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Mathematical Objects: Lottery machine

Mathematical Objects

A conversation about mathematics inspired by a lottery machine. Presented by Katie Steckles and Peter Rowlett.

lottery machine
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Mathematical Objects: Robot caterpillar

Mathematical Objects

A conversation about combinatorics, the mathematics of counting, inspired by a robot caterpillar. Presented by Katie Steckles and Peter Rowlett.

Robot caterpillar

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The smallest unique Cheshire Cat

A red Cheshire cat wearing a blue hat

At the MathsJam annual gathering, one of the many activities attendees can participate in is a competition competition – entrants each come up with a competition and submit it into a larger competition, other attendees enter each of the competitions within the competition competition, and the organisers get the chance to make long and confusing (but strictly correct) announcements that contain the word competition a lot of times.

This year, we decided, after a spectacular last-minute MathsJam bake-off entry failure on the behalf of Katie, to enter a joint competition into the competition competition. Inspired by the ‘lowest unique answer’ style of competition, which has previously featured in various MathsJam Competition Competitions (and our recent lecture on game theory) we came up with an idea – what about a competition seeking a unique entry in a non-ordered set?

Pringle stack mathematics

Pringles being stacked

Pringles ran a Super Bowl advert. In case you’re looking for ways to give Pringles more money, apparently you can buy several tubes of Pringles and mix the flavours. (Pringles are a type of food. Super Bowl is a kind of sport. None of that matters, what matters is…) The advert shows a man stacking three Pringles together and claims there are 318,000 possibilities.

The Mathematical Beauty of the Game SET

Three SET cards, forming a 0-alike SET

If you are like me, you have played the game SET and have probably been perplexed at how quickly some people can play the game! Even as the game is quite easy to explain, it takes some time to build various strategies and pattern recognition to play the game effectively. If you have never heard of SET, don’t fret because we will soon review its layout. For my final masters project at Texas A&M University, we had the autonomy to research any higher-level mathematical topic and I felt SET would be a great venue to tap into some deeper mathematics. Little did I know how truly complex and elegant SET really is with connections to combinatorial geometry, finite affine geometry, and vector spaces over finite fields, some of these problems still open in research-level mathematics. All of these topics (and more) are included in a great resource I highly recommend for some summer reading. Check out The Joy of Set by McMahon, et al. to dig deeper into what is presented below.

The chromatic number of the plane is at least 5

A long-standing mathematical problem has had a recent breakthrough – scientist Aubrey de Grey has proved that the chromatic number of the plane is at least 5.

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