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Resources tagged with Reflections similar to Frieze Patterns in Cast Iron:

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Frieze Patterns in Cast Iron

Stage: 4 and 5

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

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One Reflection Implies Another

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

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. . . .

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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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The Matrix

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

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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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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The Frieze Tree

Stage: 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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Matching Frieze Patterns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.

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Mirror, Mirror...

Stage: 3 Challenge Level: Challenge Level:1

Explore the effect of reflecting in two parallel mirror lines.

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Combining Transformations

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Does changing the order of transformations always/sometimes/never produce the same transformation?

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Plex

Stage: 2, 3, 4 and 5 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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Decoding Transformations

Stage: 3 Challenge Level: Challenge Level:1

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

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Transformation Game

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Why not challenge a friend to play this transformation game?

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Simplifying Transformations

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

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

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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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Surprising Transformations

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

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?

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Reflecting Lines

Stage: 3 Challenge Level: Challenge Level:1

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

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Triangles in a Square

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

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.

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...on the Wall

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the effect of reflecting in two intersecting mirror lines.

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Friezes

Stage: 3

Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?

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A Problem of Time

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

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?

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The Eyeball Theorem

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

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.

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Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Isometrically

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How many unique symmetrical shapes can you make by shading four small triangles?

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Screen Shot

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

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. . . .

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Tricircle

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

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. . . .

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Tablecloth

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

Colour the squares of the square tablecloth so that each square is the same colour as all the symmetrically placed squares and a different colour from the rest of the squares.

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Snookered

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Cushion Ball

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

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?

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The Fire-fighter's Car Keys

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

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 ?.

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Can You Explain Why?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you explain why it is impossible to construct this triangle?

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Orbiting Billiard Balls

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

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