Go on a vector walk and determine which points on the walk are closest to the origin.
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?
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 the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
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. . . .
If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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.
An environment that enables you to investigate tessellations of regular polygons
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?