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Resources tagged with Compound transformations similar to Rotations Are Not Single Round Here:

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Broad Topics > Transformations and constructions > Compound transformations

Frieze Patterns in Cast Iron

Age 11 to 16

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

Paint Rollers for Frieze Patterns.

Age 11 to 16

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

Squaring the Rectangle

Age 14 to 18 Challenge Level:

Can you find a way to turn a rectangle into a square?

Matching Frieze Patterns

Age 11 to 14 Challenge Level:

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

Simplifying Transformations

Age 11 to 14 Challenge Level:

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?

Combining Transformations

Age 11 to 14 Challenge Level:

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

Decoding Transformations

Age 11 to 14 Challenge Level:

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

Age 14 to 18 Challenge Level:

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.

Mirror, Mirror...

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

...on the Wall

Age 11 to 14 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

The Frieze Tree

Age 11 to 16

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

Grouping Transformations

Age 11 to 18

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.

Mathematical Patchwork

Age 7 to 14

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

Transformation Game

Age 11 to 14 Challenge Level:

Why not challenge a friend to play this transformation game?

Making Rectangles, Making Squares

Age 11 to 14 Challenge Level:

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Friezes Using Logo

Age 11 to 14 Challenge Level:

Experimenting with variables and friezes.

Trees and Friezes

Age 11 to 14 Challenge Level:

This problem is based on the idea of building patterns using transformations.

Maurits Cornelius Escher

Age 7 to 14

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .

Going Places with Mathematicians

Age 7 to 14

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .

Chess

Age 11 to 14 Challenge Level:

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

Triangular Tantaliser

Age 11 to 14 Challenge Level:

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Screwed-up

Age 11 to 14 Challenge Level:

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

Bow Tie

Age 11 to 14 Challenge Level:

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Flight of the Flibbins

Age 11 to 14 Challenge Level:

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Squares, Squares and More Squares

Age 11 to 14 Challenge Level:

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Counting Triangles

Age 11 to 14 Challenge Level:

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

2001 Spatial Oddity

Age 11 to 14 Challenge Level:

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Who Is the Fairest of Them All ?

Age 11 to 14 Challenge Level:

Explore the effect of combining enlargements.

Parallel Parking

Age 14 to 16

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.