Question

Dear Mitch, 

Tomorrow is Mother's Day and my twin daughters plan to get up early with me to make Mom breakfast in bed.  The girls are both "apples in my eyes" and I'm proud of them.  They're hiding the breakfast tray in their room and have everything else ready in a drawer of the fridge.

So now's where you come in.  What they want to do is make Mom one pancake, a real giant one the size of the skillet.  They plan on writing "# 1 MOM!" on it with strawberry syrup.  My girls are only seven years old, so I don't want to burst their bubble (as they say) but I was wondering if there's some way I can explain with simple math that smaller pancakes'll cook better,  A fellow in the hardware store said I should write to you. (And so here I am on the store's computer.)  He's going to let me know if you have any ideas before the girls start.  

--Best of Health, and Happy Holiday,

Joe in Mississippi

Answer

Dear Joe, 

First, your daughters do sound like perfect apples!

Second, Yes, there are mathematical ideas having to do with circles and what happens to them as they are made bigger or smaller, and these ideas do relate to your question Honestly, you are wise to realize this. (A lot of people never stop to think how math effects so many different parts of life every day (and every night, as well).  

The main idea that you could teach your daughters here is that circles are unique (there's nothing else in the world quite like them). And they are very different from most other shapes in a couple of ways that can become important in cooking.  The first to come to mind is this:  Since the formula for the area of a circle requires you to multiply the radius by itself (which is called "squaring" a number) for each small increase in size (the way children usually determine 'size', which is "how far across" something is) the true size of the circle (its surface area) increases MUCH more than most kids guess. 

(This can be shown by having your daughters take 2 empty containers (or cups or whatever) of the same size, filling them with something disposable, such as thin mud, and having one girl use hers to form a bunch of medium or small circles while her sister makes one giant one.  They will probably be surprised to see how many more (much, much more) medium ones they can make than the one large. 

And in cooking this means a few things:  First, the center of a large circle is further than children usually predict it will be from the circle's edge (For more on this particular topic, see the question of a few months ago in the archived q&a's on this website regarding round tables and the disadvantages and advantages of such a table). 

Anyway, the increased distance to the pancake's center means that if a person likes the taste of a pancake's edge (technically, the circle's 'perimeter' or 'circumference') there will be less of it.  Also, the center which is usually a bit thicker and requires longer cooking will comprise a higher percentage of the pancake, which often results in having to burn its edges. 

Also, if your daughters don't like the way their one pancake comes out, unless they have enough batter and time to try again, they're pretty much stuck with this first effort. 

Finally, if a portion of the one pancake is left uneaten, the sliced remains can be a bit harder to share, and then, later, when compared to a bunch of smaller cakes, a bit harder to preserve as leftovers. 

BUT , that said, on Mother's Day, neither the math nor the quality of the cooking are critical.  What matters is the spirit, and I personally would be reluctant to do or say anything to dampen the girls' excitement.  Whatever kind of pancake(s) they decide to create, will, I am certain, be perfect!!

Happy Mother's Day and Congrats on your Great Family!!, 

Mitch