You may also like

Schlafli Tessellations

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.

Napoleon's Theorem

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?

Polygon Walk

Age 16 to 18
Challenge Level

Draw the triangle pointing right such that the rightmost vertex is at $\mathbf{i}$

The coordinates of a regular $n$-gon with a centred on the origin with a vertex at $(1,0)$ are

$$\left(\cos\left(\frac{2m\pi}{n}\right), \sin\left(\frac{2m\pi}{n}\right)\right)\, \text{ where }m=0, \dots, n-1$$

For a pentagon, the coordinates become
$$
(1, 0), \left(\frac{1}{4}\left(\sqrt{5}-1\right), \frac{1}{4}\left(\sqrt{10+2\sqrt{5}}\right)\right), \left(-\frac{1}{4}\left(\sqrt{5}+1\right), \frac{1}{4}\left(\sqrt{10-2\sqrt{5}}\right)\right)
$$
along with the mirror images in the $x$-axis.

This problem builds on GCSE vector work and provides a foundation for concepts met in the later Core A Level modules.