Oreos, Ratios, and the Perfect Cookie

December 22, 2013 at 9:30 pm 8 comments

Okay, first things first. What do you call the following shape?


I call it a pill. My sons call it a racetrack. But is there a formal name for a shape formed by a rectangle with a semicircle attached to each end? If not, I feel like there should be. Place your suggestions in the Comments.

Until I hear a better suggestion, I’m gonna keep callin’ it a pill.

The following trivia question is the reason I ask.

How many pills appear around the circumference of the trademarked design on an Oreo® cookie?

What’s that, you say? You didn’t know that there were little pills along the edge of each wafer on an Oreo cookie? Then you, my friend, need to pay a little more attention.

Because there aren’t just some pills around the circumference. There are 96 of those little buggers, and each of them has a rectangle with a length-to-width ratio of approximately 3:2 between two semicircles.

See for yourself.

Oreo Design

Ironically, the ratio of 3:2 brings me to the main reason I’m writing today.

The original Oreo represented good design: a single layer of vanilla cream filling trapped between two crisp, chocolate wafers. But it always felt lacking to me. If only it had just a little more cream, then it would be perfect. A potential solution arrived in 1974, when Nabisco released the Double Stuf variety — two chocolate wafers with twice as much filling1 as its predecessor. Yet the Double Stuf teetered too far in the opposite direction. It was too sweet.

Which brings me to the delectable treat that I discovered today: the Triple Double Oreo, which is running a strong campaign for the title of World’s Best Cookie. My wife describes it as “the Big Mac of cookies.” Not two but three chocolate wafers with a thin layer of cream filling between each pair. And the pièce de résistance — one layer of vanilla cream filling, the other chocolate.

Now that’s what I call intelligent design.

Triple Double Oreo

It absolutely nails the ratio for wafer:filling.


Double Stuf

Triple Double









Ratio of W:F




The chart above makes it all clear. The ratio is too high in the original, too low in the Double Stuf, and just right in the Triple Double. Indeed, the Triple Double Oreo is the Little Bear’s porridge of the cookie world.

This reminds me of Reese’s Peanut Butter Cups. While I haven’t quantitatively analyzed the peanut butter to chocolate ratio, qualitatively I would say that the original had a little too much peanut butter, the Big Cup was disgusting with far too much peanut butter, but nirvana was captured with the peanut butter to chocolate ratio in Miniature Reese’s Peanut Butter Cups. (Insert smacking lips sound here.)

So if you read this blog and wonder why I’m so hyper sometimes, now you know. I consume an unholy amount of refined sugar.

1 There is some debate about the actual amount of filling contained in a Double Stuf Oreo cookie. Although a spokesperson for Nabisco claimed that the cookies indeed contain twice as much filling as a regular Oreo, a math class in upstate New York experimentally found that Double Stuf cookies contain only 1.86 times as much cream filling as a regular Oreo. As I generally trust unpaid high school students more than money-grubbing corporate types, I’m using 1.86.

2 The numbers for “filling” are relative to the amount of cream filling in a regular Oreo®.

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8 Comments Add your own

  • 1. Arthur Benjamin  |  December 22, 2013 at 9:40 pm

    Pill congruent to “circtangle”.

    • 2. venneblock  |  December 23, 2013 at 1:44 am

      Thanks, Art! Lots of references to “circtangle” on the web, but I’d never heard it before. Is it your original word?

      • 3. Arthur Benjamin  |  December 23, 2013 at 1:57 am

        Yes, I made up the word.

      • 4. venneblock  |  December 23, 2013 at 9:13 am

        Wow! A magician, a mathematician — and a neologist, too? You’re an amazing man, Art. My favorite made-up word: mega-nega bar. It’s a sniglet from Brad Hall, and it’s the line you write after the written-out amount on a check so the recipient can’t write in “and one million.”

  • 5. xander  |  December 22, 2013 at 11:01 pm

    Fun fact, courtesy of my mother-in-law: Oreo’s are vegan. In case you were interested for any reason.

    • 6. venneblock  |  December 23, 2013 at 1:48 am

      I have no idea why or how… but I already knew that.

      The word vegan has come to be used as an adjective meaning “without animal products of any kind.” But every dictionary considers this word only a noun, referring to people who don’t eat any animal products. Which makes your comment even funnier, Xander: to think that Oreos don’t eat animals!

      • 7. xander  |  December 23, 2013 at 12:26 pm

        Interesting. I guess that either (a) the dictionaries haven’t quite caught up to usage yet or (b) I am one of only a few people who uses the term vegan to mean “compatible with a vegan diet”. Though I rather like the notion of herds of Oreo’s roaming the plains, eating grass and tubers.

  • 8. happyland3000  |  September 26, 2015 at 10:50 am

    I call them “circlangles”


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About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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