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