All Posts Index

How to Design a Parachute

Galileo: Throwing cannonballs off The Leaning Tower of Pisa

The Coastline Paradox and Fractional Dimensions

How to Win at Rock, Paper, Scissors

Elliptical Curve Cryptography

Elliptical Curves

The One Time Pad – An Uncrackable Code?

Hyperbolic Geometry

Plotting Stewie Griffin from Family Guy

Modeling Volcanoes – When will they erupt?

Arithmetic Sequences Puzzle

Mandelbrot and Julia Sets – Pictures of Infinity

Reaction times – How fast are you?

Are you Psychic?

Medical Data Mining

Tetrahedral Numbers – Stacking Cannonballs

Hailstone Numbers

Stellar Numbers Investigation

Making Music With Sine Waves

Surviving the Zombie Apocalypse

Modelling for Zombies

Maths Puzzles

The Chinese Postman Problem

Analytic Continuation and the Riemann Zeta Function

Murder in the Maths Department

How contagious is Ebola?

The Poincare Conjecture and Grigori Perelman

Batman and Superman Maths

Zeno’s Paradox – Achilles and the Tortoise

Fourier Transforms – the most important tool in mathematics?

Non Euclidean Geometry V – The Shape of the Universe

Non Euclidean Geometry IV – New Universes

Non Euclidean Geometry III – Breakthrough Into New Worlds

Non-Euclidean Geometry II – Attempts to Prove Euclid

The Telephone Numbers – Graph Theory

Friendly Numbers, Solitary Numbers, Perfect Numbers

Using Chi Squared to Crack Codes

Why Do England Always Lose on Penalties? A look at the statistics behind penalty shootouts – how can maths maximise chances of success?

Circular inversions II – A topic which explores how to “reflect in a circle” using Geogebra.

Crypto Analysis to Crack Vigenere Ciphers – Vigenere Ciphers were thought to be unbreakable for centuries.  Here is how to use maths to crack them.

It is Rocket Science – mathematics allows us to find special Lagrange points where satellites remain “suspended” over the same place on Earth.

Championship Wages Predict League Position? – The Championship is one of the  most competitive leagues in the world – does the amount spent on wages help us to predict positions?

NSA Code Breaking Puzzle Number 2 – The US digital spy agency tweets a puzzle to entice future code-breakers to join their agency.

Modelling Infectious Diseases

Understanding how viruses and bacterial infections are spread is an essential part of preventative medicine.  Here’s how it’s done.

Circular Inversion – Reflecting in a Circle The hidden geometry of circular inversion allows us to begin to understand non-Euclidean geometry.

Code Breakers Wanted by the NSA – The US digital spy agency tweets a puzzle to entice future code-breakers to join their agency.

Premier League Wages Predict League Positions?- How strongly correlated is Premier League spending and their league positions?

Graphically Understanding Complex Roots – What does the complex root of a polynomial actually mean?  How can we plot this graphically?

Unbelievable: 1+2+3+4…. = -1/12 ? A result that at first glance looks ridiculous – and yet can be shown to be correct.  How?

Maths Studies IA Exploration Topics  A large number of ideas for investigations and also a large number of secondary data sources to use.

Visualising Algebra Through Geometry- Algebra and geometry normally are quite disconnected at school – but geometry can sometimes help understand algebra.

Fermat’s Theorem on the Sum of two Squares – A lesser known theorem from Fermat – but an excellent introduction to the idea of proof.

A Mathematician’s Lament – A brilliant essay which looks at how maths in currently taught in schools and suggests how it should be taught.

Differential Equations in Real Life – Differential equations are incredibly important in describing reality.  Here you can find out about their uses.

Is Maths Invented or Discovered? – Maths is “unreasonably effective” at describing reality.  Perhaps this is because it is the underlying reality?

Investigation into the Amazing e – e is one of the most important constants in mathematics and physics.  Here’s why.

The Mathematics of Bluffing  – Poker is a very mathematical game.  Here is some of the mathematics behind bluffing.

The Riemann Sphere – The Riemann Sphere is a way of mapping the entire complex plane onto the surface of a 3 dimensional sphere.

Divisibilty Tests and Palindromic Numbers – How do we know which numbers can be divided, and what are palindromic numbers?

Does Sacking a Manager Improve Results? – Football clubs often sack their managers min-season, but does this actually affect their results?

The Chinese Remainder Theorem – This is a method of find the lowest common multiple for numbers.

Steganograph Code, Can You Find the Hidden Message? – Sometimes codes can be hidden in plain site – such as in pictures.  Here is how to decode them.

Maths and Marking – How should marking be done in maths?   What evidence is there of which approach works best?

Mathematical Proof and Paradox – Maths is all about proof – but what happens when we can “prove” something that we know isn’t true?

Game Theory and Tic Tac Toe – Tic Tac Toe has already been solved using Game Theory – this topic also brings in an introduction to Group Theory.

Maths and Chess- Chess and maths are closely related – maybe one day maths may even be able to “solve” chess – ie. know before the first move is made what the outcome will be for an optimal strategy.

Knight’s Tour – This puzzles dates over 1000 years and concerns the ways in which a knight can cover all squares on a chess board.

The Birthday Problem – How many people would need to be in a room to have a 50% chance that 2 people would share a birthday?

War Maths – Projectile Motion – Learn about the maths behind cannon balls and stunt bike jumping.

The Goldbach Conjecture – The Goldbach Conjecture states that every even integer greater than 2 can be expressed as the sum of 2 primes.  No one has ever managed to prove this.

The Gambler’s Fallacy and Casino Maths – Why do casinos always win in the long run, and why a misunderstanding of probability can prove very costly.

Maths and Music – There is a close relationship between maths and music – discover more!

School Code Challenge! Challenge yourself and see if you can crack all the codes to make it onto the leaderboard.

Hexaflexagons – Amazing Shapes Investigation – these remarkable shapes lead to strange and unexpected patterns.

RSA Public Key Encryption – The Code that Secures the internet – An exploration of how public encryption works – using prime numbers.

Crack the Code to Become a Spy – do you have the mathematical skills to become a real life code-breaker?

Maths IA – Exploration Topics A very large list of potential Maths Exploration topics taken from the recently released Pearson’s IB SL and HL series.

Become a Maths Calendar Savant! An exploration of the wonderful world of mathematical savants – people with such remarkable mental abilities that they can calculate the day of the week for any date in history.

Maths Magic – explore the connection between mathematics and magic and learn some some amazing numerical tricks.

The Gorilla in the Room and other Great Maths Investigations – some great ideas for statistics investigations and good links to maths ToK – can we believe our senses?

Are You Living in a Computer Simulation? Nick Bostrom uses logic and probability to make a case about our experience of reality.

Utility Value – How Maths Can Make You Happier. Can understanding utility value help make decisions?

Bridge Building Lesson Plan. A lesson to introduce a practical example of maths and engineering.

Black Swans and Civilisation Collapse. How effective is maths at guiding government policies?

The Riemann Hypothesis Explained. What is the Riemann Hypothesis – and how solving it can win you \$1 million

Sierpinski Triangles and Spirolateral Investigation Lesson Plan. A lesson to introduce the mathematics in art and fractals.

How Are Prime Numbers Distributed? Twin Primes Conjecture. Discussion on studying prime numbers – in particular the conjecture that there are infinitely many twin primes.

Synesthesia – Do Your Numbers Have Colour? What happens when 2 senses get cross-wired in the brain.

Imagining the 4th Dimension. How mathematics can help us explore the notion that there may be more than 3 spatial dimensions.

e’s are good – He’s Leonard Euler. A discussion about the amazing number e.

The Mathematics of Cons – Pyramid Selling. Why exponential growth means that pyramid schemes always collapse.

A Maths Snooker Puzzle. A great little puzzle which tests logic skills.

Maths Invented or Discovered?.  A discussion about some of the basic philosophical questions that arise in mathematics.

Which Times Tables do Students Find Difficult? An Investigation. A study with accompanying graphics.

Cracking Codes Lesson. An example of 2 double period lessons on code breaking

Wau: The Most Amazing Number in the World? A great video by Vi Hart – see if you can spot the twist!

Cracking ISBN and Credit Card Codes. The mathematics behind ISBN codes and credit card codes

NASA, Aliens and Binary Codes from the Stars. A post about how pictures can be transmitted across millions of miles using binary strings.

Benford’s Law – Using Maths to Catch Fraudsters. How mathematics can help solve crimes

Simulations -Traffic Jams and Asteroid Impacts. This allows you to model the consequences of asteroid impacts on Earth.

Time Travel and the Speed of Light How travel near the speed of light can lead to “time travel” to the future.

Even Pigeons Can Do Maths A discussion about the ability of both chimps and pigeons to count

One Direction Maths Song Follow the One Direction lyrics to find the number.

Finger Ratio Predicts Maths Ability? A post which discusses the correlation between the two.

Amanda Knox and Bad Maths in Courts. When misunderstanding mathematics can have huge consequences.

Does it Pay to be Nice? Game Theory and Evolution. How understanding mathematics helps us understand human behaviour

Is God a Mathematician?. A Michio Kaku video which looks at how mathematics can be used to model the universe.

Premier League Finances – Debt and Wages. An investigation into the finances of Premier League clubs.

Why Study Maths? Careers Inspiration Lots of information to help persuade students of the value of mathematics.

Michio Kaku – Universe in a Nutshell A great video from Kaku which covers all the big ideas in physics.

Maths Podcasts Some links to great maths podcasts.

Cesaro Summation: Does 1 – 1 + 1 – 1 … = 1/2?. A post which looks at the maths behind this particularly troublesome series.

Maths Sequence Puzzles IV A quick maths puzzle to test your skills.

Champagne Supernovas and the Birth of the Universe. Some amazing photos from space.

Maths Sequence Puzzle 2 A quick maths puzzle to test your skills.

The Philosophy of Mathematics An introduction to the basic ideas in mathematical philosophy.

IB Maths Worksheets A link to TES resources for some great worksheets for IB.

Langton’s Ant – Order out of Chaos How computer simulations can be used to model life.

Fermat’s Last Theorem An introduction to one of the greatest popular puzzles in maths history.

Wolf Goat Cabbage Space – A Puzzle solved with 3D Geometry How puzzles can be translated into 3 dimensional space.

Maths Sequence Puzzle A quick maths puzzle to test your skills.

The Million Dollar Maths Problems. Some general introductions to the seven million dollar maths problems.

Chaos Theory – An Unpredictable Universe? This discusses the difficulties in mathematical modelling when small changes in initial states can have very large consequences.

Godel’s Ontological “Proof” for God An example of the link between maths, philosophy, logic and theology.

Ramanujan’s Beauty in Mathematics Some of the amazingly beautiful equations of Ramanujan.

Fractals, Mandelbrot and the Koch Snowflake. Using maths to model infinite patterns.