What does math taste like? Andrea Hawksley recently posted a recipe for Fibonacci lemonade, a drink that is inspired by the famous Fibonacci sequence: 1,1,2,3,5,8, and so on. It is a thing of beauty to behold, and as you drink it, you actually taste successive approximations of the golden ratio due to the relationship between the ratio and the sequence.

Her post got me thinking about other mathematical food. Of course, we’re talking here about food whose flavor, and not just shape, actually has something to do with math. (For food that *looks* like math, check out this post from last year.) Cooking is all about ratios (there’s even a cookbook called Ratio), so my recipe is mathematical because of the ratios of ingredients. In this case, I based the ratios on good old *e*.

The number *e* pops up all over the place in mathematics. It is the best base for exponential functions in calculus because the function e^{x} has itself as a derivative. In middle or high school, you probably ran into it in the formula Pe^{rt}, which describes how much money you have in an account with continuously compounding interest. And *e* has a cute expression as an infinite sum: *e*=1+1+^{1}⁄_{2}+^{1}⁄_{6}+^{1}⁄_{24} and so on. More clearly:

(Recall that n!, pronounced "n factorial," is n×n-1×n-2×...×1. So 1! is 1, 2! is 2, 3! is 6, and so on. By convention, 0! is defined to be 1.) To create a recipe based on the number *e*, I tried to think about the basic ratios in some common recipes. Pound cake is 1:1:1:1 (eggs:flour:sugar:fat), which wouldn’t do. A basic cookie ratio is 3:2:1 (flour:fat:sugar), also a bust. Pizza dough wouldn't work either. I gave up on baked goods and turned my attention to salads and salad dressings.

3:1 is the canonical ratio for oil to vinegar in a salad dressing, but I prefer mine tangier. 2:1 is just about perfect for me. 1 and ^{1}⁄_{2} are two terms in the series expression for *e*, so I was on the right path. Of course, mustard is excellent in salad dressings, and I use about ^{1}⁄_{3} of the amount of vinegar. So the oil:vinegar:mustard ratio is about 1:^{1}⁄_{2}:^{1}⁄_{6}. Ignoring the first 1 in the series expression for *e*, we’re doing pretty well. Instead of fighting it, I decided that the dressing *wanted* to be based on *e-1* rather than *e*. After the first few ingredients, the amounts get pretty small, but feel free to keep adding tiny amounts of other ingredients to approximate *e-1* as closely as you want. Perhaps you think the dressing needs ^{1}⁄_{21} of a gram of onion powder and ^{1}⁄_{168} of a gram of saffron. Go for it!

“e-1” dressing

*As written, this makes approximately 1.718 cups of dressing, enough for quite a few salads. The important thing is the ratios, so you don't have to start with a cup of oil. Any starting volume will do. The dressing will keep indefinitely in the refrigerator.*

1 cup extra-virgin olive oil

1/2 cup red wine or sherry vinegar

1/6 cup, or 2 2/3 tbsp, prepared dijon mustard

1/24 cup, or 2 tsp, dried oregano

1/120 cup, or about 2 grams, ground black pepper

1/720 cup, or 1/3 gram, or 2 pinches, sugar

Mix all ingredients together. Shake over salad of your choice.

Full disclosure: I am traveling all summer, so I have not had time to make this dressing, but salad dressing is very forgiving, and I’ve made enough of them that I’m pretty sure this one will taste good. If you don't like it, play around with the proportions and ingredients to create a dressing that is based on a different number!

Have you ever made food based on a mathematical constant, sequence, or function? Please share your mathematical cuisine ideas!