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Resources tagged with Rotations similar to Groups of Sets:

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Broad Topics > Transformations and their Properties > Rotations

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Shuffles

Stage: 5 Challenge Level: Challenge Level:1

An environment for exploring the properties of small groups.

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Zodiac

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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Cubic Rotations

Stage: 4 Challenge Level: Challenge Level:1

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

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The Frieze Tree

Stage: 3 and 4

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

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Overlaid

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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Cubic Spin

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

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In a Spin

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

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Attractive Tablecloths

Stage: 4 Challenge Level: Challenge Level:1

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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A Resource to Support Work on Transformations

Stage: 4 Challenge Level: Challenge Level:1

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

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Coke Machine

Stage: 4 Challenge Level: Challenge Level:1

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly. . . .

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Thebault's Theorem

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

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Paint Rollers for Frieze Patterns.

Stage: 3 and 4

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

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Rose

Stage: 5 Challenge Level: Challenge Level:1

What groups of transformations map a regular pentagon to itself?

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Hand Swap

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

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Garfield's Proof

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

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Twizzle Arithmetic

Stage: 4 Challenge Level: Challenge Level:1

Arrow arithmetic, but with a twist.

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Footprints

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make a footprint pattern using only reflections.

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Matrix Meaning

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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Symmetric Trace

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points off a rolling wheel make traces. What makes those traces have symmetry?

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Illusion

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

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Stereoisomers

Stage: 5 Challenge Level: Challenge Level:1

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.

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A Roll of Patterned Paper

Stage: 4 Challenge Level: Challenge Level:1

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

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Interpenetrating Solids

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!

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Quaternions and Rotations

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

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Plex

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

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Rots and Refs

Stage: 5 Challenge Level: Challenge Level:1

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

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Cut Cube

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the shape and symmetries of the two pieces of this cut cube.

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Middle Man

Stage: 5 Challenge Level: Challenge Level:1

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

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Get Cross

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

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The Matrix

Stage: 5 Challenge Level: Challenge Level:1

Investigate the transfomations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0. -1 and +1.

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Arrow Arithmetic 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

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Arrow Arithmetic 1

Stage: 4 Challenge Level: Challenge Level:1

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

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Napoleon's Theorem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

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Rotations Are Not Single Round Here

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .

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Arrow Arithmetic 3

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How can you use twizzles to multiply and divide?

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Complex Rotations

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?

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Frieze Patterns in Cast Iron

Stage: 3 and 4

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.