MEDIEVAL GEOMETRY IN LIVERPOOL DOCKS

Here is one of Jesse Hartley's lock-keeper's huts that are a common sight in the Liverpool Docks system:

This particular example was restored and moved as part of the Albert Dock refurbishment some years ago.  How very satisfying for me to discover just now, whilst attempting a measured drawing of it, that the octagonal geometry is as perfectly co-ordinated as the geometry of a medieval church.  Look in my sketch drawing below how the ground plan; the openings, and the roof profiles are all co-ordinated with great care along a system of interlocking 'octagrams':

...this was a necessary tool in the Middle Ages, when masons didn't have sophisticated calculating techniques at their disposal.  It also enabled them to imbue their buildings with a sense of divinity - they believed that the Universe had been planned on geometrical principles.  
The two west towers of Laon Cathedral in northern France are planned on exactly the same system:

Here is a page from Villard de Honnecourt's sketch book of about 1230 in which he draws a plan of the towers.  I have superimposed the underlying system in red.

But this little building was created by a bluff engineer in the middle of the 19th century for new docks in a rapidly expanding commercial enterprise.  Hartley may not have wanted a 'divine' quality for his buildings, but he was using geometry as a protection against arbitrariness - How deep should the roof overhang be? - let the geometrical system be the decider.