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Pi, a Very Special Number
Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.
More on Mazes
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Calendars
Calendars were one of the earliest calculating devices developed by civilisations. Find out about the Mayan calendar in this article.
Leonardo of Pisa and the Golden Rectangle
Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.
Going First
This article shows how abstract thinking and a little number theory throw light on the scoring in Go.
Arclets
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NFRICH website.
Ever Had the Feeling You Are Going Round in Circles
This article teaches you how to draw cardiods, limacons, nephroids and ellipses - a lot easier than they sound! All you need is a pair of compasses and a pencil.
The Secret World of Codes and Code Breaking
When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.
History of Morse
This short article, gives an outline of the origins of Morse code and its inventor and how the frequency of letters is reflected in the code they were given.
Muggles, Logo and Gradients
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
Some Circuits in Graph or Network Theory
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
The Cyclic Quadilateral
This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.
A Knight's Journey
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
Ding Dong Bell
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
The Golden Ratio, Fibonacci Numbers and Continued Fractions.
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
When the Angles of a Triangle Don't Add up to 180 Degrees
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.
Latin Squares
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
What Are Numbers?
Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.
The Frieze Tree
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Logic, Truth Tables and Switching Circuits Challenge
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record your findings.
Truth Tables and Electronic Circuits
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Roasting Old Chestnuts
Mainly for teachers. A discussion and examples of some of the school mathematics of yesteryear.
Tangles
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
Elastic Maths
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Curvature of Surfaces
How do we measure curvature? Find out about curvature on soccer and rugby balls and on surfaces of negative curvature like banana skins.
Continued Fractions I
An article introducing continued fractions with some simple puzzles for the reader.
Divisibility Tests
Tim Rowland takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Pythagorean Triples I
The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it!
Pythagorean Triples II
This is the second article on right-angled triangles whose edge lengths are whole numbers.
Whole Number Dynamics I
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
Euler's Formula and Topology
Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.
Whole Number Dynamics II
This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.
Whole Number Dynamics IV
Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?
Whole Number Dynamics V
The final of five articles which containe the proof of why the sequence introduced in article IV either reaches the fixed point 0 or the sequence enters a repeating cycle of four values.
Geometry and Gravity 1
This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.
Geometry and Gravity 2
This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
Magical Maze - Lecture Summary
An introduction to Ian Stewart's RI Christmas Lectures on Mathematics and Nature with investigations and activities on mathematical patterns in cosmology, music, snowflakes, and flowers, animal movement, probability and risk, and patterns in the regularity and irregularity in nature.
Magic Squares
An account of some magic squares and their properties and and how to construct them for yourself.
Frieze Patterns in Cast Iron
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Picturing Pythagorean Triples
This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.
Impossible Sandwiches
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
Magic Squares for Special Occasions
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Classifying Solids Using Angle Deficiency
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
Cricket Ratings
Like all sports rankings, the cricket ratings involve some maths. In this case, they use a mathematical technique known as exponential weighting. For those who want to know more, read on.
Squareo'scope Determines the Kind of Triangle
A description of some experiments in which you can make discoveries about mathematics.
Mouhefanggai
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
What Is the Circle Scribe Disk Compass?
Introducing a geometrical instrument with 3 basic capabilities.
A Story about Absolutely Nothing
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
Sufficient but Not Necessary: Two Eyes and Seki in Go
The game of go has a simple mechanism. This discussion of the principle of two eyes in go has shown that the game does not depend on equally clear-cut concepts.
Round-robin Scheduling
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
Dancing with Maths
An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?
Paper Folding - Models of the Platonic Solids
A description of how to make the five Platonic solids out of paper.
Sprouts
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with significant food for thought.
Coordinates
Has it ever occurred to you how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.
Adding with the Abacus
Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?
High Jumping
How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...
Where... over There...
This introduction to polar coordinates describes what is an effective way to specify position. This article explains how to convert between polar and cartesian coordinates and also encourages the creation of some attractive curves from some relatively easy equations.
Infinity Is Not a Number - It's a Free Man
Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.
Parallel Parking
Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.
Grouping Transformations
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
The Chinese Remainder Theorem
In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."
Proof by Contradiction
An introduction to proof by contradiction, a powerful method of mathematical proof.
Taking Chances Extended
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
The Naked Pair in Sudoku
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Corresponding Sudokus
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Sums of Powers - A Festive Story
A story for students about adding powers of integers - with a festive twist.
Card Shuffle
This article for students and teachers tries to think about how long would it take someone to create every possible shuffle of a pack of cards, with surprising results.
Student Guide to Getting Started with Rich Tasks
This article gives advice on getting started with exploring rich mathematical tasks.
The Random World
Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.
Shaping the Universe II - the Solar System
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
Shaping the Universe III - to Infinity and Beyond
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Women in Maths
Most stories about the history of maths seem to be about men. Here are some famous women who contributed to the development of modern maths and prepared the way for generations of female mathematicians.
How Many Elements Are There in the Cantor Set?
This article gives a proof of the uncountability of the Cantor set.
Symmetric Tangles
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
A Brief History of Time Measurement
Noticing the regular movement of the Sun and the stars has led to a desire to measure time. This article for teachers and learners looks at the history of man's need to measure things.
From A Random World to a Rational Universe
In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings. So have things changed?
The Four Colour Theorem
The Four Colour Conjecture was first stated just over 150 years ago, and finally proved conclusively in 1976. It is an outstanding example of how old ideas can be combined with new discoveries. prove a mathematical theorem.
Geometry: A History from Practice to Abstraction
This article for students and teachers gives a brief history of the development of Geometry.
Stretching Fractions: A Discussion
This article extends and investigates the ideas in the problem "Stretching Fractions".
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