Explore the effect of reflecting in two parallel mirror lines.
Explore the effect of combining enlargements.
Sort the frieze patterns into seven pairs according to the way in
which the motif is repeated.
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Does changing the order of transformations always/sometimes/never
produce the same transformation?
See the effects of some combined transformations on a shape. Can
you describe what the individual transformations do?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your. . . .
Why not challenge a friend to play this transformation game?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
These images are taken from the Topkapi Palace in Istanbul, Turkey.
Can you work out the basic unit that makes up each pattern? Can you
continue the pattern? Can you see any similarities and. . . .
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
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?
I took the graph y=4x+7 and performed four transformations. Can you
find the order in which I could have carried out the
Numbers arranged in a square but some exceptional spatial awareness probably needed.
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
Points off a rolling wheel make traces. What makes those traces
Arrow arithmetic, but with a twist.
Introduces the idea of a twizzle to represent number and asks how
one can use this representation to add and subtract geometrically.
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.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
How can you use twizzles to multiply and divide?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
Plex lets you specify a mapping between points and their images.
Then you can draw and see the transformed image.
Explore the two quadratic functions and find out how their graphs