Rational and irrational numbers

There are 24 NRICH Mathematical resources connected to Rational and irrational numbers
Making Rectangles, Making Squares
problem

Making rectangles, making squares

Age
11 to 14
Challenge level
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How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Rational Round
problem

Rational round

Age
16 to 18
Challenge level
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Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
Spirostars
problem

Spirostars

Age
16 to 18
Challenge level
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A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
Impossible square?
problem

Impossible square?

Age
16 to 18
Challenge level
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Can you make a square from these triangles?
Equal Equilateral Triangles
problem

Equal equilateral triangles

Age
14 to 16
Challenge level
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Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?
The Square Hole
problem

The square hole

Age
14 to 16
Challenge level
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If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?
All is Number
article

All is number

Read all about Pythagoras' mathematical discoveries in this article written for students.
The Dangerous Ratio
article

The dangerous ratio

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.
What Are Numbers?
article

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.