There are 16 NRICH Mathematical resources connected to Inequalities, you may find related items under Algebraic expressions, equations and formulae.Broad Topics > Algebraic expressions, equations and formulae > Inequalities
Some diagrammatic 'proofs' of algebraic identities and inequalities.
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
The challenge is to find the values of the variables if you are to solve this Sudoku.
Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.
Three fences of different lengths form three sides of an enclosure. What arrangement maximises the area?
Kyle and his teacher disagree about his test score - who is right?
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
A bag contains 12 marbles. There are more red than green but green and blue together exceed the reds. The total of yellow and green marbles is more than the total of red and blue. How many of. . . .
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
What fractions can you find between the square roots of 65 and 67?
Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to. . . .