Resources tagged with: Compound transformations
There are 40 NRICH Mathematical resources connected to Compound transformations, you may find related items under Transformations and constructions.
Broad Topics > Transformations and constructions > Compound transformations
Twice as Big?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Who is the fairest of them all ?
Explore the effect of combining enlargements.
...on the Wall
Explore the effect of reflecting in two intersecting mirror lines.
Mirror, Mirror...
Explore the effect of reflecting in two parallel mirror lines.
Transformation Game
Why not challenge a friend to play this transformation game?
Paint Rollers for Frieze Patterns.
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
Which Quadratic?
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.
Square Tangram
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
Grouping Transformations
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
Simplifying Transformations
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
Does changing the order of transformations always/sometimes/never produce the same transformation?
Decoding Transformations
See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?
Mathematical Patchwork
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
Maurits Cornelius Escher
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 intertwined.
Going Places with Mathematicians
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 things.
Squares, Squares and More Squares
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
Matching Frieze Patterns
Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.
Transforming the Letters
What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?
Bow Tie
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.
Reflect Again
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.
Rots and Refs
Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
Transformations Tables
These grids are filled according to some rules - can you complete them?
Trees and Friezes
This problem is based on the idea of building patterns using transformations.
The Use of Mathematics in Computer Games
An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.
The Frieze Tree
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Frieze Patterns in Cast Iron
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Making Rectangles, Making Squares
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
Midpoint Triangle
Can you cut up a square in the way shown and make the pieces into a triangle?
Square to L
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Flight of the Flibbins
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 the new planet?
Triangular Tantaliser
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Counting Triangles
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Squaring the Rectangle
Can you find a way to turn a rectangle into a square?
Screwed-up
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?
2001 Spatial Oddity
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.
Sine Problem
In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
Cut and Make
Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
Cutting Corners
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?