., based on 2006 data, the average take from a bank heist was $4,330. In the U.K., it was much bigger: £20,331, based on 2007 data (or about $40,000 based on the exchange rates that year). A third of the robberies yielded nothing, meaning that the average take from a successful robbery was around £…

YouTube artist and multi-instrumentalist Michael John Blake has been exploring the musical patterns within mathematics, by assigning each note on the major scale a numeral. In this wonderful composition he plays Tau, a number used in a similar way to Pi, for calculating values of circles and whatnot.

This is a story about how a simple puzzle ended up haunting me for over 20 years. It's a story of hubris blocked by a mountain of cold mathematics, and the obsession spawned by knowing an answer is out there, but not knowing how to find it.
Growing on a remote island, my youthful thirst for new reading material was quenched in regular bursts from the Scholastic catalogue, a thrilling piece of folded A3 paper that flaunted great collections of tremendously exciting tomes on everything from monsters to maths. The best were the ones that combined the two.
Popular at the time, these…

I grew up in the days of the SNES and the Sega Megadrive. Even then, furious debates would rage about the harm (or lack thereof) that video games would inflict on growing children. A few decades later, little has changed. The debate still rages, fuelled more by the wisdom of repugnance than by data. With little regard for any actual evidence, pundits like Baroness Susan Greenfield, former Director of the Royal Institution, claim that video games negatively "rewire" our brains, infantilising us, depriving us of our very identities and even instigating the financial crisis.
Of course, the fact…

There's a few days left in our October DonorsChoose challenge, and even after that there are many more great projects out there waiting for our help.
A few weeks ago, wonderful educator-science-historian-cultural-studies-expert-mother-blogger Leslie Madden-Brooks responded to a plea to help fund some projects, and I was deeply moved by what she wrote to the classroom, so I wanted to share it with you...
I gave to this project because I had such a tough time learning math, and I wish I had been able to develop this kind of mathematical and critical thinking through reading interesting authors…

MarkCC has a post about quaternions and the fact that they can be used for rotation, so I thought I'd chime in with exactly how they represent rotations.
A 2D rotation by an angle θ can be represented by the complex number on the unit circle
cos θ + i sin θ
Then multiplying complex numbers is the same as multiplying rotations.
A 3D rotation by an angle θ about a line defined by a unit vector (b,c,d) can be represented by the quaternion on the unit hypersphere
cos θ/2 + sin θ/2(bi + cj + dk)
Then multiplying quaternions is the same as multiplying rotations.
But why is it θ/2 instead of θ?
Well…

Baseball's World Series is played over the best of seven games. The first
two games are played at the home field of one team (we will call
this one team A), the next three at the home field of team
B, and the last two at the home field of team A. Given that
teams are more likely to win games on their home fields, does
this give team A an advantage?
Keith Burgess-Jackson
href="http://analphilosopher.blogspot.com/2004/07/myth-of-home-field-advantage-if-youre.html">argues that neither team has an advantage:
Every Series goes either four, five, six, or…

Suppose you had a pair of dice and were wondering if they were fair. The average number you will get on a pair of fair dice is seven, so one way you could check your dice is to roll them a few times and look at the average of the results. Trouble is, you aren't likely to get an average of exactly seven. Suppose you get an average of 9. Are the dice fair? Well, that depends on how many times you rolled them.
I rolled\* a pair of dice twice and averaged the results. I repeated the experiment 1000 times and plotted all the averages. 95%…

This was my first ever on-line posting, to sci.math in 1988. The world wide web wasn't invented until 1989 so we didn't have links---I added them in 2004 when I posted this to my blog.
Kristian Damm Jensen wrote:
Consider a string of matching parentheses, i.e. a string of parentheses where each prefix contains more left-parentheses than right-parentheses.
Now, given n left- and right parentheses, in how many ways can you order them and still get a string of matching parentheses?
"The Invisible Man" replied:
Here's as far as I got. Possibly far enough, perhaps too…