# MathsJam Gathering 2010

Here are some titles and, where possible, blurbs from talks given at the 2010 MathsJam conference. Unfortunately, we don't have any slides.

#### Martyn Parker : When 1 hour just will not do....

Many talks are 1 hour lectures or workshops, but what about ideas for longer more in depth sessions? Drawing from experience of running summer schools we'll illustrate some mathematics that has proved successful for session of anywhere from just over 1 hour to entire weeks. The material has appeal to a wide age range.

#### Samuel Hansen : Let's Make this Graph magic

Graph Labelings are at the same time one of the deepest and one of the most fun areas of study within Graph Theory. Coupling together the joy of drawing diagrams with the thought required by any great mathematical puzzle a good graph labeling question can engage anyone with any interest in mathematics. I will define a specific type of Graph Labeling called Integer-Magic and give a couple of examples while still leaving plenty of area to be discovered.

#### Stella Dudzic : Socks

Alice and Bernice are twins. Alice always wears a pair of socks that match in colour. Bernice always wears a pair of socks which are different colours. Each twin has n pairs of white socks and n pairs of black socks. The socks are mixed in a drawer and chosen at random. Who is likely to have a pair first? What if they pick from one drawer and as soon as there is a pair the same, Alice is finished but as soon as there is a pair that is different, Bernice is finished?

#### Julia Collins : Slice knots

Every knot is the boundary of a 2-dimensional surface, but those surfaces always have holes in them. Special knots, called "slice knots" can be pushed into the 4th dimension so that the holes in the surfaces disappear. How can we tell which knots are slice? You have to play with pictures of the knots and see if there is a special 'move' you can make which would unknot it.

There is ONE knot left which may or may not be slice. Will *you* be the one to find the lucky slice move?

#### Tony Mann : Pi needles

Demo of how one can get extraordinarily accurate approximations to pi with Buffon's needle and a little guile

#### Jonny Griffiths : Hikorski Triples

A new integer triple a la Pythagorean triples.

And a connected conjecture that looks easy but hasn't been solved yet.

#### Katie Steckles : The Listener Series

The Listener series is unique among newspapers in publishing numerically-based puzzles. They often involve some very advanced and interesting mathematical deduction. I have produced a handout featuring some recent mathematical Listener crosswords and their solutions, for anyone who would like to try them!

#### Mike Frost : Artistic Justice

Three minutes of whimsy, a new twist on an old tale. With an unfortunate denoument.

#### Adam Atkinson : some semi-chestnuts

Some things seem like they ought to be chestnuts yet I don't see them around remotely as often as other problems.

Here are some I want to help reach chestnut status.

#### Adam Atkinson : Applications of Vampires

I will talk utter nonsense for 5 minutes about applications of vampires in medicine, law enforcement, electricity generation and so on.

#### Rufus Roberts : The 27 Card Trick

Your victim picks one of 27 face down cards, looks at it and places it back anywhere in the deck. Your victim then tells you any number between one an 27. You deal the cards out into three face up piles and your victim tells you which pile their card is in. You deal out the cards two more times and after the third deal you have found their card and placed it at a position in the deck corresponding with their number.

#### Alison Kiddle : Take 3, 4, 5...

In this short talk, I will share a problem taken from the NRICH website (Take 3 from 5), together with some of the follow-up questions it prompted for me the first time I met it.

#### Tom Button : Doubling a Square, Cantor Ternary set in base 3

I will state 2 problems briefly in a time of less that 5 minutes:

- Doubling a square using only a straight edge.
- The Cantor Ternary Set is quite interesting if you consider it in base 3.

#### Tarim : Why You Might Want To Play The Lottery

A brief look at a game with a non-intuitive expected win and why the expected win of a game isn't quite the whole story.

#### Geoffrey Morley : Some astonishing deformable tilings

Empirical data suggest that any tiling of a rectangle by (possibly unequal) isosceles right triangles is a subdivision of an instance of an underlying deformable rectangle tiling (U-tiling) with an invariant aspect ratio by pseudoquadrangles and pseudotriangles. Also, a U-tiling is often a subdivision of the tiling in a fundamental domain, when a rectangle, of a deformable edge-to-edge trivalent periodic tiling (M-tiling) by pseudoquadrangles.

#### Peter Rowlett : Thinking outside of the box

I propose to show an old puzzle - that of drawing a limited number of straight lines to form a continuous path through every dot in a grid - and discuss students' attempts to solve it. In my experience, students typically approach this problem with so many preconceptions that they define a new problem which cannot be solved.

#### Peter Rowlett : A curious fact about almost every integer

Almost every integer has a digit 3 in it: True or false?

#### Colin Wright : How High the Moon

Using a stopwatch and a pendulum, can we calculate the distance to the Moon?

Yes, we can!

#### Michael Borcherds : What comes next? Great icosahedron, Octahedron, Cuboctahedron, Icosahedron, Octahedron, ?

Some interesting things I found when trying to reproduce this: http://dogfeathers.com/java/octicos.html

#### Chris Sangwin : Trace once round the boundary to measure the area..... Mad but true!

What, if any, is the connection between the perimeter of a plane shape and its area? This talk will explain how to measure the area of a plane shape by tracing one around the perimeter, using only a simple tool made from a bent coat hanger.

#### Colin Graham : Paper-folding problems

There are three basic ideas/problems I can introduce, two of them definitely 5-minute activities, the other would need 10.

1. Origami and making squares into other regular polygons 2. Origami and dividing a square into parts which are non-binary 3. Tangrams - make and reshape (10 minutes +)

#### David Bedford : Maths and the Imagination

My favourite subjects at school were Mathematics and English. My Form teacher thought this was strange as English requires imagination whereas Maths does not. I should have shown him these two problems: The Hungarian Racing Driver, and The Ants on a Metre Ruler.

#### Bernard Murphy : Tiling rectangles with and without dominoes

It all started with planning a masterclass on, amongst other things, fault-free tilings when I realised my 99p charity shop purchase of 251 dominoes left one of the 14 sets one domino short. 'Doesn't matter', I thought, 'if they place 17 dominoes in a 6 by 6 grid then it's obvious where the missing one must go.' But 17 seems a bit wasteful - what if I gave them only 6 dominoes - could that determine a unique tiling? And what about a 6 by n grid? ...

#### Todd Rangiwhetu : Lies and Damn Lies

Watch or listen to any news broadcast or read a newspaper and, on average, you will be assailed with 3.1 statistics. The following week, you may well be presented with statistics that seem to contradict last week's conclusions. The contradictory conclusions may even be based on statistics from the same raw data. This talk is intended for a general audience and will be decidedly average.

#### Lucas Garron : Math and the Rubik's Cube

The Rubik's Cube has recently been in the news because God's number has been established: any position can be solved in 20 moves. But what does that mean?

I will start by going into an overview of the math and computer science behind the result (pruning, two-phase, cosets).

Then, I will give a quick introduction of the way that math is related to practical concerns in speedcubing.

I won't have much time to demonstrate related puzzles or speedsolves, but feel free, say, to ask me about a puzzle or to show you a blindfolded Rubik's Cube solve and explain it.

#### Micky Bullock : The 1-in-10 Gay Problem!

A talk initially about probability, specifically considering the problem where there are n people in a room, where each person has a 1/n chance of having a particular characteristic, and we want to know what is the probability of there being at least one person in the room with that characteristic.

Abstraction of the problem follows, along with some interesting and unusual surd maths. We end by discovering some hidden discrete solutions to a discontinuous function.

#### James Grime : One coin trick for the pub

I present a trick or puzzle or scam that can be performed anywhere with just a few coins... unless I decide to talk about something else.

#### David Bedford : Euler's Infinite Tetration

Euler considered the infinite tetration x^x^x^x^...=2. So will we.

#### Hugh Hunt : Puzzling Pulleys

A description can be found here: The Pulley Question

#### Matt Parker : Irrational Powers

Matt will talk about irrational powers for about five minutes.

#### Matt Parker : Knotting a loop

Matt will talk about knotting loops for about five minutes.

#### Michael Borcherds & Chris Sangwin : Shapes of Constant Width

Some interesting and unexpected facts about shapes of constant width

#### Neil Calkin : Counting the rationals with a binary tree

Cantor's proof that the rationals are countable is beautiful, but it has some computational difficulties. In particular, it is rather hard to tell what the 10^400th rational is. We'll discuss an alternative approach, labelling a binary tree with the rationals in lowest terms in a very natural manner, in which the rationals appear in a different order which makes it easy to compute which rational appears when.

#### David Singmaster : Some reminiscences of Martin Gardner

I corresponded intermittently with Gardner for over forty years and had the pleasure of visiting him twice. Here are a few personal reminiscences of this remarkable man.

#### Sian Bedford : The trials and tribulations of growing up with a mathematician

#### Ron Knott : Two solutions in search of a puzzle

I have two new(ish) methods of producing the Fibonacci numbers. Can you find a puzzle for them?

#### Luke Pearce : The Cube - My Favourite Visualisation Problem

I just want to share my favourite problem about cubes with everyone. I first encountered this problem during my own Cambridge maths interview, but it can be used with KS3 pupils... That's how versatile it is and how little knowledge it requires.

#### Richard Lissaman : Hard as nails

A really nice physical problem involving nails. It illustrates that a problem can be inspiring because it has a surprising and beautiful solution.

I'll probably couple this with a proper pen and paper maths problem which I think has the same appeal.

#### Alex Bellos : Land of the Rising Sums

Snapshots from my mathematical tour of Japan, including the amazing phenomenon of Flash Anzan.

#### Phil Chaffe : Some temperaments are more equal than others

Western polyphonic music is based around instruments being tuned to use equal temperament but is this the best way to do things? This talk is a whirlwind tour around the history of musical instrument tuning from Pythagoras onwards and poses the question "Is there a better way to do this?"

#### Sue de Pomerai : Seasonal vegetables

Sprouts - A couple of little pencil and paper games!

#### Joel Haddley : Dissecting a Circle

We can dissect a square into congruent pieces that don't all touch the centre. Can we do the same for a circle?

#### Francis Hunt : Setting the Prisoners Free

#### Rob Eastaway : The Gardner Index:

The CD of Martin Gardner's complete works means you can use a word search to find the frequency with which different maths ideas crop up in his books. It gives an indication of which topics he (and therefore his public) found most and least interesting in maths."