Paper Thin Stone Walls
The last time I visited King's College Chapel Cambridge I noticed a small poster which talked about the construction. It turns out that just before they built it they discovered an innovation which allowed them to use much less masonry. The poster said that if you build an arch such that it is possible to draw a catenary between the inside and outside wall, then the arch will be stable. This discovery meant that they could make the walls of King's College Chapel as thin as they wanted, subject to their ability to measure accurately. This got me thinking. Why should that be? Then I realised that it all has to do with the name: catenary . A catenary is a hyperbolic cosine like $cosh(x)$. (Obviously if you stretch or translate along the x or y axes it is still a catenary.) The name comes from catena or "chain", because it is the shape a chain makes if held in two places at the same height. Now imagine a chain being held in that manner. Each link has a w