Card game fans might be familiar with the game of Dobble, in which a set of cards featuring symbols is laid out on the table, and family members tear each other’s hands off/eyes out in order to find the one symbol a given pair of cards has in common. Well, it’s now also available virtually!
You're reading: Posts By Katie Steckles
From the Mailbag: Golfing Combinatorics
Sam’s dad is in a mathematical conundrum – so she’s asked Katie, one of our editors, if maths can save the day.
Dear The Aperiodical,
My dad is going away on a golfing holiday with seven of his friends and, since I know a little bit about mathematics, he’s asked me to help him work out the best way to arrange the teams for the week. I’ve tried to work out a solution, but can’t seem to find one that fits.
They’ll be playing 5 games during the week, on 5 different days, and they’d like to split the group of 8 people into two teams of four each day. The problem is, they’d each like to play with each of their friends roughly the same amount – so each golfer should be on the same team as each other golfer at least twice, but no more than three times.
Can you help me figure it out?
Sam Coates, Manchester
The Topological Tverberg Conjecture is False
Attention, Topological Combinatorialists! The topological Tverberg Conjecture, described as ‘a holy grail of topological combinatorics’, is false.
The conjecture says that any continuous map of a simplex of dimension $(r−1)(d+1)$ to $\mathbb{R}^d$ maps points from $r$ disjoint faces of the simplex to the same point in $\mathbb{R}^d$. In certain cases the conjecture has been proven true, but there have been found counterexamples in the case where $r$ is not a prime power, for sufficiently large values of $d$: the smallest counterexample found is for a map of the 100-dimensional simplex to $\mathbb{R}^{19}$, with $r=6$.
The result was recently unveiled at the Oberwolfach Maths Research Institute, which is situated in the Black Forest in Germany and regularly hosts bands of fiercely clever mathematicians. The disproof, by Florian Frick, is found in the paper Counterexamples to the Topological Tverberg Conjecture.
More Information
From Oberwolfach: The Topological Tverberg Conjecture is False, at Gil Kalai’s blog
Counterexamples to the Topological Tverberg Conjecture, by Florian Frick on the ArXiv
Florian Frick’s TU Berlin homepage
via Gil Kalai on Google+
Manchester MathsJam recap, January 2015
Manchester’s first MathsJam of 2015 (and indeed, all the other first MathsJams of 2015 in cities all over the world) met on 20th January, rousing us all from a Christmas-induced slumber and gently easing us back into a year of recreational maths. Here’s a round-up of what we did.
Follow Friday: 13/2/15
Remember when we used to do a regular Follow Friday post, recommending mathematically interesting Twitter accounts? Well, this is like that, only not hugely regular. Enjoy it while it lasts!
Carnival of Mathematics 119
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of January, and compiled by Frederick Koh, is now online at White Group Mathematics.
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 – February 2015
Puzzlebomb is a monthly puzzle compendium. Issue 38 of Puzzlebomb, for February 2015, can be found here:
Puzzlebomb – Issue 38 – February 2015
The solutions to Issue 38 can be found here:
Puzzlebomb – Issue 38 – February 2015 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.