Pi in the Kitchen

Happy Pi, Day!

In honor of Pi Day, I'm going to use pi to solve a frequent baker's problem: what size baking pans are equivalent? While actual pie pans have sloping sides, no one bakes a pie crust in a square or straight-sided pan if they can help it, because the crust will get wrinkly. So the problem occurs with straight-sided pans for baking cakes, and with how much filling goes in a pie.

Obviously, if you want the same depth of batter when you change pans for a cake recipe, you need to find a substitute pan with close to the same number of square inches of area. (The amount of frosting also scales something like that, but would vary depending on if you iced the sides of the cake. OR used jam between the layers.) In any case, what we need to start with is the number of square inches per pan type.

First the basic calculations. The area of a circle is π times the radius squared. So:

8 inch round pans have diameter 8, radius 4 so they have 3.14 x 4 x 4 = 50 square inches of area
9 inch round = 63.5 sq. in.
10 inch round = 87.5 sq. in.
8 inch square = 64 sq. in.
9 inch square = 81 sq. in.
9 by 13 inch = 117 sq. in.

Some equivalents:

• An 8 inch square and a 9 inch round are virtually identical.
• A 9 inch square and a 10 inch round are less than 10% apart.
• Two 8 inch squares are very close to a 9 x 13 inch rectangle.

But here's another important consequence of this arithmetic: if you make the right amount of filling for a round pie in one size (8- 9- or 10- inches in diameter), it will be really wrong for a pie only one inch different in diameter. The sloping sides of most pie pans make the difference even worse: a 10 inch pie probably holds close to twice as much filling as an 8 inch pie. The consequence also applies to the amount of pie crust that is needed. Not intuitive, exactly, unless you are one of my many mathematician readers.

Did you wonder why today is Pi Day? Because π = 3.14 and today is March 14. Actually 22 July (22/7) is a better Pi Day as well as being my birthday. I always felt kind of transcendental. And the best Pi Minute will be in a few years at 3/14/15 9:26 AM. I guess the best Pi Day ever would have been back in the Renaissance before sufficiently accurate clocks --

3/14/1592 6:53 AM

Thanks to my whole family for long discussions of this important Day.