Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
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. . . .
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.
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.
Four jewellers share their stock. Can you work out the relative values of their gems?
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.
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.
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
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?
If you think that mathematical proof is really clearcut and universal then you should read this article.
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
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 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.
Can you find the areas of the trapezia in this sequence?
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
Can you rearrange the cards to make a series of correct mathematical statements?
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
An article which gives an account of some properties of magic squares.
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
Can you discover whether this is a fair game?
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?