Believe it or not, you have been making pancakes wrong your entire life. Now that I have your attention, I want to talk about pancake packing. Imagine your pan as a large circle and each pancake as a smaller circle that you must fit inside the pan. How could you could maximize the amount of space your pancakes use?
Obviously, the easy answer would be to just pour batter on the entire pan. A full pan pancake will use all the space. As a diagram:
However, you may not want to eat a bunch of gigantic pancakes (also called crepes in my family). Instead, what if you wanted to make 2 or 3 pancakes per pan by making them smaller? How you could position them on the pan to make the best use of space?
For 2 pancakes, the setup looks like this:
Not a very good use of space. Most of you have probably never made just 2 pancakes on the pan (unless you were out of batter) because it just looks so inefficient. See all the wasted space at the top and bottom? The pan is practically begging you to add another pancake somewhere. Instead, you probably make 3 pancakes. And I bet you positioned them like this:
Using some careful math, you can show that the 2 pancake setup uses only 50% of the pan. While the 3 pancake setup uses 64.6% of the pan. That is a big improvement in pan coverage and it probably explains why no one makes only 2 pancakes. But what if you made more?
The best way to position 4 pancakes is like so:
And this uses 68.6% of the pan. Unless you are very mathematically minded, it probably never occurred to you to try and fit more pancakes in the pan. The efficiency gained by trying to squeeze in that 4th pancake only added 4% more coverage. This is hardly worth most people’s effort.
However, there is something very interesting about this 4 pancake setup. It actually beats out the 5 pancake setup!
The above 5 pancakes only cover 68.5% of the pan! And it gets worse with 6:
Now we are only covering 66.7%. See all that wasted space in the middle! 6 pancakes is a terrible way to cook. It is only when we hit the lucky number 7 that we finally have an increase in pan coverage:
Here, we get 77.7% coverage. So technically, if you wanted to maximize the space on your pan making small pancakes, you should make 7 pancakes at a time. However, I think that at this point, the pancakes become too small to make sense from a meal perspective, even if it makes sense from a math perspective.
If you really wanted to go for it, you could pack 61 pancakes on the pan. This gets your coverage up to 81.3% and the image looks quite nice:
However, these pancakes are more like flecks of batter than true food.
To sum it up, you should probably make 4 pancakes instead of 3. Your intuition correctly told you that 3 is more efficient than 2. However, you were fooled into stopping at 3. You should really continue on and perfect your 4 pancake skills. If you have to cook a large batch of say 20 pans of pancakes, your 4 pancake method will be able to do it in only 19 pans. Math just saved you 5 minutes. You’re welcome.
Pictures courtesy of Wikipedia: https://en.wikipedia.org/wiki/Circle_packing_in_a_circle
One of my readers mentioned to me that in Sweden, they often make mini-pancakes. They are called plättar and I am told they are very good. Do you know how many they make per pan?
I guess I shouldn’t have been so quick to write off the 7 configuration as too small to make sense. A very interesting cultural connection!