What Geometry Is Good For

At some point, everybody who's taken geometry in school has said, "When am I ever going to need geometry?"  The surprising answer: baking.  You really do need to know about degrees and angles and circles and triangles and rectangles (and various other geometric ideas) to bake and construct certain baked goods.  Listen up, class - today's lesson is on checkerboard cakes.

The idea of a checkerboard cake is that when you slice a piece, the inside of the cake isn't just one cake, but two different types arranged in alternating squares, like a chess- or checker-board.  The first time I saw a checkerboard cake, I actually thought that somebody had taken two cakes, sliced them up into little cubes, and then glued each cube into place with frosting.  I suppose you could make a checkerboard cake like this, but it's much easier to use geometry.

The key is to use circles to make the squares.  Hang on, what?  It's just like being in math class all over again.  To make a checkerboard pattern, you need to have the cake colors alternate.  You've got two round cakes and when you slice out a wedge, you want to see interlocking squares.  But the squares are really an optical illusion.  Instead, you cut out circles of cake and stack them so that the colors switch back and forth both horizontally and vertically.  (Or you can buy a pan that separates the rings for you.)

This sounds complicated but it's easy to see when you look at a picture.

A special pan for baking checkerboard cakes.  One color batter goes in the inner and outer rings, and the second color goes in the middle ring.  Swap colors in the next pan, and then stack the cakes vertically.  Cutting out the rings after the cakes are baked lets you skip using the special pans.

To make a two-layer checkerboard cake with six squares, you need two layers of cake where the inner and outer ring are the same color horizontally and a different color vertically.  You can achieve that part by simply stacking up two cakes like you normally would.  To make the middle squares be alternating colors, slice out a ring of cake from the middle, then switch the middle ring of one cake with the other one.  When you look at them horizontally, they make a pattern: Color 1, Color 2, Color 1.  The other layer will have the opposite pattern:  Color 2, Color 1, Color 2.  Then stack the two layers, and each ring will be sitting either on top or below of a ring of different color:

Color 2  Color 1  Color 2
Color 1  Color 2  Color 1

This is how you put together rings to make alternating squares when a wedge is cut.

See?  Geometry at work.