2. What is the area enclosed by the stage 2 squareflake? What about the stages 3 and 4 squareflakes?
3. If replacing each line segment on the edge with the zig-zag is […]
Describe the different symmetries. Draw the picture yourself. Draw your own designs using this idea. Can you explain how this 2-dimensional picture appears to show a 3-dimensional object?
You could use paperclip […]
Copy this pattern. You could use toothpicks or paper sticks or draw the pattern on isometric paper (download here).
Make or draw the next 3 patterns in the sequence. How would you explain to someone else on the telephone how to do this when you could not point to the diagram?
The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .
Can you fit them together to make an enlargement of the shape? What is its area?
Can you fit trisquares together to make enlargements of scale factors 3, 4 and 5? What are their areas?
Is it […]
How do you find the coordinates of the centre of square 1 if you know that (0, 3), (3, 4), (4, 1) and (1, 0) are vertices?
What are the coordinates of the centre of the 20th square?
Imagine the sequence of […]
The centre square has the area of 1 (one) square unit.
Draw the diagram. You can download square dotty paper here.
What is […]
Click here to download a sheet so you can cut out your own pieces and try different arrangements.
The first of these examples shows a symmetrical arrangement, the second […]
What are the similarities and differences between the patterns?
Diagram B is unchanged when you rotate […]
A container holds 4 yellow balls, 2 blue balls and a red ball. The balls are identical in all ways except colour. When you shake the container the balls settle into a hexagonal pattern as shown in the diagram.
You win if two blue balls touch.
How many different ways can […]