[math-fun] Roman arches

Q. What do semicircular arches and viruses have in common? A. They both comprise many copies of the same thing. The capsid (coat) of a virus is typically icosahedral or helical, containing many copies of the same proteins in a way that exploits the full automorphism group of these symmetrical shapes. Similarly, a semicircular arch can be constructed from many copies of a single stone, whereas the optimal arches (parabolae, catenaries, cycloids etc.) cannot. This should help to reduce production costs if only a single template is necessary. We must also not forget that this symmetry gives Roman arches (and viruses, I suppose) a particular aesthetic appeal. Sincerely, Adam P. Goucher