Tag 'food'

Each platonic solid is made using smarties, hot glue, and patience. I used some of the extras to make this scary scary skeleton:

I built this starting from the top with one piece, and following the simple rule that for each layer, put a new piece below the spots where there is exactly one candy corn bottom corner. The process is explained with diagrams in a new page on candy corn.

There are 60 lollipops arranged with icosahedral symmetry, five each of 12 flavours. The first photo shows the whole ball, looking down at one of the 3-fold axes. The bulkiness of the wrappers makes it difficult to see the structure from the outside, but an inside view centered on one of the 5-fold axes reveals that the sticks are carefully arranged.

Each of the twelve pentagons has one of the twelve flavours circling it. I still have a bunch of extra lollipops, so there may be some more lollipolyhedra in the future... but there's so much other Halloween candy to mathematically explore as well!

They've been appended to the end of the fruit polyhedra page in the Mathematical Food Index.

The new page has some new photos and results of a couple fruit-drying experiments, such as slicing the apply from top to bottom, or removing the skin before drying. There is still much work to be done in this delicious field of research; let me know if you have any ideas!

The large roundity of melonness made this easier than carving the apple, and I'd also had more practice! The lack of core also made it easy to carve out the faces to achieve Leonardo-style edible polyhedreality. For now I snuck these photos in at the bottom of the fruit polyhedra page, but I'm considering doing more advanced melon-carving in the future... I also know what I'm doing with my pumpkins this Halloween.

I'm sure there's others of you out there who have, or at least understand, the compulsion to make all five platonic solids once you've made just one. They're currently sitting in the fridge, waiting for the sun to come back out so that I can cut them up some more and take more photos, and then put together a savvy webpage.

In other news, scientific testing of the hyperbolic properties of dried apple slices is progressing. More on that soon.

This observation brings up two very important questions. Firstly, why do apple slices do this? There's some transformation that is turning a flat Euclidean slice into a hyperbolic one. One would think that in the drying process all cells would get uniformly smaller, which would make the whole slice simply shrink into a smaller flat slice. I'm currently conducting some more research to try to gain insights into this process, which will soon turn into a webpage.

Secondly, why is there nothing on the whole googlable internet about this? Is it really that no one has noted this before, despite that we see hyperbolicness every day in dried food such as potato chips? I can begin to answer this by asking why I myself never noticed this before, and by asking why people have in fact noticed the negative curvature of Pringles, which are relatively hyperbolic.

I think the answer lies in that people are not used to the many forms the hyperbolic plane can curl into, when embedded in Euclidean space. I myself didn't see these "wild" hyperbolic planes as what they were until I started playing with, visualizing, and drawing hyperbolic planes in different configurations, and even then it took someone else pointing it out to me, based on one of those unconstrained drawings. People saw it in the Pringle because the Pringle takes a more standard and recognisable saddle-shape, yet missed the connection that Pringles are an idealized version of potato chips, which have similar geometry. This speaks of the value of mathematical art, and collaboration between fields and people.