# Search by Topic

#### Resources tagged with Reflections similar to What's a Group?:

Filter by: Content type:
Stage:
Challenge level:

### There are 27 results

Broad Topics > Transformations and their Properties > Reflections

### Shuffles

##### Stage: 5 Challenge Level:

An environment for exploring the properties of small groups.

### Screen Shot

##### Stage: 4 Challenge Level:

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

### Orbiting Billiard Balls

##### Stage: 4 Challenge Level:

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

### 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?

### 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?

### Snookered

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

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

### A Problem of Time

##### Stage: 4 Challenge Level:

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

### 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.

### Rose

##### Stage: 5 Challenge Level:

What groups of transformations map a regular pentagon to itself?

### Retracircles

##### Stage: 5 Challenge Level:

Four circles all touch each other and a circumscribing circle. Find the ratios of the radii and prove that joining 3 centres gives a 3-4-5 triangle.

### Tricircle

##### Stage: 4 Challenge Level:

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

### The Fire-fighter's Car Keys

##### Stage: 4 Challenge Level:

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

### 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

### Matrix Meaning

##### Stage: 5 Challenge Level:

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

### Surprising Transformations

##### Stage: 4 Challenge Level:

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

### 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.

### Quaternions and Reflections

##### Stage: 5 Challenge Level:

See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes 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.

### 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?

### Reflect Again

##### Stage: 5 Challenge Level:

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

### Two Triangles in a Square

##### Stage: 4 Challenge Level:

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

### Cushion Ball

##### Stage: 5 Challenge Level:

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

### The Eyeball Theorem

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

Two tangents are drawn to the other circle from the centres of a pair of circles. What can you say about the chords cut off by these tangents. Be patient - this problem may be slow to load.

### One Reflection Implies Another

##### Stage: 4 Challenge Level:

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .

### 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. . . .

### 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.

### Footprints

##### Stage: 5 Challenge Level:

Make a footprint pattern using only reflections.