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Can You Find a Perfect Number?
Can you find any perfect numbers? Read this article to find out more...
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.
Going Places with Mathematicians
This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping things.
Friezes
Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?
All Is Number
Read all about Pythagoras' mathematical discoveries in this article written for students.
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.
Got It! Article
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
History of Measurement
This article tells you all about some early ways of measuring as well as methods of measuring tall objects we can still use today. You can even have a go at some yourself!
Pythagoras
Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.
Liethagoras' Theorem
Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.
A-maze-ing
Did you know that ancient traditional mazes often tell a story? Remembering the story helps you to draw the maze.
An Introduction to Magic Squares
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
Algebra from Geometry
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
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.
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.
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.
Truth Tables and Electronic Circuits
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
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.
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.
Bands and Bridges: Bringing Topology Back
Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.
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?
Shuffles Tutorials
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
The 1999 Cricket World Cup: A Simulation Game for the Classroom
This article describes a simulation which can be played out in the classroom.
Divisibility Tests
Tim Rowland takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
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.
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.
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.
Zooming in on the Squares
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
An Investigation Based on Score
Class 2YP from Madras College was inspired by the problem in NRICH to work out in how many ways the number 1999 could be expressed as the sum of 3 odd numbers, and this is their solution.
Ways of Summing Odd Numbers
Sanjay Joshi, age 17, The Perse Boys School, Cambridge followed up the Madrass College class 2YP article with more thoughts on the problem of the number of ways of expressing an integer as the sum of odd numbers.
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.
The Codabar Check
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.
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
Volume of a Pyramid and a Cone
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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.
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.
Go Forth and Generalise
This article begins to look at what it means to generalise and the importance of looking beyond spotting patterns to understanding why the patterns are there.
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.
Mathematical Patchwork
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
On Time?
This article for students explains how Greenwich Mean Time was established and in fact, why Greenwich in London was chosen as the standard.
History of Fractions
Who first used fractions? Were they always written in the same way? How did fractions reach us here? These are the sorts of questions which this article will answer for you.
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.
History of Money
If you would like a new CD you would probably go into a shop and buy one using coins or notes. (You might need to do a bit of saving first!) However, this way of paying for the things you want did not always exist. Find out more ...
Logic
What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.
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?
The Dangerous Ratio or to Be Male Is Odd
This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.
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.
Grouping Transformations
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
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.
Back to the Practical?
In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain why the pattern occurs.
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.
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.
Circles, Circles Everywhere
This article for pupils gives some examples of how circles have featured in people's lives for centuries.
Shaping the Universe I - Planet Earth
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.
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.
Maths in the Victorian Classroom
What was it like to learn maths at school in the Victorian period? We visited the British Schools Museum in Hitchin to find out.
Plaiting and Braiding
This article for students gives some instructions about how to make some different braids.
Celtic Knotwork Patterns
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Drawing Doodles and Naming Knots
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
How Many Elements Are There in the Cantor Set?
This article gives a proof of the uncountability of the Cantor set.
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
