The geometry of baking with Alex Bellos and Evil Mad Scientist Laboratories

Alex Bellos has written some of my* favourite posts at the UK’s Guardian science blogs (for example, my Dec. 18,2012 posting about Bellos’ discussion of the math genius Ramanujan and my Oct. 17, 2012 posting about Bellos’ exploration of mathematics as a spiritual practice in Japan). Earlier this week in a June 26, 2013 posting Bellos wrote about a ‘new craze’, edible mathematics,  in a way that makes me wish I could revisit grade 10 geometry but with a good teacher this time (Note: Links have been removed),

When you slice a cone the surface produced is either a circle, an ellipse, a parabola or a hyperbola.

These curves are known as the conic sections.

And when you slice a scone in the shape of a cone, you get a sconic section – the latest craze in edible mathematics, a vibrant new culinary field.

On their fabulous website, the folk at Evil Mad Scientist provide a step-by-step guide to baking the sconic sections.

Here’s a sconic section image from the June 25, 2013 ‘Sconic sections’ posting by Lenore on the Evil Mad Scientist website,

To highlight the shapes even further, you can color in the cut surfaces with your favorite scone topping. Here, raspberry preserves show off a hyperbolic cut. [downloaded from http://www.evilmadscientist.com/2013/sconic-sections/]

Bellos highlights other edible mathematics projects including Maths on Toast and Dashing Bean but since I’ve always loved Escher I’m going to feature one of the other projects Bellos mentions, George Hart and his Möbius bagel,

After being cut, the two halves can be moved but are still linked together, each passing through

Hart is serious about his Möbius bagel, from the bagel posting (Note: A link has been removed),

It is much more fun to put cream cheese on these bagels than on an ordinary bagel. In additional to
the intellectual stimulation, you get more cream cheese, because there is slightly more surface area.

Topology problem: Modify the cut so the cutting surface is a one-twist Mobius strip.
(You can still get cream cheese into the cut, but it doesn’t separate into two parts.)

Calculus problem: What is the ratio of the surface area of this linked cut
to the surface area of the usual planar bagel slice?

Note: I have had my students do this activity in my Computers and Sculpture class.  It is very successful if the students work in pairs, with two bagels per team.  For the first bagel, I have them draw the indicated lines with a “sharpie”.  Then they can do the second bagel without the lines. (We omit the schmear of cream cheese.) After doing this, one can better appreciate the stone carving of Keizo Ushio, who makes analogous cuts in granite to produce monumental sculpture.

Hope you enjoyed this mathematical ‘amuse-bouche’. If you want more, Bellos has included a few ‘how to’ videos, as well as, other images and links to websites in his posting.

* ‘my’ added to sentence on Aug. 12, 2015.