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# Napoleon's Theorem

You might like to make a tessellation with copies of $\Delta ABC$ and three triangles drawn on the sides of $\Delta ABC$ and prove your conjecture from the tessellation. This uses only elementary geometry. An alternative method is to use the Cosine Rule.

Alternatively you can use vectors or complex numbers.

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### LOGO Challenge 5 - Patch

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### LOGO Challenge - Tilings

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Age 14 to 18

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You might like to make a tessellation with copies of $\Delta ABC$ and three triangles drawn on the sides of $\Delta ABC$ and prove your conjecture from the tessellation. This uses only elementary geometry. An alternative method is to use the Cosine Rule.

Alternatively you can use vectors or complex numbers.

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

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.

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.