The Big Internet Math-Off is a just-for-fun tournament that I and a few friends have organised on The Aperiodical, ostensibly to find the World’s Most Interesting Mathematician.

The idea is really to show off lots of fun maths, but I’ve found that a competition is a good hook to get people engaged. I’ll be doing my best to discourage anyone from taking it too seriously.

16 mathematicians will compete in a tournament. In each match, the two competitors will ‘pitch’ a fun maths thing in a post on The Aperiodical and the public will vote on which is most interesting. The voting is open for 24 hours, and the winner goes on to the next round.

The pitches don’t need to be great works of art: the short timescale of the competition is a strong disincentive against going to too much effort. A short video, or a text of under 1,000 words with a couple of images, has done well in the past. Long essays have not historically done well.

What I really enjoy about the competition is meeting new fun maths people, and seeing

the creativity in the pitches. I’ve deliberately left the brief quite broad: I’ll take pitches in any format that can go in a blog post, and on any topic that could charitably be described as mathematical.

Previous participants include stand-up mathematician Matt Parker, Grant Sanderson of 3blue1brown, Marianne Freiberger and Rachel Thomas of Plus! magazine, ubiquitous maths communicator Katie Steckles, and World’s Most Interesting Mathematicians 2018 and 2019, Prof Nira Chamberlain OBE and Dr Sophie Carr.

This is the fourth time the Math-Off has run (we didn’t name a Most Interesting Mathematician in 2020).

You can look at the previous matches in The Math-Off archive.

If you take part, this is what would be required:

- Confirm you’re taking part, by 15th June.
- A one-line bio about you and a photo or other pictorial representation of you, to go with each pitch.
- Between 1 and 4 pitches, depending on how far through the tournament you get, delivered to me 24 hours before the start of the match.
- There will be at least 5 days between the start of each round. Results will be announced 24 hours after the start of each match, leaving 3 days to make the next pitch.
- The first match will start on Monday July 1st, with the final on July 23rd.
- If you win, I’d like to send you a trophy. If you don’t win, I can send a participation medal if you’d like one, along with other fun maths stuff.

If that sounds like something you’d like to take part in, please email me at root@aperiodical.com.

## Previous pitches

A few people have asked for a list of maths covered in previous pitches. Here you go!

Year | Name of entrant | Title | Short description |

2020 | James Arthur | Cleaving Cats | the Arnold Cat map – a chaotic transformation that eventually gives the same thing back |

Andrew Stacey | Absolutely Marvellous | The function whose plot looks like batman | |

Pat Ashforth | Tilting at Windmills | Pinwheel patterns | |

James Munro | The Eggbox Puzzle | Three eggs in a line with six spaces. How to visit every possible position, by moving one egg one space at a time? | |

Katie Severn | Infinity | The uncountability of the reals | |

Brad Ashley | Counting on your hands | Different ways of counting on your hands, in different bases | |

Christian Lawson-Perfect | Fusible Numbers | What times can you measure using fuses? | |

Pat Ashforth | Counting pane | Representing prime factorisations graphically | |

Sam Shah | Self-graphing functions | Tupper’s self-referential formula | |

Zoe Griffiths | What’s wrong with Geistes Blitz (Ghost Blitz)? | Geistes Blitz doesn’t get the combinatorics right | |

Kyle D Evans | A Curious Auction | Game theory of an auction where everyone pays, not just the highest bid | |

CreativeCrocheter | Crocheting Symmetries | Making symmetric patterns in crochet | |

James Arthur | Lesser Spotted Functional Equations | How to solve an equation involving an unknown function | |

Emma Bell | A beautiful cuboid puzzle | Given the pairwise products of the lengths of a cuboid’s side, what’s its volume? | |

Sam Hartburn | Phi (Where’d You Come From?) | A poem about finding phi in a pentagon | |

Tom Edgar | Complementary Sequences | Rayleigh’s theorem: floor and ceil of integer multiples of an irrational number partition the natural numbers | |

Ian Stephenson | Why your projects are always late | The difference between the mean and the mode | |

Andrew Stacey | Keep Them Shutters Rollin’ | Patterns that a camera’s rolling shutter can make | |

Sam Hartburn & Lucy Rycroft-Smith | No-one is Going Anywhere | Zeno’s paradox | |

Zeno Rogue | Truly Self-Referential Formula | Tupper’s self-referential formula | |

Pat Ashforth | Maths or Art? | Curves of pursuit | |

Peter Rowlett | Quarto games of different sizes | How many pieces would you need for a bigger game of Quarto? | |

Nikki Rohlfing | The Phoenix Number | 142857 is a cyclic number | |

Matthew Scroggs | Interesting Tautologies | Logical tautologies, and how his bot generates them | |

Colin Beveridge | Binet’s formula | Binet’s formula to calculate the Nth fibonacci number | |

Colin Beveridge | Conway’s Circle, A Proof without words | ||

Christian Lawson-Perfect | Interesting Esoterica | The site collecting all sorts of maths papers | |

Christian Lawson-Perfect | Putting coins in order | How many moves does it take to sort a list by swapping two items at a time? | |

Pat Ashforth | Dragon Curves | The Dragon curve | |

Alex Cutbill | Difference of two squares | A geometric proof of the difference of two squares identity | |

Peter Kagey | Counting Stacks | How many different ways of stacking N Lego pieces are there? | |

Colin Beveridge | The Young Rowlett’s Robot Caterpillar | How many different ways of putting together the bits of a robot caterpillar are there? | |

Andrew Stacey | What’s the time, Mister Wolf? | Working out the exact time from two clocks, each of which gives different information | |

Peter Rowlett | Art Gallery Problems | How many guards do you need to be have every point of a polygon visible to at least one guard? | |

Will Barrass Hemmens | The Simplex Family and Empty Space | Simplexes: counting vertices, faces, edges, etc | |

Alex Corner | The Sofa Moving Problem | What’s the biggest shape you can fit past a right-angled corner in a corridor? | |

Matthew Scroggs | A surprising fact about quadrilaterals | if you take any quadrilateral and join the midpoints of its sides, then you will form a parallelogram | |

Vicky Neale | The Big Lock-Down Math-Off 2020 Even More Unofficial Offline Hedgehog Sticker Book | Arranging swaps of stickers, similar to kidney exchange chains | |

Nikki Rohlfing | Star Polygons | Different ways of drawing polygons that look like stars | |

Mark Cloud | Stuck In Another World: A Problem in a Non-Euclidean Space | The taxicab metric | |

Peter Rowlett | Ox blocks | About the game “Ox Blocks” | |

Peter Rowlett | Moving on a strange diagonal | The puzzle asking how to draw six straight lines through a 4×4 grid of dots, going through each dot once | |

Fergus Powell | Have a little patience | How often should you expect to win the solitaire game “Clock”? | |

Martin Harris | Double Dobble | A set of Dobble cards with the property that each pair of cards shares two symbols | |

James Tanton | Tie folding and a link to Artin’s conjecture | What fractions can you easily make by folding a tie? | |

Pat Ashforth | Thoughts | Thoughts about becoming a mathematician | |

Clare Wallace | A Princess Problem | The sleeping beauty probability problem | |

Karen Campe | Easy Angles | What angles can you easily make by folding a piece of paper? | |

Tom Briggs | Venus Transits and the Size of the Solar System | How you use Kepler’s laws and parallax to work out how far away Venus is | |

Nikki Rohlfing | Mathematical card trick | The “guess your number” trick using binary representation | |

Colin Beveridge | The Miracle Sudoku | How a really hard sudoku was solved by CrackingTheCryptic | |

CreativeCrocheter | Three Geometries in Crochet | Crocheting Euclidean, hyperbolic and spherical surfaces | |

2019 | Sam Shah | Round 5 | A grid coloured so that no rectangle has the same colour at all four corners |

Sophie Carr | Testing for pregnancy | Applying Bayes’ theorem to pregnancy tests | |

Sophie Carr | Simpson’s paradox | Simpson’s paradox | |

Becky Warren | My favourite rep-tile | The L rep-tile | |

Lucy Rycroft-Smith | Your maths is on fire | ??? | |

Sam Shah | Round 4 | The law of small numbers – when patterns don’t continue as you expect | |

Colin Beveridge | My favourite shape | The icosidodecahedron | |

Becky Warren | Summing consecutive numbers | Geometric proof about triangular numbers | |

Vicky Neale | Prime scarves | Knitted scarves showing numbers mod 6 and 7, noting where primes are | |

Sophie Carr | Bayes’ theorem | The Monty Hall problem | |

Marianne Freiberger and Rachel Thomas | GPS, geometry and relativity | How GPS works | |

Jorge Nuno Silva | Older than pi | The history of calculating the area of a circle | |

Alex Corner | Tantrix | A link between Tantrix tiles and siteswap notation for juggling, through permutations and braids | |

Grant Sanderson | Primes and e | Near the number e^10, which is about 22,026, the density of primes is about 1 in 10. | |

Colin Beveridge | Left as an Exercise: Pascal’s Triangle | Negative rows of Pascal’s triangle | |

Anna Haensch | Piece of cake! | the Lazy Caterer’s problem, which asks for the maximal number of slices that can be obtained by slicing a tasty round thing a fixed number of times. | |

Vicky Neale | Euclid’s algorithm | Showing Euclid’s algorithm with rectangles | |

Christian Lawson-Perfect | The largest small hexagon | The biggest six-sided shape with diameter 1 | |

Marianne Freiberger and Rachel Thomas | Fourier transforms of images | Some stuff about what you can do with Fourier transforms of images | |

Sam Shah | Geometric surprises! | Plot equally-spaced points on a circle. The product of the lengths of all the chords is a whole number | |

Alex Corner | The wobbly table theorem | You can make a four-legged table stable by rotating it | |

Alaric Stephen | Alaric’s sieve | A sieve for square numbers | |

Kyle D Evans | Fred the lazy frog | Convergent infinite sums | |

Anna Haensch | MENACE | The box of cards that learns to play noughts and crosses | |

Jim Propp | Calculus is deeply irrational | The constant value theorem is equivalent to the completeness of the reals | |

Sunil Singh | A Wormhole to Eigenvectors: “Cows” | Cows in the classroom puzzles extend to linear algebra | |

Vincent Pantaloni | The Cantor tartan | A tartan made of two copies of the Cantor set | |

Sam Shah | The unfolding of a magic trick | The Fitch Cheney card trick | |

Lucy Rycroft-Smith | Counting | How do you count on your fingers? What order do you use the fingers? | |

Alaric Stephen | Tournament maths | How do you schedule matches in a tournament so everyone plays someone new each round? | |

Kyle D Evans | T-shirts of Hanoi | The towers of hanoi puzzle with t-shirts | |

Becky Warren | Reflecting circles | Reflecting points and lines in circles, in GeoGebra | |

Jim Propp | The sphere packing problem | What’s the most efficient packing of spheres in space? | |

Sophie Carr | Navier-Stokes | Appreciating the Navier-Stokes equation | |

Vincent Pantaloni | A cone, a sphere and a cylinder | Archimedes’ theorem that a cone and a sphere together have the same volume as a cylinder with the same diameter | |

Jorge Nuno Silva | Latin Erdős | A game involving Latin squares | |

Lucy Rycroft-Smith | Object graphs | Making graphs with physical objects | |

Grant Sanderson | Understanding e to the i pi in 3.14 minutes | Explaining Euler’s formula | |

Becky Warren | Sonobe shapes | Making polyhedra from Sonobe origami units | |

Anna Haensch | How to Become an Oligarch | Modelling accumulation of wealth with a Boltzmann equation | |

Sophie Carr | Bernoulli’s equation | Appreciating Bernoulli’s equation | |

Sunil Singh | The Correct Algebra Behind Mathematical Incorrectness | Incorrect maths moves that give the right answer | |

Jorge Nuno Silva | The roots of perfection | Perfect numbers | |

Sam Shah | What are the odds?! | The 100 prisoners problem with keys in lockers | |

Grant Sanderson | Keep/kill/divide | An infinite series for pi | |

Alaric Stephen | Bidding Game | A game where you bet on a biased coin | |

Colin Beveridge | Left as an Exercise: The Sagrada Família | Maths found in the Sagrada Familia | |

Kyle D Evans | Koch snowflake | Appreciating the Koch snowflake | |

Vicky Neale | Patterns and structures | Crocheted multiplication tables | |

Jim Propp | The Muffin Curse | find the way to divide 24 muffins among 25 people that makes the smallest piece as large as possible | |

Marianne Freiberger and Rachel Thomas | The Sydney Opera House | The sydney opera house is made of parts of a sphere | |

Vincent Pantaloni | Lines on a torus | If you follow a straight line on a torus, how many times does it loop round before getting back to the start? | |

Alex Corner | Coya’s Law: A Curious Operation | $x^{\ln y} = y^{\ln x}$ | |

Lucy Rycroft-Smith | Wet bias | What does X% chance of rain mean? | |

2018 | Nira Chamberlain | Mathematical modelling | Nira’s favourite mathematical models he’s worked on |

Matt Parker | Naively adding fractions | (a+c)/(b+d) is between a/b and c/d | |

Edmund Harriss | Touching Calculus, the mathematics of curvature | Curvahedra | |

Matt Parker | Pathological voting | Pathological cases in alternate voting systems | |

Nira Chamberlain | Schelling’s model | Schelling’s model produces segregation | |

Zoe Griffiths | The ‘phantom’ parabola | The parabola of solutions to a quadratic equation with no real solutions lies in the imaginary plane | |

Matt Parker | The projective plane | How to construct the projective plane | |

Jo Morgan | the Klein bottle | the Klein bottle | |

Evelyn Lamb | Sphere packing in 8 and 24 dimensions | Sphere packing in 8 and 24 dimensions | |

Zoe Griffiths | Benford Needs YOU! | Benford’s law about leading digits | |

Paul Taylor | Non-transitive dice and Non-non-transitive dice | Transitive dice made from rock-paper-scissors symbols | |

Edmund Harriss | The Collatz sequence | Showing the Collatz sequence graphically | |

Nira Chamberlain | Black heroes of mathematics | Black heroes of mathematics | |

Alison Kiddle | Ebert’s hat problem | A hat problem where you can maximise your probability of winning | |

Jo Morgan | Hexaflexagons | Hexaflexagons | |

Tony Mann | The secrets of the universe in random numbers | Finding/Encoding information in random numbers | |

Jim Propp | The mystery of the vanishing rope trick | Two knots on a rope can’t cancel each other out | |

Zoe Griffiths | The aeroplane seating problem | People getting on a plane sit in random seats if theirs isn’t available. What’s the chance the last person sits in the right seat? | |

Matt Parker | Machine Learning with Beads in Matchboxes | MENACE | |

Matthew Scroggs | Mathsteroids | Asteroids on different manifolds | |

Tiago Hirth | Non-abelian Borromean rings | Applying the picture hanging problem to borromean rings | |

Evelyn Lamb | The Wallis sieve | A fractal like a square Sierpinski gasket | |

Edmund Harriss | Penrose tiles | Penrose tiles | |

Colin Wright | 13 piles of 4 cards | Put cards into 13 piles. Can you pick one card from each pile to go on top so each pile has a different card on top? | |

Peter Rowlett | Parabolic curves | The thing where you make a parabola by joining evenly-spaced points of two axes with straight lines | |

Alison Kiddle | Haga’s theorem | How to divide a square into thirds by folding | |

Samuel Hansen | Your friends have more friends than you do | The network-theoretic fact that on average your friends have more friends than you do | |

Paul Taylor | How to really know Pythagoras’ theorem is true | For Pythagoras’ theorem, you can put any shape on the sides, not just squares. If you use the triangle you started with, you get a visual proof of the theorem. | |

James Tanton | Infinite Cake, Anyone? | The trick where you cut and rearrange a cake and it looks like you gain some area | |

Nira Chamberlain | The Reynolds Equation in Formula 1 | An application of the Reynolds equation |