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My favourite shape

Helicoid Alex Doak

My favourite shape is the helicoid, as it has many interesting geometric properties. Firstly, it is a ruled surface. The helicoid is constructed by moving a straight line in space; in this case by rotating it about an axis while moving along said axis at a constant speed. Ruled surfaces are very popular in architecture, such as hyperboloid cooling towers and, of course, helicoid staircases. Secondly, it is a minimal surface. In fact, it has been proven that the helicoid, along with the plane, are the only ruled minimal surfaces!

Routes You start at A and are allowed to move either to the right or upwards. How many different routes are there to get from A to B?

Source: Answers at

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spring 2016

Chalkdust, Issue 03  

Popular mathematics magazine from UCL

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