# MathsJam Gathering 2013

This is a list of the talks presented at the 2013 conference, along with slides where we have them. If you'd like to send us your slides, or more detail about your talk, please email .

## Saturday

### Session 1

#### Get Set - Sam Headleand and Robie Basak

#### Every 823 years - Andrew Taylor

Every so often, a meme goes round about the date being interesting -- 11/12/13 14:15:16 or whatever. It looks impressive, but it usually annoys me by claiming it "won't happen again for 823 years" when in fact there are so many date formats and 'interesting' strings of numbers that I figured it would effectively happen all the time. So I tried to demonstrate it using Twitter, Python and the OEIS, and if anything, it worked *too* well...

- Today is Special (@823years) on Twitter.
- The OEIS

#### Poetry in motion - Phil Ramsden

A sestina is a seven-stanza poem, each of whose first six stanzas consist of six lines each. The sestina, and its intricate rhyme scheme, date back to the twelfth century.

#### Why John Buridan should be remembered for more than cruelty to animals - Tony Mann

Until very recently I knew very little about the fourteenth-century philosopher John (or Jean) Buridan. I'm now astonished that nobody told me about his mathematical ideas and I want to share my new enthusiasm.

#### An enneahedron for Herschel - Christian Perfect

A talk about the funky nine-sided polyhedron I made based on the Herschel graph.

#### No-one quite knows if we're ripping you off - Adam Atkinson

Something from A-level maths (or which plausibly _could_ be in A-level maths even if it isn't in current syllabuses) was useful at work a few years ago, when I needed to compare different tariffs for phone calls.

#### Triangle numbers - Phil Harvey

I will only refer to a restricted number of interesting facts about triangle numbers. I would also like to make reference to odd socks and high bus numbers. And I would like to attempt a couple of tricks.

#### The Chris Tarrant Problem - Colin Beveridge

A twist on the Monty Hall problem: should you switch your best guess after going 50-50?

#### Hexagonal-shaped boards - Rita Santos & Tiago Hirth

I'd like to introduce the MathsJam audience to four Mathematical Games. A short introduction and historical background might be given as well as the reason of choice.

### Session 2

#### Betting for the same team - Alistair Bird

Many people love to gamble with each other. Unfortunately, sometimes people agree, especially with their friends. Here's one possible way of betting against another person when you both believe in the same outcome.

#### Biased coins - Michael Gibson

A coin is tossed once and the result is heads. What is the probability that next time this coin is tossed the result is heads again? Clearly if the coin is fair, the answer is ½, but what if we know the coin could be biased?

#### Chess and mathematics - John Foley

The corner attack puzzle combines chess and mathematics. Although outwardly simple and easy to solve, it contains hidden depth. There is a piece in each corner of the board. There is a number in each corner which represents the number of times that the corner is attacked by the pieces in the other corners. The puzzle is to find out what the pieces are.

#### A glance at a couple of maths's weakish links - Ken McKelvie

Ken discusses which skills are taught as part of a mathematics course - and which ones should be!

#### The 2½ mile talk - Ewan Leeming

The sport of Navigational Rallying is somewhat akin to trying to solve a sudoku on a roller-coaster. I will introduce it and show how it lends itself to an interesting selection of problem-solving activities for all ages and abilities, and also to activities suitable for Maths and Geography classrooms.

#### Some named curves - Yuen Ng

Yuen presents some named curves. They appear in some curious locations, not just on graph paper!

#### Excelling at Maths (part 3 of the Egyptian trilogy) - Liz Hind

Previously on Maths Jam... So we've seen a couple of examples of great maths from ancient Egypt, but did they excel at maths? Here's another example and some thoughts on what we've learned.

#### Diffy - Rob Eastaway

Diffy is a simple subtraction game for primary school kids...yet it has spawned several serious maths papers, and contains some delightful mathematical surprises. How long can you make YOUR Diffy last?

### Session 3

#### 5 minutes, 3 proofs, no solutions - David Bedford

#### Fun with 2D glasses - Michael Gibson

2D glasses, yes you read correctly, 2D glasses - not 3D glasses, which are very old-hat. 2D glasses are easy to make by cutting pairs of 3D glasses in half and joining together pieces of the same colour. By making graph paper with 2 different types of scale, each printed in a different colour, it is possible to plot some data just once, but view it from 2 different points of view, depending on what colour glasses you view it through.

#### Ben Folds (A)4 - Ben Sparks

A4 paper is a fascinating source of interesting mathematical tidbits. Here are some.

#### Prove Pythagoras by folding A4 - Noel France

An Easy Paper folding Exercise - 'The Triangle on the hypotenuse'

#### Quarto games of different sizes - Peter Rowlett

We have a game called Quarto, which uses pieces with four different properties (colour, shape, etc.) and the object is to place four-in-a-row sharing one of the properties on a 4x4 board. Talking about noughts and crosses, we tried to simplify Quarto using a 3x3 setup and found this was impossible. I would like to describe Quarto and the (simple) maths behind which sizes of game do and don't work.

#### Dual inversal numbers - Katie Steckles

An interesting property of certain numbers, which was described to me by a mathematician I once met, and my response to his initial findings.

#### Here be dragons - Pat Ashforth & Steve Plummer

A crafty look at dragon curves.

#### Botanica Mathematica - Julia Collins

I will describe a maths/textiles project I've been running this year with Madeleine Shepherd, called Botanica Mathematica. It's about taking very simple mathematical rules and using them to build shapes which are mirrored by nature, such as trees, fungi and seashells. Part of the Year of Maths for Planet Earth 2013.

#### Matt almost understands Bitcoin - Matt Parker

Bitcoin is a cryptocurrency. Or is a cryptocommodity? Either way it involves computers. And a lot of maths. Matt Parker will try to explain that maths. He may get some of it wrong.

## Sunday

### Session 1

#### The three-pinned arch - a graphical construction - Hugh Hunt

Engineers do more geometry than mathematicians, especially when it comes to understanding the forces in arches.

#### Pretty polynomials - Martyn Parker

#### A dance with ropes - Pedro Freitas

We'll present a dance in which two ropes get entangled, and disentangled again.

- Rational tangles, on Wikipedia

#### Developing mathematical creativity - Alison Kiddle

In my day job working for NRICH, I am currently working on a project looking at developing school students' mathematical creativity. I'd love to share a little bit about the project, and find out if any MathsJammers can help!

#### Hyperbolic knots - Nicholas Jackson

There are three types of two-dimensional geometry: Euclidean, spherical and hyperbolic. In three dimensions there are eight. The (three-dimensional) space around a knot has a canonical geometry - in almost all cases this is hyperbolic, and tells us useful information about the knot.

#### Perfect squared Klein bottle myths - Geoffrey Morley

A minimum of nine unequal squares is needed to tile a rectangle. I shall show how surprisingly few unequal squares can tile a M�bius band or Klein bottle and debunk a few myths.

#### Bijections - Colin Wright

People often say with infinite sets that |A| ≥ |B|, and that |B| ≥ |A|, and then take it for granted that |A| = |B|. Is this actually true?

### Session 2

*k* more things to do with a square (chessboard) - Alison Kiddle

Last year, I shared n things to do on squared paper, where n=5. This year, instead of squared paper, I will share k things to do with a chessboard, where k=the number I can get through in five minutes!

#### 3^m = 2^n = Ben Sparks

Does 3^m = 2^n for some integers m,n ?

#### one three hundred and eighty fourth (1/384) - John David Read

A derivative tweet led to thinking more deeply about an interesting pattern in structural mechanics that it turns out also occurs in another area of maths.

#### Gabriel's horn - Luke Bacon

A lecturer once told me that "integration is smooth and cuddly, but differentiation is ragged and dangerous". I wasn't quite convinced and would like to present some counterexamples.

#### Ox Blocks probabilities - Peter Rowlett

I will talk through what the Ox Blocks game is and how it is played, and an investigation I did of the unusual dice that are involved.

#### "There are two X, but at least one is Y" - Rob Eastaway

The problem with so-called probability questions like the "Tuesday Boy Problem", and indeed "The Thursday Girl Problem" is that they depend on who poses the problem. I've been investigating who it is that says things like "I have two of X, one of which is a Y."

#### Some Geogebra things - Michael Borcherds

Michael talked about implicit Graphs and (x+iy)^n.

#### Non-attacking bishops - David Singmaster

David Singmaster presents a selection of puzzles.

#### Ying-yang theorem - Emma McCaughan

Emma examines puzzle 15 from this set, and presents a theorem.

### Session 3

#### Picture-hanging puzzle - Ross Atkins

Borromean has asked his cunning butler to hang a picture-frame on the wall. For extra security, Borromean requests that the hanging cord be entangled over two nails in the wall instead of one. Borromean's bad butler must do as his master requests, but would very much like to increase the probability that this picture falls. Can you find a way to entangle a cord over two nails, such that if either nail is removed, then the picture is not held up by the other one?

#### Tescoefficient - Joel Hadley

Joel calculates the density of Tesco stores in a given city.

#### Crypto-graphs - Paul Taylor

In the August 2013 edition of Puzzlebomb, we included a puzzling set of graphs without bars. I will describe how the puzzle was conceived, and how it could be improved.

#### Saros and Inex - Mike Frost

On the pseudo-periodicities of solar eclipses.

#### Proof that root 2 is irrational - Francis Hunt

By folding a square piece of paper, I will prove that the square root of 2 is irrational.

#### nth root of 2 - Julia Collins

A proof that the nth root of 2 is irrational.

#### Centrifugal force at the bottom of a tuning fork makes a noise at double the frequency - Hugh Hunt

If the prongs vibrate symmetrically then the handle is a node.