This article explores the links between maths, art and history, and suggests investigations that are enjoyable as well as challenging.

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Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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Join pentagons together edge to edge. Will they form a ring?

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An environment that enables you to investigate tessellations of regular polygons

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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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.

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If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

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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. . . .

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Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

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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. . . .

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. . . .

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Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

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L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

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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. . . .

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. . . .

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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.

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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?