Before Christmas, we launched a winter-themed maths competition – to design a sensible hexagonal snowflake, using a square grid, which could be used to knit a wintery jumper and not a) look terrible or b) have non-hexagonal symmetry. We had a deluge of entries, some valid and others less so – in fact, we may have had at least one entry break each of the rules we set. Below is a round-up of all the entries we received.
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New Mersenne prime discovered, and promptly printed out
Breaking news! On 19th January 2016, the Great Internet Mersenne Prime Search discovered a new largest prime number – we know 49 Mersenne primes, the largest of which is now $2^{74207281}-1$, a number containing over 22 million digits and full of primey goodness.
Internet Maths Person Matt Parker has responded to the news in spectacular style, by issuing a 14-minute long video explaining the discovery and its implications, as well as somehow scoring an interview with the actual discoverer of the new prime, Curtis Cooper.
Carnival of Mathematics 130
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of December, and compiled by Brian, is now online at Bit Player.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
Puzzlebomb – January 2016
Puzzlebomb is a monthly puzzle compendium. Issue 49 of Puzzlebomb, for January 2016, can be found here:
Puzzlebomb – Issue 49 – January 2016
The solutions to Issue 49 can be found here:
Puzzlebomb – Issue 49 – January 2016 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.
MathsBombe Competition
From the team that brought you the Alan Turing Cryptography competition, Manchester Uni’s maths department are running another schools maths puzzle competition, this time called MathsBombe.
Aimed at students up to Year 13 (England and Wales), S6 (Scotland), Year 14 (Northern Ireland), the competition starts on 13th January, and teams of up to 4 can register.
The puzzles will be released every two weeks, in four sets, and there’s a prize for the team solving each puzzle set first. There are plenty of other prizes too, and it’s free to enter. There’s still time!
More information: MathsBombe website.
Aperiodvent, Day 24: Tree Stump Dodecahedron
Looking for something to do with your Christmas tree, when it gets to twelfth night? Here’s an idea: cut it into a beautiful platonic solid. Follow these step-by-step instructions from Dan Beyer.
This the last entry in the Aperiodical Advent Calendar. We hope you’ve enjoyed it, and we wish you and yours a wonderful holiday season. See you in the new year!
Aperiodvent, Day 23: The Robin-Lagarias Theorem
Today’s entry is a Theorem of the Day:
The Robin-Lagarias Theorem:
Let $H_n$ denote the n-th harmonic number $\sum_{i=1}^n \frac{1}{i}$ , and let $\sigma(n)$ denote the divisor function $\sum_{d \vert n} d$. Then the Riemann Hypothesis is equivalent to the statement that, for $n \geq 1$, $\sigma(n) \leq H_n + \ln(H_n) e^{H_n}$ .
While this isn’t the traditional Christmas kind of Robin, it is equivalent to the Riemann Hypothesis. For more information, see the full listing at Theorem of the Day: the Robin-Lagarias Theorem.
This is part of the Aperiodical Advent Calendar. We’ll be posting a new surprise for you each morning until Christmas!