Sunday, January 31, 2010

Breakfast Time Maths Musings

Do you ever think about maths (the Europeans refer to mathematics as “maths” not “math”) while eating breakfast? Normally I don’t as I inhale some caffeine to start my transition to a waking state, but the other morning my thoughts meandered to topology as I was eating an “Everything” bagel. It seems a lot of breakfast foods remind me of common topological shapes and their properties.

Take my bagel for example, it is really just a toroidal shaped piece of bread, or that matter so are a variety breakfast cereals that frequently have “loop” or “O” in their names. Of course there is the spherical “puff” or a random 2-manifold surface, the “flake.” The puffs have the distinction of being perhaps the most dangerous cereal for a toddler to have stuck up her/his nose.

My research shows (through anecdotal experience) that the puff, having the smallest surface area-to-volume ratio, absorbs milk the slowest. Flakes, on the other hand, soak up milk far too quickly and are generally soggy by the time I get to the bottom of the bowl no matter how quickly I eat. A further inconvenience is that due to their flat shape, flakes tend to spatter poured milk out of the bowl and all over anything that happens to be on the table, most likely a preprint research paper in gravitation or cosmology. Whether cereal or milk goes into the bowl first is not up for debate as far as I’m concerned. Milk first? Breakfast heresy.

Finally, there is the torus or “loop” if you choose a more banal moniker. I haven’t crunched the numbers on its surface area-to-volume ratio, either for Froot Loop-sized or Cheerio-sized pieces, but it doesn’t take too large a sample size to realize that loops are superior. They hold milk well due to the center hole, but also maintain a more broadly distributed crunchy center than a puff. I’ve also found that at a typical rate of consumption, the torus maintains a reasonable level of crunchiness until the end of the bowl.

See? Even in the early morning hours as you struggle for consciousness, you can have fun by considering abstract mathematics. Give it a try tomorrow morning!

1 comment:

Thank you for choosing to leave a comment for the Physics Groupie. Much appreciated!