Go on a vector walk and determine which points on the walk are closest to the origin.

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

An environment that enables you to investigate tessellations of regular polygons

Three examples of particular tilings of the plane, namely those where - NOT all corners of the tile are vertices of the tiling. You might like to produce an elegant program to replicate one or all. . . .

are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures. This problem considers the eight semi-regular tessellations which pose a demanding challenge in terms of. . . .

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

A geometry lab crafted in a functional programming language. Ported to Flash from the original java at web.comlab.ox.ac.uk/geomlab