# MathsJam Gathering 2011

## Saturday

#### Francis Hunt - Some Mathematical Results from Physical Reasoning

From Mark Levi's book, Francis presents two interesting mechanical problems. For example, a fish tank shaped like a triangular prism, mounted to rotate around a pole at one corner. Resolve the forces?

#### Derek Couzens - Five mechanical puzzles

Derek provides us with a bag of five lovely mechanical toys, which we spend the whole weekend playing with.

#### Stella Dudzic - Cliff Top Welly Wanging

Throwing a welly is a well-known sport, and achieving the greatest distance is the aim. If standing on top of a cliff, can we increase our range, and by how much?

#### Tony Mann - A Textbook Problem

Tony presents a problem from the first known maths textbook - but is it a realistic, useful and correct question?

#### Yuen Ng - Cryptarithmetic Puzzles

Yuen presents Cryptarithmetic puzzles of the form SATURN + JUPITER = PLANETS, in which each letter stands for a digit from 0-9, and the sum is valid. He also informs that he has used the names of 38 MathsJam delegates to create similar puzzles - so it turns out SAMUEL + HANSEN = ANGLES, COLIN + WRIGHT= THRILL and JAMES + GRIME = CAESAR!

#### John Read - Sit down for some qualitative structural engineering maths

John presents a lovely equation, which was used in the construction of the Eiffel Tower, and a nice structural engineering teaser.

#### Andrew Lobb - Painting my wall

Andrew is attempting to paint his wall, using the sequences (1/3)^n and the list of fractions 1/1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5,... but will he ever finish?

#### Phil Harvey - A Partition of the first 16 integers

The puzzle is to find a partition of the numbers 1 to 16 in which each set has the same sum, the same sum of squares, and the sum of cubes. It is possible, but Phil demonstrates a lovely method working modulo 9.

#### 6th Form College Farnborough - Maths questions to be asked at interview for different jobs

Staff and students from Farnborough 6th form college present a lovely selection of problems, each of which could be given at a job interview - but not for a job working in mathematics! For example, an ice cream vendor could be asked "If you have 5 flavours of ice cream, and one cone holds 3 scoops, how many different ice creams can you make?"

#### Rob Eastaway - Pi-Thagorean triples

Rob presents a nice way to construct 3,4,5 triangles using a piece of A4 paper - and suggests how such triangles might have been named. But what does Thagorean mean?

#### Peter Rowlett - An Annoying Puzzle

Peter expresses his annoyance at poorly-set puzzles - ones in which assumed boundaries are crossed, without specifying that this is permitted. If you have a light bulb in a room, and outside are three switches, one of which controls the bulb, how can you tell which? If you're allowed to leave one of them on for 10 minutes to see if it makes the bulb hot, then specifying this in the question makes it too easy, and not specifying it makes the puzzle poorly defined. If we can do that, why can't we look under the door?

A probability paradox - two games, in both of which you're on average likely to lose. But if we play either one or the other at random, you are on average likely to win! This paradox has other applications - see Peter Rowlett's talk on Unforeseen Applications.

#### Jorge Nuno Silva - Erdos latino

Latin Squares are a very old and well-known mathematical curiosity. Jorge presents a way to play a competitive game by taking turns to enter numbers until someone can't go - and suggests a way to decide the winner in the event a perfect latin square is formed. And Erdos Latino is a real board game!

#### Colin Graham - If you don't like a strip tease, get knotted!

Colin demonstrates the fantastic things that can be made with strips of paper. If you cut a square off a piece of A4 paper, the remaining strip can be made into a Cairo tile, with fun tessellation properties, by folding opposite corners to meet. Long thin strips of paper can be knotted or braided into regular polygons - but which ones? And can we braid 12 pentagons on the same strip so that they can be assembled into a dodecahedron?

#### Michael Borcherds - Smiling Equations

A nice demonstration of the Geogebra software - altering the parameters on the equation for two off-centre circles multiplied together results in some pretty patterns.

#### Mike Frost - 17 Sides

Using a ruler and compass, which regular polygons can be constructed? Mike talks us through the history of polygon construction, and some extreme cases - and finishes with an animation of a 17-gon being constructed in 64 steps.

#### Alex Bellos - The World's Favourite Number

What is your favourite number? And do you find it a silly question? Alex Bellos used to, until he started a global project to find out everyone's favourite number. The answers have been astonishing and sometimes touching.

#### David Percy - The Optimal Dartboard?

The arrangement of the numbers around the dartboard is carefully chosen to make the game difficult. But is it optimal? David suggests mathematical ways to create a board arrangement which alternates odd and even numbers, and makes the penalty for missing your target maximal.

#### Katie Steckles - Choreographies

Katie presents some nice animations of particle motion she has discovered during her research.

#### Liz Hind - Maths in Ancient Egypt

Liz presents a puzzle from an Ancient Egyptian recreational maths papyrus (presumably used at Maat's Jam) - can we help her work out how they've solved it?

#### Tom Button - A Mathematical Medley

Tom presents some excerpts from his favourite mathematical songs, and accompanying nice mathematical facts. He finishes with his own composition, and entry for the 'largest prime number mentioned in a song' competition - sing along for yourself!

#### Samuel Hansen - Why your friends have more friends than you do

Some interesting social network theory about why your friends have more friends than you do, as a quirk of graph theory and a possible explanation for how his kick-starter got funded!

#### Peter Rowlett - Unforeseen Applications

A recent article in Nature, written by a group of mathematicians (including several MathsJam attendees!), listing uses of pure maths for things that weren't conceived of when the original maths was worked out.

#### Ray Hill - A perfect bridge deal - what are the chances?

Ray asks what the chances are of a perfect bridge deal, where each player is deal 13 cards from the same suit - and offers a possible explanation why this vanishingly unlikely event may have occurred in several local bridge games, resulting in news coverage.

#### Christian Perfect - Writing maths for the web is easy now!

Christian presents some useful tools for maths blogging - how to make your formulae look good, and a nice tool for finding the LaTeX code for any symbol!

#### James Grime - A nontransitive talk

James Grime presents Grime Dice, a specially designed new set of non-transitive dice, which has some lovely properties.

#### David Singmaster - Editing Sam Loyd's Cyclopedia

Sam Loyd's Cyclopedia of puzzles was published after his death in 1914, and has been reprinted since. David has been tasked with producing a new version - but some of the puzzles haven't got clear solutions! Can you help?

## Sunday

#### Tony Mann - What jokes tell us about mathematicians

Tony attempts to find some maths jokes non-mathematicians might find funny.

#### Joel Haddley - Piano Hinged Dissections

From Greg Frederickson's book, Joel presents some lovely paper folding activities.

#### Christopher Hext - A Calculation in Arithmetic

Christopher talks us through a method for cube rooting a 7-digit number on paper. Can you follow his method?

#### Neil Monteiro - The Meaning of Numbers

Neil teaches us how to count to ten in Chinese sign language - on one hand!

#### Sam Holloway - My favourite interview question

Two ways to prove which of e^pi and pi^e is the larger number.

#### Alison Kiddle - Amazing Card Tricks

Alison presents some lovely maths card tricks, which she's written up for the NRICH website. Now, what does NRICH stand for again?

#### Laurie Brokenshire CBE - Magic Squares

Laurie presents several mathematical curiosities, including a method for generating a 4×4 magic square for any given total, and a nice trick involving a hole in the wall.

#### John Mason - Properies of Sets of Integers and Rolling Tennis Balls

• John's slides (PDF)
• John's slides (PPTX)
• #### Colin Graham - It's a square world after all...

Origamists have long known how to fold regular polyhedra - but now Colin shows us some lovely ways to project the globe onto a polyhedron, and demonstrates how Carlos Furuti has created printable maps you can fold up into a globe!

#### Adam Atkinson - A*: a sales pitch

Adam presents the A* algorithm and heuristic functions by means of a wooden sliding puzzle - what is the distance between a given state and solved?

#### Owen Jones - Generalising prime numbers

Owen Jones tells us what a prime number is - but in the Gaussian integers!

#### Ben Sparks - Most Irrationally Pretty

Ben asks, if I put down a blob and then turn through some decimal value of a full turn, and repeat, what pattern do I get? Using this Geogebra file, you can see which values give stripes (a nice way to teach fractions), and which values give the maximally well packed arrangement of dots, and hence are the least 'rational'…

#### Tiago Santos Hirth - Paperstrip Clip Trick World Record and Other Officetime Recreation

A whole room full of MathsJammers performing a paperclip trick at the same time? Surely a world record!

#### Ken Wilshire - On the Mental Calculations World Championship

Ken gives us a run down of the world's mental calculation competitions, and lists some of the types of mental feat involved - from naming the day of the week on a given date, to adding up ten ten-digit numbers, to unforeseen challenges designed to test the younger competitors.

#### Tarim - How much does an egg timer weigh?

Tarim poses a puzzler - does a sand timer which is running weigh more, less or the same as one that is finished? He presents some convincing arguments, but it's up to you to make up your own mind...

#### David Bedford - The car, the key and the goat problem

The Monty Hall Problem, in which two goats and a car are hidden behind doors and you must find a strategy to win the car, is well known. This variation involves the car key being hidden behind another door, and two players must work together so that one finds the car and the other its key.

#### Ken McKelvie - A pattern in number sequences

Ken demonstrates a pattern in multiples of the numbers 123456789 and 1234; why do certain multiples result in a number consisting of the same digits in a different order? Is it connected to the square root of the number of digits, and multiples thereof?

#### Elizabeth A. Williams - Hark, the mathematicians sing

Elizabeth gives us the words to some of her mathematical rewrites of popular Christmas carols. Singalong at the December MathsJam, anyone?

#### Tony Sudbery - Quadruple Sudoku

The normal Su Doku puzzle has been stumping commuters all over the world. Tony suggests a way to extend it into the fourth dimension. Try doing that on the tube!

#### Matt Parker - Matt talks about a thing

Matt presents a curious stamp-collecting fact he's found about numbers whose cube roots start with the same digits as the number itself, e.g 98. He also recommends you have a go at the programming challenges on Project Euler!

#### Bernard Murphy - How do some rationals beat the odds and recur?

Bernard presents a pattern in recurring decimals.

#### Alison Kiddle - Summing Consecutive Numbers

A charming puzzle about which numbers can be made using sums of consecutive numbers - and in how many ways?

#### Micky Bullock - Making Graphs Dance

Micky shows us some dancing graphs - what do we get if we take a point a fixed distance along a tangent at each point on a curve? Using Geogebra, we can animate this and it looks lovely. He also calculates the odds of winning Play Your Cards Right!

#### Suzanne McEndoo - Beatboxing the Schrodinger Equation

Suzanne tells us about the Quantum Circus, a project designed to get artists and physicists working together and presenting physics in a beautiful way. We see a video of the Schroedinger equations, beatboxed by a clown, and all feel a bit funny afterwards.

#### Sally Robinson - The square on the hypotenuse

Having discovered many references to mathematics in Gilbert & Sullivan shows, Sally (and friends) treat us to some excerpts!

#### Christopher Douglas - How to Make a Paper Model of RP^2

Chris presents a nice cut-out and assemble model of an embedding of this four-dimensional object in 3D, designed by Ulrich Brehm.