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#### Resources tagged with Rotations similar to Quaternions and Reflections:

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### There are 34 results

Broad Topics > Transformations and their Properties > Rotations

### Quaternions and Rotations

##### Stage: 5 Challenge Level:

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

### Rots and Refs

##### Stage: 5 Challenge Level:

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

### Stereoisomers

##### Stage: 5 Challenge Level:

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

### In a Spin

##### Stage: 4 Challenge Level:

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

### Attractive Tablecloths

##### Stage: 4 Challenge Level:

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?

### 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.

### Twizzle Arithmetic

##### Stage: 4 Challenge Level:

Arrow arithmetic, but with a twist.

### Illusion

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

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?

### 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?

### Footprints

##### Stage: 5 Challenge Level:

Make a footprint pattern using only reflections.

### Shuffles

##### Stage: 5 Challenge Level:

An environment for exploring the properties of small groups.

### Rose

##### Stage: 5 Challenge Level:

What groups of transformations map a regular pentagon to itself?

### 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.

### Matrix Meaning

##### Stage: 5 Challenge Level:

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

### Cubic Rotations

##### Stage: 4 Challenge Level:

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?

### Arrow Arithmetic 1

##### Stage: 4 Challenge Level:

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.

### Symmetric Trace

##### Stage: 4 Challenge Level:

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

### A Roll of Patterned Paper

##### Stage: 4 Challenge Level:

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

### Interpenetrating Solids

##### Stage: 5 Challenge Level:

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

### Coke Machine

##### Stage: 4 Challenge Level:

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

### Middle Man

##### Stage: 5 Challenge Level:

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?

### Hand Swap

##### Stage: 4 Challenge Level:

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. . . .

### Cut Cube

##### Stage: 5 Challenge Level:

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

### Thebault's Theorem

##### Stage: 5 Challenge Level:

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?

### Get Cross

##### Stage: 4 Challenge Level:

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?

### Overlaid

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

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

### Rotations Are Not Single Round Here

##### Stage: 4 Challenge Level:

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. . . .

### Napoleon's Theorem

##### Stage: 4 and 5 Challenge Level:

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?

### Complex Rotations

##### Stage: 5 Challenge Level:

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?

### Arrow Arithmetic 3

##### Stage: 4 Challenge Level:

How can you use twizzles to multiply and divide?

### The Matrix

##### Stage: 5 Challenge Level:

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

### Cubic Spin

##### Stage: 5 Challenge Level:

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

### Arrow Arithmetic 2

##### Stage: 4 Challenge Level:

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