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Resources tagged with Rational and irrational numbers similar to Eyes Down:

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Broad Topics > Numbers and the Number System > Rational and irrational numbers Rationals Between...

Age 14 to 16 Challenge Level:

What fractions can you find between the square roots of 65 and 67? The Clue Is in the Question

Age 16 to 18 Challenge Level:

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself? Impossible Triangles?

Age 16 to 18 Challenge Level:

Which of these triangular jigsaws are impossible to finish? Approximations, Euclid's Algorithm & Continued Fractions

Age 16 to 18

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

Age 16 to 18 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.) Irrational Arithmagons

Age 16 to 18 Challenge Level:

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

Age 16 to 18 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. Age 16 to 18 Short Challenge Level:

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

Age 16 to 18 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. What Are Numbers?

Age 7 to 18

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. Continued Fractions II

Age 16 to 18

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

Age 14 to 18

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

Age 14 to 16 Challenge Level:

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ? An Introduction to Irrational Numbers

Age 14 to 18

Tim Rowland introduces irrational numbers Proof Sorter - the Square Root of 2 Is Irrational

Age 16 to 18 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. Equal Equilateral Triangles

Age 14 to 16 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 ? Be Reasonable

Age 16 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

Can you make a square from these triangles? Good Approximations

Age 16 to 18 Challenge Level:

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

Age 16 to 18 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?