(This post is completely unrelated to the category of cones. Apologies if you were mistakenly directed here by a fuzzy search engine.)
In May 2013, the category theorist Dr Eugenia Cheng (whom you may recognise from her quotations on the Imre Leader Appreciation Society) wrote a paper on the ideal cream tea. This received a lot of media attention, including from the Daily Mail, Telegraph and The Aperiodical (in increasing order of accuracy).
The paper discusses the optimal proportions of cream, strawberry preserve and scone for an ideal cream tea. Unlike most academic papers, this one has an accompanying video:
I was slightly disappointed that there was no category theory in the paper, despite the author being a category theorist. It did, however, explicitly mention that the preserve should be added before the cream, in the style of the Cornish. By comparison, residents of Devon advocate the reversed approach of adding the cream first. The fact that these are genuinely different outcomes can be neatly abstracted into the statement that this diagram in the category of scones does not commute:
The other shortcoming of Eugenia Cheng’s otherwise brilliant paper is that it doesn’t mention that cream teas can be augmented by the addition of a bisected strawberry, as in the image below. The left-hand scone has been prepared using the Devonian order of morphism composition, whereas the right-hand scone has been prepared using the (strictly superior) Cornish method:
Jacob Aron mentioned on Twitter that if the scone has a diameter of 2 centimetres, the clotted cream would need to be infinitely tall, distributed in the form of a Dirac delta function† , where V is the desired volume of cream.
† Disclaimer: This is not a function in the pure-mathematical sense.
There have been other recent examples of gastronomical mathematics in the last year. I presume that you’ve seen the integral banana I posted several months ago. Additionally, Evelyn Lamb has reviewed a multitude of videos involving both mathematics and food, including the culmination of Vi Hart’s flexagon series of videos.
Evident from the construction of the simplest hexaflexagon is that we are dealing with a Möbius strip, which is folded to form a multiple cover of the hexagon. The automorphisms of the Möbius strip (C18) quotiented by the automorphisms of the resulting hexagon (C6) gives the group of flexations (C3).
With three of the strips used to build a hexaflexagon, one can also construct a Boerdijk-Coxeter helix. Twenty cyclic Boerdijk-Coxeter helices of 30 tetrahedra each are obtained by partitioning the 600-cell (a four-dimensional regular polytope) according to a discrete Hopf fibration.