… if $B_1$, $B_2$, $\ldots$, $B_n$ are $n$ bases of an $n$-dimensional vector space $V$ (not necessarily distinct or disjoint), then there exists an $n \times n$ grid of vectors ($v_{ij}$) such that
1. the $n$ vectors in row $i$ are the members of the $i$th basis $B_i$ (in some order), and
2. in each column of the matrix, the $n$ vectors in that column form a basis of $V$.
Fan of the site Ravi Fernando has written in to tell us about his high score at the “is this prime?” game: a cool century!
I’ve been a fan of your “Is this prime?” game for a while, and after seeing your blog post from last May, I thought I’d say hi and send you some high scores. Until recently, my record was 89 numbers (last March 12), which I think may be the dot in the top right of your “human scores” graph. But I tried playing some more a couple weeks ago, and I found I can go a little faster using my computer’s y/n buttons instead of my phone’s touch screen. It turns out 100 numbers is possible!
Watch in amazement:
But, to the delight of prime fans everywhere, he didn’t stop there:
Today I even got 107 – good to have a prime record again.
Well done, Ravi!
Now is a good time to point out that the data on every attempt ever made at the game is available to download, in case you want to do your own analysis: at time of writing, there have been over 625,000 attempts, and 51 is still the number that catches people out the most.
It was George Boole’s bicentenary in 2015, so the Heslam Trust is a bit slow to reveal its plans to erect a statue of the great man in his home town of Lincoln.
There’s already a bust of Boole in University College, Cork, installed in plenty of time for the bicentenary. Here’s a picture of me and HRH Poppy Dog standing next to it, last Summer.
This year has been frankly ridiculous. And while we’ve done our best to cover all the hot maths topics throughout, we have inevitably missed a few. Here’s some mathematical news bits and bobs from 2016 which we (and you!) may have not noticed.
Aperiodipal numero uno Samuel Hansen’s acclaimed podcast series Relatively Prime is back, on a new monthly schedule, with an episode about how PhD student Ibrahim Sharif designed a lottery to award licences to sell cannabis in the state of Washington.
When the stakes are so high (geddit?! – Ed.) you have to be really sure that your lottery is fair. That’s where a lot of fun maths comes in.
You can listen to Lottery Daze on relprime.com. Sam intends to fund this new incarnation of Relatively Prime through Patreon – you can pledge to pay Sam a certain amount (starting at a dollar) for every episode he releases, with perks for paying more such as a postcard from Sam or placing an ad in one of the episodes.