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