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?
An environment that enables you to investigate tessellations of
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. . . .
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. . . .
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. . . .
L triominoes can fit together to make larger versions of
themselves. Is every size possible to make in this way?
Which hexagons tessellate?
If the yellow equilateral triangle is taken as the unit for area,
what size is the hole ?
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?
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.
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Using the interactivity, can you make a regular hexagon from yellow
triangles the same size as a regular hexagon made from green
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. . . .
This article explores the links between maths, art and history, and
suggests investigations that are enjoyable as well as challenging.
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
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. . . .