Tessellations
problem
Semi-regular Tessellations
Age
11 to 16
Challenge level
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
problem
Napoleon's Theorem
Age
14 to 18
Challenge level
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?
problem
Shapely Tiling
Age
7 to 11
Challenge level
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?
problem
Bow Tie
Age
11 to 14
Challenge level
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.
problem
Schlafli Tessellations
Age
11 to 18
Challenge level
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 'elegant' LOGO procedures.
problem
LOGO Challenge - Tilings
Age
11 to 16
Challenge level
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 of
these.
problem
LOGO Challenge - Triangles-Squares-Stars
Age
11 to 16
Challenge level
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.
problem
LOGO Challenge 5 - Patch
Age
11 to 16
Challenge level
Using LOGO, can you construct elegant procedures that will draw
this family of 'floor coverings'?