2D shapes and their properties

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

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.

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

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.

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

See if you can anticipate successive 'generations' of the two animals shown here.

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