Level Runner-up (2024)

The Lighthouse: a beacon of mathematical genius. (the 'why' of shapes)

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For centuries, lighthouses have allowed ships to safely navigate treacherous waters but couldn’t do this without careful calculation. I was lucky to get to climb up the 152 steps to the top of this one. The lighthouse at Ardnamurchan, has a tower height of 35 metres, and a total height above sea level of 55 metres. This height allows the light to be visible for 18 nautical miles, around the curvature of the Earth. Other lighthouses are built to different heights, depending on their situation on cliffs, or near sea-level, and depending on how far away the light needs to reach. This means all lighthouses are different shapes and sizes, although many people think of them as the same sized cylindrical tower.
Shape is also important in the lantern section, with the iconic triangular panes of glass key to performance. These triangles, created using diagonal astragals, are more structurally sound than rectangular panes, and this strength allows the metalwork to be much slimmer. This means it is less likely to create shadow and interrupt the light from the optic. This was a new design introduced by the engineer Alan Stevenson in 1849 and considered so successful that they were retro-fitted to all of his other lighthouses. If you look very closely, you might manage to see the lionhead cast into each astragal junction, which I think might symbolise the strength of this triangular design.
The type of optic seen in this photo is a newer style LED lens. Its ellipsoid shape allows small and efficient LEDs to be magnified into a strong beam of light. Each lighthouse is assigned a flash pattern, which helps sailors to distinguish what lighthouse they can see. The sequence used at Ardnamurchan is a group flash of 2 lights, every 20 seconds.
So, as you can see, mathematical shape is key to the function of a lighthouse and helps to keep seafarers safe.

— Thomas Davies (S2)