### Cotehele Hall, textiles and maths

I have lots of photos of Cornwall, which I haven't sorted through.

One place I went to, for which we have no photos, was Cotehele Hall. It belongs to the National Trust and photography was banned inside the house: there are numerous extremely large tapestries covering many of the walls. It would have taken many man-years to produce all of them: it took a year for one person (usually a man) to produce one square yard of tapestry. A single tapestry might take several men three-four years to complete.

They had several "Liberal Arts" series tapestries - "Grammar", "Arithmetic" and "Geometry" in different parts of the house.

"Geometry" is of particular interest: it depicts Euclid sitting next to a globe of the Earth, with a lady measuring distance. Of course, the word "geometry" comes from the words for Earth-measurement, so from the prospective of a speaker of Ancient Greek - which included many educated men of the Renaissance - the imagery is apt. However, it is entirely inappropriate for a historian of mathematics.

At the time of the creation of the tapestry, the mathematical subject of geometry was that described in the first books of Euclid's Elements. This is the part of geometry we know call "Euclidean Geometry". It's the geometry we get taught in schools, where the angles in a triangle add up to 180 degrees. However, the geometry of the sphere is different! On a sphere the angles of a triangle don't add up to 180 degrees, and the other axioms of Euclidean geometry don't work either.

In the nineteenth century, mathematicians gained a much wider understanding of geometry. Euclidean geometry is a special case of more general geometries, and depends on the "space" in which it is measured having a constant curvature of zero. The curvature of a sphere is also constant, but it is not zero: it is related to the radius of the sphere. Globes do not conform to Euclidean geometry!

I find this rather amusing.

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