It should come as no surprise that food, chemistry and mathematics meet in baking. For once I will leave the chemistry aside for a while and turn to the mathematical aspects of baking. More precisely I will delve into geometrical problems encountered in baking. When cutting cookies from a rolled out dough or placing cookies on a sheet for baking you actually attempt to solve a mathematical problem known as a packing problem. The purpose is to maximize the distance between the cookies and maximize the size of the cookies, paying attention that the cookies should not touch. Many will perhaps start with a square packing (see below), but soon figure out that a hexagonal packing will fit even more cookies onto the rolled out dough or onto the baking sheet (especially when the dough/sheet is large compared to the cookies). The optimum way of placing 2-17 circles in a square are shown below (and the solution for up to 10.000 circles is also available).

My challenge for you however is a different one as I’m interested in eliminating the leftover dough when cutting cookies. To achieve this the cookies cannot be circular. Using a square cookie cutter (or simply a knife) would be the easiest way to leave no gaps, but how cool are square cookies? What I’m really looking for are cookie tessallations which are aesthetically pleasing, and at the same time transferable to a baking sheet. Oh yeah: a tessallation “is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gap” according to Wikipedia. So – no gaps – no leftover cookie dough!

Should you ever want to place circular cookies on a square baking sheet, this is how to maximize the size of the cookies! (Illustrations CC-BY-SA by Toby Hudson)

This is one way of solving the problem with leftover dough shown in the top picture. A tree can quite easily be transformed into a shape that fills the plane without any gaps. This image was made using the Tess software mentioned below.

Tessellations are frequently encountered in the art of M. C. Escher, and his Regular Division of the Plane Drawings are all based on tessellations. Most of Escher’s drawings however are not useful for making cookies because they are too interlocking – it would be impossible to take the cookies apart and transfer them to the baking sheet (and baking them “interlocked” would not be an option as cookie dough inevitably will raise/expand a little, making everything stick together). But I did find one example of an Escher inspired cookie cutter as well as some other nice examples of cookie cutters especially designed to make tessellations:

Over at Thingiverse the design file for this Escher inspired cookie cutter can be downloaded (Photo by Bas Pijls via Thingiverse). And should you want to transfer your own designs into a 3D printable format, check out this cookie-cutter-generator.

From Cox & Cox you can buy this Jigsaw cookie cutter (Photo from Cox & Cox product page). If you have access to a 3D printer you can also print your own jigsaw cookie cutter.

These elaborate cookie cutters are designed by Keith Kritselis. Over at Kickstarter you can find more information about his special cookie cutters for Halloween and Christmas. What makes them special is that each tessellation is made up of three or four different shapes.

If you rather want to make your own tessellations there are a couple of different software and online apps available, but I’ve found Tess to be one of the best. An evaluation copy of Tess (no save function) can be downloaded for free. Below are a couple of designs I’ve made. The patterns are nice, but would I want to each cookies with these shapes?

And finally the challenge for you all: Make your own cookie tessallations and share it! It’s not a competition, but rather an invitation to contribute. If the design is great I might have it 3D printed on a friends MakerBot or order it in metal from Shapeways and blog about it here If you send me a picture (preferably at least 620 pixels wide/high, email to webmaster/a/khymos.org) I’ll put up a gallery to display the submitted designs.

I thought I’d do a twist on some chocolate cookies my Mom always makes for Christmas for TGRWT #13. I tried two versions with added caraway (and a litte bitter orange peel) – one where I omitted all the spices except cocoa and one where they were added together with all the spices in the original recipes.

Chocolate cookies with caraway
100 g butter
200 g sugar
350 g flour
30 g cocoa powder
3 g caraway
1 g bitter orange peel
1/2 t baking soda or baking powder
1 egg
3 T strong coffee

Mix all ingredients in the given order. If you have a cookie extruder (aka cookie press), extrude about 6-8 cm and form into a circle. Bake for about 10 min at 180 °C or until ready (Note that you really can’t tell if they’re done from the color!). Dust with powdered sugar.

The original recipe had the following spices:
1-1 1/2 t cloves
1-1 1/2 t cinnamon
1-1 1/2 t ginger
1-1 1/2 t star anise
1-1 1/2 t cardamom
1-1 1/2 t nutmeg
1-1 1/2 t bitter orange peel

(these teaspoons are not measuring teaspoons, but more like actual teaspoons!)

Verdict: In the stripped down version with only cocoa, caraway and some bitter lemon peel there you first notice the cocoa, then there is an aftertaste of caraway. I like caraway, so I was very pleased with the result. But my wife (who isn’t very fond of caraway) wasn’t particularily fond of them. Anyhow I think the 10:1 ratio of cocoa to caraway worked very fine. And the aroma brought back memories from the chocolate sauerkraut cake I made some time ago which was really delicious. With all the other spices present I wasn’t able to single out the carawa flavor, but it (probably) added to the overall complexity. I really recommend the recipe – even if you decide to omit caraway!