this post was submitted on 19 Jan 2024
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I don't believe that a torus is homeomorphic to a cube, so in fact the stuffed crust is not adequately explained by the cube model. We can approximate the stuffed crust by modelling either as sushi or calzone and receive adequate results.
The sushi model is more robust as it more accurately defines the thermal dynamics of the stuffed crust system. A calzone model includes closed off face, while the faces can be pinched to an infinitesimal point to create a stuffed crust like pizza. Those faces still introduce a thermal graduate to the cheese and won't replicate the results of when we cook our awesome pizza. If instead we permit the sushi model to exist in non-eucludian space we can accurately define a stuffed crust pizza with the sushi model by bending our dimensions. As a result of this the cheese-face interface is better described however it also must exclude the calzone model for describing a stuffed crust pizza.
Thank you for coming to my bullshit TED talk.
I realise that we have thus far only considered the crust as a separate entity, which is of course toroidal (and for which we should evidently add a new form to the model for - I would propose the 'doughnut'), however the full pizza with a stuffed crust is not - it has no hole. By compressing the centre of a calzone until the top and bottom faces meet we reach the full stuffed crust pizza. Perhaps we've been wrong all along...
By George I think you have it! Using radial coordinates and a calzone model a pizza is toast but a stuffed crust pizza is a calzone. How could I have never seen this before?! It's brilliant!