Going First
This article shows how abstract thinking and a little number theory throw light on the scoring in the game Go.
This article shows how abstract thinking and a little number theory throw light on the scoring in the game Go.
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
Leonardo who?! Well, Leonardo is better known as Fibonacci and this article will tell you some of fascinating things about his famous sequence.
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.
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.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
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.
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.
The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates why they are useful.
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.
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.
Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.
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.
Mainly for teachers. A discussion and examples of some of the school mathematics of yesteryear.
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.
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
An article introducing continued fractions with some simple puzzles for the reader.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Can one example help us to perceive the generality?
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!
This is the second article on right-angled triangles whose edge lengths are whole numbers.
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
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.
In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.
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?
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.
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.
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.
An account of some magic squares and their properties and and how to construct them for yourself.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.
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.
A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.
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.
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.
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.
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
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.
Introducing a geometrical instrument with 3 basic capabilities.
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.
This article explains the use of the idea of connectedness in networks, in two different ways, to bring into focus the basics of the game of Go, namely capture and territory.
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.
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
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?
A description of how to make the five Platonic solids out of paper.
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.
Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.
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?
How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...
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, 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.
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.
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."
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
An introduction to proof by contradiction, a powerful method of mathematical proof.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A story for students about adding powers of integers - with a festive twist.
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.
Here we look back at the year with NRICH and suggest mathematical summer holiday activities for students, parents and teachers.
Need some help getting started with solving and thinking about rich tasks? Read on for some friendly advice.
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.
Weekly challenges are here for NRICH! To celebrate this event, we've collected a set of 20 essential problems for you to try.
Hilbert's Hotel has an infinite number of rooms, and yet, even when it's full, it can still fit more people in!
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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.
This article gives a proof of the uncountability of the Cantor set.
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
Some explanations of basic terms and some phenomena discovered by ancient astronomers
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.
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 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.
This article gives a brief history of the development of Geometry.
This is the first of a two part series of articles on the history of Algebra from about 2000 BCE to about 1000 CE.
This is the second article in a two part series on the history of Algebra from about 2000 BCE to about 1000 CE.
The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.
This article extends and investigates the ideas in the problem "Stretching Fractions".
An introduction to a useful tool to check the validity of an equation.
In this article, we look at solids constructed using symmetries of their faces.
In this article, Rachel Melrose describes what happens when she mixed mathematics with art.
This article explains how tree diagrams are constructed and helps you to understand how they can be used to calculate probabilities.
Uncertain about the likelihood of unexpected events? You are not alone!
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.
We need computer programmers! Logo is a great entry-level programming language - and you can create stunning graphics while you learn.
A introduction to how patterns can be deceiving, and what is and is not a proof.
When making estimates, it is easy to be quite wrong, but it only takes a little thought to be almost right. In this article, we explore a few techniques and methods which will make our estimations better.
Simon Singh describes PKC, its origins, and why the science of code making and breaking is such a secret occupation.
Dr James Grime takes an Enigma machine in to schools. Here he describes how the code-breaking work of Turing and his contemporaries helped to win the war.
How do decisions about scoring affect who wins a combined event such as the decathlon?
