The Geometry of Dessert–figs and cake, a story problem

This one is for you, Mr. Frank, my high school algebra and geometry teacher from Freeland High School, 1966-67, 1967-68.  I think you’re out there…

Shown in these photos, pan de higo, a fig and almond cake from Spain. This exotic confection dates back to Muslim rule of Spain (711-1492), when, seeing the plentiful fig crop that was beyond the limits of human consumption, some ingenious Spaniards or Moors decided to squash figs and almonds together in a cake pan or pie plate–a form of some sort. You get the idea. They probably rolled it in fig leaves, set it aside, and let it dry. The result: a thick, dense, sweet, figgy, almondy treat. When you eat it, the seeds go pop! with each bite you take.

We saw giant slabs of pan de higo at one of the local markets the other day, post-Christmas. All the dark chocolate was sold out. What’s a sweet tooth to do?  

We bought a huge chunk of the stuff, betting we would like it. We won that bet. 

Back home, chewing my way through the first couple bites, I started thinking about the geometry of dessert. Certain sweets, like cakes and pies, have a clearly defined geometric shape. Our slab looked quite a bit like a right triangle. How do you figure the area of a right triangle of pan de higo?  I searched my memory for that formula, A = ab/2. But I realized that I was also looking at a circular edge. I was looking at a quarter of a circle.

My teeth got stuck together.  And that was okay.  Fig cake will do that. 

Calculate the area of the circle and multiply it by the height. This pan de higo was 12 inches in diameter…

Suddenly, and with great delight, I was transported back to 10th grade, the fall of 1967, sitting in Mr. Frank’s geometry class. The perennial question in math education, the question disgruntled math students ask themselves is: When am I ever going to use this? I sat next to Les Propp in Mr. Frank’s class. Les asked that question repeatedly. You could see it in his face, in his demeanor. When am I ever going to use this? He would rather have been in town playing pinball at Abe Awad’s restaurant. 

Rick and Tizi go to Cantoro’s market the day after Christmas and buy a quarter of a pan de higo. If the chunk they buy is 6 inches in diameter and 1.5 inches thick, how many cubic inches of pan de higo did Rick and Tizi buy? Show your work.

Sitting on the table right in front of me was… a story problem. 

I know. Who the hell cares about cubic inches of pan de higo? Les Propp wouldn’t care. John Spindler and Linda Conger probably wouldn’t care. Tizi doesn’t care. Just cut her another bite and get on with your life.  Mr. Frank would care, I cared. And celebrated the fact that I remembered how to calculate the area of a circle (A = πr2) and that to determine volume of a cylinder you multiply the area of a circle by height of the cylinder. (A = πr2) * h

A = π*6² = 113 square inches, 

height = 1.5, 

volume = 169.5 cubic inches of pan de higo. 

169.5/4 – 42.39 cubic inches

“Tizi,” I said, “we bought 42.39 cubic inches of pan de higo.”


“I just figured out how much pan de higo we bought.”

“Gee, that’s nice.”

“But there’s more. How much does it weigh per cubic inch?”

“Gee, that’s nice.”  

“Are you even listening to me?”

This conversation did not take place. Tizi, ex-automotive designer, is a highly geometrical girl, but she wouldn’t care a fig about the geometry of dessert. In that respect (and only that respect), she’s a little bit like Doug Propp. 

Thinking about it now, it occurs to me that we need a formula to calculate the amount of pleasure one derives from a dessert. We look at labels. How much sugar? How much salt and fat? How many calories? There ought to be a pleasure quotient. How much pleasure in this can of peas? In this rhubarb pie? In this thin slice of mortadella? In this pan de higo? We could assign a Greek letter to represent the pleasure quotient. Pi is in use. Delta has a job. Theta has been pressed into service.  How about Omricon? The Greek letter Omricon is written like this, capital and lower case: Oo. Oo would be great. And to represent pleasure, let’s add an exclamation mark.  Oo!

The pleasure quotient would be a factor between zero and one, zero being no pleasure at all, one being a state of bliss that renders one unconscious. (We have an Uncle Walter we frequently quote, who said one time eating a dish of cappelletti: “I could kill myself eating these things.” The fact that he could say that meant the pleasure quotient is not 1 Oo!. He would have been dead if the food was a 1 Oo!)  

One person’s pleasure is another person’s poison.  Yes, we’re in a very subjective territory here. But if wine super-tasters can assign a number to a wine (92 Parker points, 93 Wine-Spectator points), then super tasters ought to be able assign an Oo! factor to a dessert. Or to a can of peas.  

I volunteer. This pan de higo weighed in at .9 Oo!   To be really good, to achieve maximum accuracy and reliability at this, I need to assess many tastes of this pan de higo. And look forward to tasting many other pan di higo. The pleasure quotient. Oo!


  1. Sherrie English says:

    I want some of that cake!

  2. marymtf says:

    I’m sure I was one of those disgruntled math students. 🤭 Never thought I’d be saying it about a math related post, but yours was fun and delightful.

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