This article explores the links between maths, art and history, and
suggests investigations that are enjoyable as well as challenging.
A triomino is a flat L shape made from 3 square tiles. A chess
board is marked into squares the same size as the tiles and just
one square, anywhere on the board, is coloured red. Can you cover
the. . . .
Using these kite and dart templates, you could try to recreate part
of Penrose's famous tessellation or design one yourself.
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.
Which hexagons tessellate?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
How many different ways can I lay 10 paving slabs, each 2 foot by 1
foot, to make a path 2 foot wide and 10 foot long from my back door
into my garden, without cutting any of the paving slabs?
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. . . .
What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?
What mathematical words can be used to describe this floor
covering? How many different shapes can you see inside this
Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .
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. . . .
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
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?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
Using LOGO, can you construct elegant procedures that will draw
this family of 'floor coverings'?
A geometry lab crafted in a functional programming language. Ported
to Flash from the original java at web.comlab.ox.ac.uk/geomlab
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.
An interactive activity for one to experiment with a tricky tessellation
Can you make these equilateral triangles fit together to cover the
paper without any gaps between them? Can you tessellate isosceles
This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your. . . .
Can you find out how the 6-triangle shape is transformed in these
tessellations? Will the tessellations go on for ever? Why or why
An environment that enables you to investigate tessellations of