2D shapes and their properties

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Weekly Problem 1 - 2006
The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?

Weekly Problem 45 - 2008
The diagram shows a regular pentagon with two of its diagonals. If all the diagonals are drawn in, into how many areas will the pentagon be divided?

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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.

Weekly Problem 53 - 2007
The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.