# Stage 2 Articles

##### Stage: 2 Challenge Level:

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### A-maze-ing

Did you know that ancient traditional mazes often tell a story? Remembering the story helps you to draw the maze.

### The New Millennium: When Did it Begin?

Not everybody agreed that the Third Millennium actually began on January 1st 2000. Find out why by reading this brief article.

### 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.

### I've Submitted a Solution - What Next?

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

### Clever Carl

What would you do if your teacher asked you add all the numbers from 1 to 100? Find out how Carl Gauss responded when he was asked to do just that.

### 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.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

### A History of Astronomy

Astronomy grew out of problems that the early civilisations had. They needed to solve problems relating to time and distance - both mathematical topics.

### The Moving Planets

Mathematics has always been a powerful tool for studying, measuring and calculating the movements of the planets, and this article gives several examples.

### Measure for Measure

This article, written for students, looks at how some measuring units and devices were developed.

### Eclipses of the Sun

Mathematics has allowed us now to measure lots of things about eclipses and so calculate exactly when they will happen, where they can be seen from, and what they will look like.

### 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.

### On What Day Did it Happen?

Read this article to find out the mathematical method for working out what day of the week each particular date fell on back as far as 1700.

### 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.

### 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.

### 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.

### 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.

### Got It Article

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

### Calendars

Calendars were one of the earliest calculating devices developed by civilizations. Find out about the Mayan calendar in this article.

### From One Shape to Another

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

### 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!

### St Ives

As I was going to St Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks and wives, how many were going to St Ives?

### Fibonacci's Three Wishes 1

First or two articles about Fibonacci, written for students.

### Mathematical Symbols

A brief article written for pupils about mathematical symbols.

### Fibonacci's Three Wishes 2

Second of two articles about Fibonacci, written for students.

### 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.

### 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.

### 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.

### Olympic Measurements

Alan Parr offers some thoughts on various measurements recorded during the Olympic Games. From the accuracy of timing in the pool to the point system in the heptathlon, Alan gives us food for thought.

### Generic Examples: Seeing Through the Particular to the General

Can one example help us to perceive the generality?

### 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?

### 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.

### Sprouts Explained

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.

### Cracking Codes

Jenny Murray describes how she developed her interest in making and breaking codes.

### On Time?

This article 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.

### Maurits Cornelius Escher

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be intertwined.

### Coordinates and Descartes

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.

### 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.

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 Naked Pair in Sudoku

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

### Making Squares

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

### Using Dice Here and There

Bernard's article reminds us of the richness of using dice for number, shape and probability.

### Peg and Pin Boards

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

### Mathematical Ways to Spend Your Summer

Here we look back at the year with NRICH and suggest mathematical summer holiday activities for students, parents and teachers.

### What Is the National Young Mathematicians' Award?

This brief article, written for upper primary students and their teachers, explains what the Young Mathematicians' Award is and links to all the related resources on NRICH.

### Circles, Circles Everywhere

This article for pupils gives some examples of how circles have featured in people's lives for centuries.

### Lucky Numbers

This article for pupils explores what makes numbers special or lucky, and looks at the numbers that are all around us every day.

### 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.

### 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!

### 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?

### Why Do People Find Probability Unintuitive and Difficult?

Uncertain about the likelihood of unexpected events? You are not alone!

### Keeping it Safe and Quiet

Simon Singh describes PKC, its origins, and why the science of code making and breaking is such a secret occupation.

### What Did Turing Do for Us?

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.

### Arrays, Multiplication and Division

This article explores the use of the array to support children's thinking around multiplication and division.