**All Posts Index**

- The Barnsley Fern: Mathematical Art: Using Python programing to create beautiful fractals.
- Galileo’s Inclined Planes: The mathematics that Galileo used to show that velocity in free-fall is independent of mass.
- Finding focus with Archimedes: How we can gain a new understanding of quadratics by constructing them like the ancient Greeks. Links to lenses and telescopes!
- Finding the average distance between 2 points on a hypercube: An investigation using computer programing and entering higher dimensions.
- Find the average distance between 2 points on a square: A nice investigation using a variety of mathematical techniques.
- Generating e through probability and hypercubes: A remarkable appearance of e in an unexpected setting.
- Have you got a Super Brain? How to solve a tough maths challenge problem with a lots of different approaches.
- IB HL Paper 3 Practice Questions Exam Pack
- 3D Printing: Converting 2D images to 3D: A nice trick to turn Desmos images into 3D graphics.
- Complex Numbers as Matrices: Euler’s Identity: A remarkable result which demonstrates that Euler’s identity still holds in matrix form.
- Sierpinski Triangle: A picture of infinity: How we can use Python to create beautiful fractals.
- Sphere packing problem: Pyramid design: How to pack spheres in a Pyramid case – an investigation.
- Martingale II and Currency Trading: An exploration of the maths behind the Martingale system.
- Time dependent gravity and cosmology! A very tough investigation into what would happen if gravity was not constant.
- The Tusi couple – A circle rolling inside a circle: A beautiful result which creates a lovely piece of mathematical art.
- IB Maths Exploration Guide
- The Martingale system paradox: An exploration into the mathematics behind the Martingale system.
- Projectiles IV: Time dependent gravity! A very tough investigation into what would happen if gravity was not constant.
- Projectile Motion III: Varying gravity What would happen if you did projectile motion on different planets?
- Projectile Motion Investigation II
- Envelope of projectile motion: An extension to the standard projectile motion investigations.
- Classical Geometry Puzzle: Finding the Radius: A nice geometrical proof.
- Further investigation of the Mordell Equation : Adventures in number theory.
- The Mordell Equation : Adventures in number theory.
- Can you solve Oxford University’s Interview Question? Modeling the midpoint of a slipping ladder.
- Modelling the spread of Coronavirus (COVID-19) Written when the global cases were in the hundreds!

- Square Triangular Numbers : How many numbers are both square numbers and also triangular?
- Rational Approximations to Irrational Numbers – A 78 Year old Conjecture Proved : Dive into some very high level maths proofs.
- When do 2 squares equal 2 cubes? A nice number theory problem solved in a variety of ways.
- Hollow Cubes and Hypercubes investigation
- Ramanujan’s Taxi Cab and the Sum of 2 Cubes
- Waging war with maths: Hollow squares
- Finding the volume of a rugby ball (or American football)
- The Shoelace Algorithm to find areas of polygons
- Soap Bubbles, Wormholes and Catenoids

- IB Applications and Interpretations SL and HL Resources
- IB Analysis and Approaches SL and HL Resources
- Simulating a Football Season
- The Van Eck Sequence
- Solving maths problems using computers
- Stacking cannonballs – solving maths with code
- Plotting the Mandelbrot Set
- What’s so special about 277777788888899?
- Normal Numbers – and random number generators
- Crack the code to win $65 million?
- Volume optimization of a cuboid
- Projective Geometry
- Narcissistic Numbers
- Quantum universe: Probability.
- Modeling hours of daylight
- The Gini Coefficient – measuring inequality
- Is Intergalactic space travel possible?
- How to avoid a troll – a puzzle
- Zeno’s Paradox – Achilles and the Tortoise
- Fourier Transforms – the most important tool in mathematics?
- Non Euclidean Geometry – An Introduction
- The Telephone Numbers – Graph Theory
- Friendly Numbers, Solitary Numbers, Perfect Numbers
- Ford Circles

- Modelling more Chaos
- Farey Sequences
- Modelling Chaos
- Modelling tides: how does the moon affect the tide?
- Circular Motion: Modelling a Ferris wheel
- The Folium of Descartes
- Project Euler: Coding to Solve Maths Problems
- Spotting Asset Bubbles
- Measuring the Distance to the Stars
- The Remarkable Dirac Delta Function
- The Rise of Bitcoin
- Fun with Functions!
- A geometric proof for the arithmetic and geometric mean
- Euler’s 9 Point Circle
- Log Graphs to Plot Planetary Patterns
- Modeling with springs and weights
- Predicting the UK election using linear regression
- Optimization of area – an investigation
- Cracking ISBN and Credit Card Codes
- Modelling a Nuclear War
- IGCSE Past Paper Revision Videos
- NASA, Aliens and Codes in the Sky
- Sequence Investigation
- Bedford’s Law to catch fraudsters
- IB Standard Level Revision Videos
- Simulating Traffic Jams and Asteroids
- Time Travel and the Speed of Light
- Even Pigeons Can Do Maths
- Maths of Global Warming – Modeling Climate Change
- Make 2017 – A Puzzle
- Finger Ratio Predicts Maths Ability?
- Modelling Radioactive Decay
- Amanda Knox and Bad Maths in Courts
- Does it Pay to be Nice? Game Theory and Evolution
- Graham’s Number – literally big enough to collapse your head into a black hole
- The Cesaro Sum
- The Mathematics of Crime and Terrorism
- The Watson Selection Task – a logical puzzle
- The Si(x) Function
- The Most Difficult Ever HL maths question – Can you understand it?
- P3 Calculus May 2016 – some thoughts
- Why is IB HL Maths so hard
- Could Trump be the next President of America?
- How to Avoid The Troll: A Puzzle
- The Gini Coefficient – Measuring Inequality
- Quantum Mechanics – Statistical Universe
- Projective Geometry
- Crack the Beale Papers and find a $65 Million buried treasure?
- Bullet Projectile Motion Experiment
- The Monkey and the Hunter – How to Shoot a Monkey
- Alan Turing Cryptography Competition

Galileo: Throwing cannonballs off The Leaning Tower of Pisa

The Coastline Paradox and Fractional Dimensions

How to Win at Rock, Paper, Scissors

The One Time Pad – An Uncrackable Code?

Plotting Stewie Griffin from Family Guy

Modeling Volcanoes – When will they erupt?

Mandelbrot and Julia Sets – Pictures of Infinity

Reaction times – How fast are you?

Tetrahedral Numbers – Stacking Cannonballs

Surviving the Zombie Apocalypse

Analytic Continuation and the Riemann Zeta Function

Murder in the Maths Department

The Poincare Conjecture and Grigori Perelman

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

Non Euclidean Geometry – An Introduction

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.

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.

Graham’s Number – literally big enough to collapse your head into a black hole An unimaginably big number – warning, thinking about this number could be fatal!

Maths Podcasts Some links to great maths podcasts.

Fun Maths KS3 and GCSE Quizzes A link to TES resources for free downloads of quizzes.

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.

Maths Pictionary A link to a great download.

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.

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