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. . . .
A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.
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.
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 discover whether this is a fair game?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Four jewellers share their stock. Can you work out the relative values of their gems?
This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
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
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.
A huge wheel is rolling past your window. What do you see?
If you think that mathematical proof is really clearcut and
universal then you should read this article.
Which hexagons tessellate?
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.
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
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.
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. . . .
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?
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.
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
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. . . .
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?
Is the mean of the squares of two numbers greater than, or less
than, the square of their means?
Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Find the smallest positive integer N such that N/2 is a perfect
cube, N/3 is a perfect fifth power and N/5 is a perfect seventh
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Can you see how this picture illustrates the formula for the sum of
the first six cube numbers?
The nth term of a sequence is given by the formula n^3 + 11n . Find
the first four terms of the sequence given by this formula and the
first term of the sequence which is bigger than one million. . . .
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
An article which gives an account of some properties of magic squares.
Three points A, B and C lie in this order on a line, and P is any
point in the plane. Use the Cosine Rule to prove the following
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.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Can you rearrange the cards to make a series of correct mathematical statements?
What fractions can you divide the diagonal of a square into by simple folding?
You have twelve weights, one of which is different from the rest.
Using just 3 weighings, can you identify which weight is the odd
one out, and whether it is heavier or lighter than the rest?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Can you find all the 4-ball shuffles?
Can you make sense of these three proofs of Pythagoras' Theorem?
This article stems from research on the teaching of proof and
offers guidance on how to move learners from focussing on
experimental arguments to mathematical arguments and deductive
A introduction to how patterns can be deceiving, and what is and is not a proof.