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#### Resources tagged with Rational and irrational numbers similar to Approximations, Euclid's Algorithm & Continued Fractions:

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### There are 20 results

Broad Topics > Numbers and the Number System > Rational and irrational numbers

### Approximations, Euclid's Algorithm & Continued Fractions

##### Stage: 5

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

### Impossible Square?

##### Stage: 5 Challenge Level:

Can you make a square from these triangles?

### Good Approximations

##### Stage: 5 Challenge Level:

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

### The Square Hole

##### Stage: 4 Challenge Level:

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

### Continued Fractions II

##### Stage: 5

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

### Irrational Arithmagons

##### Stage: 5 Challenge Level:

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

### Proof Sorter - the Square Root of 2 Is Irrational

##### Stage: 5 Challenge Level:

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

### An Introduction to Proof by Contradiction

##### Stage: 4 and 5

An introduction to proof by contradiction, a powerful method of mathematical proof.

### An Introduction to Irrational Numbers

##### Stage: 4 and 5

Tim Rowland introduces irrational numbers

### Be Reasonable

##### Stage: 5 Challenge Level:

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

### Rationals Between...

##### Stage: 4 Challenge Level:

What fractions can you find between the square roots of 65 and 67?

### Equal Equilateral Triangles

##### Stage: 4 Challenge Level:

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

### What Are Numbers?

##### Stage: 2, 3, 4 and 5

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.

### Rational Round

##### Stage: 5 Challenge Level:

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

### The Clue Is in the Question

##### Stage: 5 Challenge Level:

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .

### The Root Cause

##### Stage: 5 Challenge Level:

Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)

### Road Maker 2

##### Stage: 5 Short Challenge Level:

Can you work out where the blue-and-red brick roads end?

### Rational Roots

##### Stage: 5 Challenge Level:

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

### Impossible Triangles?

##### Stage: 5 Challenge Level:

Which of these triangular jigsaws are impossible to finish?

### Spirostars

##### Stage: 5 Challenge Level:

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?