Saddle up for maximum snack satisfaction (mathematically speaking)
May 21st, 2012
03:30 PM ET
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Stephanie V.W. Lucianovic is a Bay Area writer and editor. Her first book Suffering Succotash: A Picky Eater's Quest to Understand Why We Hate the Foods We Hate, a humorous non-fiction narrative and exposé on the lives of picky eaters, will be released by Perigee Books on July 3.

My husband is a calculus professor and one who brings food items into the classroom with surprising regularity. No, he doesn't bring pies on Pi day - though he can recite the string up to a couple dozen digits - but he does bring Pringles. As a teaching aid.

This afternoon when I walked into his study, I nearly tripped over a plastic Safeway bag filled with six red cans of Pringles. "Is it Pringles Day already?" I asked, nudging the bag. Pringles Day is the day Dr. Mathra lectures on the classification of critical points in multivariable calculus, and he uses the saddle-shaped Pringles to illustrate his points.

After class, the students get to eat his illustrations. It's their favorite day.

However, this Pringles Eve, Dr. Mathra is kicking himself because in addition to stocking up on Pringles, which were invented by Proctor & Gamble & heaven in the 1960s, he also got an oblong can of Lays Stax, the parvenu potato chip that's only been around since 2003.

Personally, I've never been turned on by Lays Stax. Not only are they covered with the stink of being the unoriginal upstart that is so obviously trying to rip-off the adored-for-decades potato chip, but they're not thin and delicate enough, they're not oily enough, and they're not addictive enough. However, none of the above is Dr. Mathra's complaint with them.

"It's ridiculous!" he fumed, "They set themselves up as a Pringles competitor, but it's an entirely different curvature!"

The shape of the Lays Stax - known as a parabolic cylinder - is way less mathematically interesting than the hyperbolic paraboloid of a Pringles, which is also known as a saddle. In math, the Pringles saddle shape exemplifies how you can stand at the flat point of a surface and not be at the highest point of your surroundings or at the lowest point of your surroundings.

Basically, you could call the saddle "the taint" of critical points. T'aint the highest point, t'aint the lowest. "Um, sure. If you wanted to be crass about it," Dr. Mathra mumbles.

The big three types of critical points in multivariable calculus are the bottom of a bowl (aka the local min), the top of a dome (the local max), or in the middle of a saddle (saddle point).

"The Lays Stax shape isn't even as interesting as a bowl - it's a wishy-washy bowl. I mean, you can make the Lays shape with a piece of paper," Dr. Mathra explains. (In my twelve years of being married to him, I have frequently found that being able to make something with paper is met with derision.) See, you can't replicate the Pringles saddle shape with a piece of paper without cutting the paper and actually adding more paper to it and that makes it more mathematically desirable.

Sensing he has my attention throughout all of this raving, Dr. Mathra continues, "They've got these Lays Stax right next to the Pringles as though they are equivalent. How can they do that? One is a positive semi-definite quadratic form and the other is an indefinite quadratic form - they're not even the same definiteness!"

When I don't react, he insists, "Oh, come on - that will KILL in class tomorrow!"

And why should you, the non-calculus student, care about the Pringles saddle form? The principal application of calculus is optimizing, or determining whether you are at a maximum. You use calculus whenever you want to optimize, well, anything. "If you are at a local max (the top of a dome), everywhere you go moves you down. If you're at a saddle, there's a way you can go that will take you up." Knowing this is important when thinking about increasing filthy lucre, precious time, diminishing resources, or a supply of Pringles.

And that, my friends, is why Pringles will always, always beat Lays Stax.

Flavor is subjective. Math is irrefutable.

soundoff (191 Responses)
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    November 28, 2013 at 2:41 am |
  2. restuarant

    Hi, thanks for sharing. restuarant

    April 9, 2013 at 3:30 am |
  3. Taouba

    (Paperback) Gelfand was one of the leaders of the great soohcl of mathematics which, somehow, thrived in Soviet Union. I used uncountable times the copy of our library, as the original English edition, in the excellent translation of R. Silvermann, became very hard to find. I put it in the top of the list of books I wanted to buy. Now Dover put it into their catalogue. Great choice. I already ordered my copy!This is the best book on the Calculus of Variations. It contains, for instance, a wonderful treatment of Noether's theorem, hardly to be surpassed. The Hamilton-Jacobi equation is also treated with brilliance and clarity. Gelfand (and Fomin!) developed a style in which the precision of the mathematics does not interfere with the general panorama. The applications are very well selected and perfectly illustrate the theory. A great book, a great mathematician who can write, a great translator, by less than 10 bucks!

    December 25, 2012 at 8:30 am |
  4. Gene Chase

    I haven't used Pringles in my Calculus. I have distributed fig Newtons and Leibniz biscuits, given that these men founded Calculus. Also appreciated.

    May 23, 2012 at 5:39 pm |
  5. Ruby Blue

    Eww. An otherwise interesting and entertaining article was ruined by a vulgar joke about halfway through. This is an article written for CNN, not a casual conversation for friends (at which point the joke would be more appropriate, assuming you know your audience). Totally unnecessary and unprofessional – you should learn to filter the content and respect your varied audience.

    May 23, 2012 at 12:37 pm |
    • skaai

      if you're referring to ""taint", the context in which it was used was appropriate and not vulgar as the word 'taint is not in itself vulgar, rather, the frequent association with the perineum in the jocular form is what leads dirty-minded folks to assume this innocuous word is guilty by association.... Some terms are perfectly innocuous (i.e., the "Hairy Ball Theorem") and perfectly appropriate for their application, it's the dirty-minded people who misinterpret such terms that ruins things.

      December 12, 2012 at 3:30 pm |
  6. Lou Cypher

    Dr Mathra and Stephanie need to invest in better-quality lubricants.

    May 23, 2012 at 9:54 am |
  7. JohnQPubliqu

    Now I remember why I hated calculus...don't like the parafin taste of Pringles!

    May 23, 2012 at 9:08 am |
  8. Chipoholic

    I love the way Pringles fit on your tongue. It allows the most flavor sensation all at the same time.

    Speaking of chips, the absolute best chip ever made was Mrs. Gibbles Nibbles sour cream flavor. If anyone knows where you can get these let me know. I beilieve they are no longer on the market.

    May 22, 2012 at 8:46 pm |
  9. Keith

    Now I remember why I took Calculus

    May 22, 2012 at 8:05 pm |
  10. Scott2

    This made me hungry. Does that add up?

    May 22, 2012 at 5:00 pm |
  11. FloridaErik

    Claiming a superior potato chip shape under the ruse of mathematics is the t'ain't of journalism.

    May 22, 2012 at 4:18 pm |
  12. chuck

    How do you know the Stax aren't *negative* semidefinite?

    May 22, 2012 at 2:27 pm |
  13. Scott

    ...and all of this just makes me wonder why Pringles Park in Jackson, TN is not shaped like a hyperbolic parabaloid (not even close). Think it's not possible? Check out a picture of ANZ stadium and see if it doesn't look at least a little like a Pringle (or the stadium in Capetown where they played part of the World Cup, or the design for Qatar's proposed lusail stadium).

    May 22, 2012 at 2:12 pm |
  14. Natlaie

    I love the math!! I think pringles is still owned by proctor and gamble. Proctor and gamble has a long history of animal testing for cosmetics and cleaners. I try to avoid their products, even ones that were not tested on animals, because I don't support that kind of animal testing.

    May 22, 2012 at 1:43 pm |
    • robert wills

      I know, making rabbits take a math test is just cruel!

      May 22, 2012 at 5:00 pm |
      • Keith

        If you don't let them use their toes

        May 22, 2012 at 8:06 pm |
  15. Joolio

    Could you ask Dr. Mathra if Pringles stack better than Lays? My guess is yes since I think there would be 'gaps' as you stacked the Lays Stax from the "positive definite curvature'

    May 22, 2012 at 12:26 pm |
    • Little Timmy

      A lay is always better than bring pringled in the can.

      May 22, 2012 at 12:39 pm |
  16. Rebyl.Ella

    Reblogged this on Trail Mix and commented:
    And THIS, my dear friends, is just one more reason to love Pringles.

    May 22, 2012 at 11:52 am |
  17. Mocker

    The "taint" of critical points. Mathematicians are clueless. They even have a theorem called the "Hairy Ball Theorem"...

    May 22, 2012 at 10:50 am |
    • UncleJohn

      The genteel version is, "tain't one or the other."

      Yes, I know what you were thinking.

      May 22, 2012 at 1:48 pm |
    • KWDragon

      Actually, it is the mathematicians that are "in" on the jokes. They know EXACTLY what they are saying. :-)

      May 22, 2012 at 3:42 pm |
  18. FedUpwithLA

    My kid beat up your calculus student, and then ate his potato chips. So, there! Welcome to the real world!

    May 22, 2012 at 10:48 am |
    • Jon

      Cool, and then he grew up and made minimum wage while my calculus-studying son became a doctor.

      May 22, 2012 at 10:54 am |
      • Allah_speaking

        It's unlikely your son who grew up to be a doctor took a whole lot of calculus...more likely organic chemistry and biology...although the generalized logistic differential equation does have a few applications in terms of blood pressure. But face facts, calculus is more the language of engineering, not medicine...

        May 22, 2012 at 11:14 am |
        • finallyamom

          Too funny! My BS, MS, PhD engineer husband who then became a neurosurgeon swears that his engineering classes/background did almost nothing to get him into or through medical school. But it sure comes in handy when he spends his free time calculating the mathematics of practically everything around him :)

          May 22, 2012 at 7:43 pm |
        • anon

          Dr.'s like any other profession, start out in college the same as everyone else, which means often they will take classes that they don't need, like swimming, or country line dance. At least in the very beginning. It's a way for colleges to milk money off mom and dad.

          Calculus is offered even in high school, and in college, if you want a phd in any of the sciences, eventually you'll have to take it. Besides, I don't care how good they are at biology, if they don't have the critical thinking skill to pass calculus, then I don't want them so much as removing a hangnail off my little toe!! I know plenty of smart people who just can't do caluclus, but tinkering with my body is something I just don't think you can go cheap on.

          May 23, 2012 at 9:46 am |
    • Josh

      Are you Nelson Muntz's mom?

      May 22, 2012 at 11:18 am |
    • TAK

      In school, the jocks and bullies called the nerds many things. After graduation, do you know what they call them? Boss.

      May 22, 2012 at 11:44 am |
      • big w

        Called them for a job.

        May 23, 2012 at 6:27 am |
    • Angela Birch

      The real world of the minimum wage worker who needs to perfect the right intonation when asking " do you want fries with that?" The real world of engineers, scientists, doctors. Nope. Got to wonder about a parent who thinks the real world consists of ignorant idiots beating up on the educated who will be the people who employ them, save their lives and build bridges that the minimum wage worker can bicycle home across.

      I see that bumper sticker on occasion, I always wonder what sort of parent thinks it is funny. I have come to believe it is a parent who needs an assistant french fry bagger.

      May 23, 2012 at 12:27 am |
    • jake

      As the beat-up calc student – now all grown up and earning an awesome salary.... I say let the morons eat pringles, and take my trash, and my dig ditches, and serve my buttery popcorn when I go to the movies.

      Welcome to the real world indeed.

      May 23, 2012 at 9:45 am |
  19. King-Ding-a-Ling

    I was hoping this article would say that a cylinder whose height is twice the radius has the minimum surface area and maximum volume. I learned this when I took Calculus using Lagrange Multipliers.

    May 22, 2012 at 10:01 am |
    • fred1369

      is that the same as the height is equal to the diameter?

      May 22, 2012 at 10:51 am |
    • David

      twice the radius? silly way to put that...

      May 22, 2012 at 10:59 am |
      • Paul

        Twice the radius is clearly superious. Diameter? Please.

        May 22, 2012 at 11:20 am |
        • Gezellig

          Really? "height is twice the radius" takes fewer letters than "height is equal to the diameter". So is the former really better? In fact, is this a linguistic or mathematics question?

          May 22, 2012 at 11:28 am |
        • Scott

          Well, this is why we teach elementary kids that the formula is Pi*D but when we study it in more advanced classes we say 2*pi*r. Everything is based on the Radius where possible, because the very formula for the shape is based on the distance of the object from the point in space it occupies. When you are doing formulaic comparisons for volume versus surface area, you use the integral of pi*r^2 dh for the disks and washers method of calculating volume and the integral of 2*pi*dr*h for the cylindrical shells method, so then keeping the usage of radius versus diameter makes lots of sense here so that you don't have to keep switching back and forth. All serious math folks know that you worry about Radius rather than diameter.

          May 22, 2012 at 1:59 pm |
        • King-Ding-a-Ling

          I'm a Civil Engineer and I took Calculus: I,II,III DifEq, Statics, Dynamics, Physics: Mechanics, E&M, Thermo, Quantum et al. We never used a formula that involved diameter. Always used radius here.

          May 22, 2012 at 3:22 pm |
        • jacob

          I got my BS in electrical engineering and masters in telecommunications engr... Just wondering why you'd take E&M and Quantum as a Civil engr... I took those classes since E&M was required and quantum because I got a minor in physics.

          May 22, 2012 at 5:07 pm |
        • King-Ding-a-Ling

          I went to the University of Illinois at Urbana-Champaign. For CEE majors you have to take Physics: Classical Mechanics, and E&M. You then must take either quantum OR thermo. After I took Classical Mechanics and E&M, I went to a community college to retake E&M. In order for the credit to transfer back to UIUC, I had to take a total of 2 physics classes at the community college. At the community college they combine quantum and thermo in 1 course. So I ended up taking everything at the community college and got all A's :)

          May 22, 2012 at 5:41 pm |
        • Gezellig

          Well we also have the problem here in the South where the teacher says "Remember class, Pi R Squared". One student replied, "No teacher, Pie are Round, Cornbread are Squared!"

          May 22, 2012 at 8:40 pm |
        • Scott

          That comment about cornbread in the south being square is so not true. Everyone knows that true southern cornbread is made in a well-seasoned cast iron skillet (round). At least everyone with any modicum of math knowledge on here appears to agree that Radius is indeed the superior defining characteristic of circular objects (computer guy here with both math and computer science degrees for what it's worth).

          May 23, 2012 at 9:53 am |
  20. Abe

    I am quite sure there is no such title as "Calculus Professor"..."Professor of Mathematics" who teaches calculus (and usually other courses), yes...but NOT "Calculus Professor"...

    May 22, 2012 at 9:58 am |
  21. chairweaver

    Oops, forget one of my two previous comments. (stumble fingers)

    May 22, 2012 at 9:56 am |
  22. chairweaver

    By design I weave the seats of my benches in hyperbolic parabolas. Very comfortable, I use to like Pringles but now prefer the unpredictable shape of thicker, kettle cooked chips. Sort of chaotic.

    May 22, 2012 at 9:53 am |
  23. chairweaver

    I use to like Pringles but have moved onto less predicable shapes of thicker chips. However, almost daily, I weave the seats of my benches, which are hyperbolic parabolas, designed on purpose. Very comfortable.

    May 22, 2012 at 9:50 am |
  24. Bull Dung

    This broad and her husband have to be on crack. Pringles are nasty. They weren't made in heaven. In fact, they were crafted in the worst recesses of hell. They don't taste like potato chips. They taste like nasty mashed potatoes which were shaped into a potato chip.

    May 22, 2012 at 9:43 am |
    • Angela Birch

      The flavor isn't the question. Some people like them and some do not. What is great is that a teacher is using their shape to teach kids

      May 23, 2012 at 12:37 am |
  25. Pringlesareinherentlyfunny

    Sounds like perfect fodder for Sheldon on The Big Bang Theory!

    May 22, 2012 at 9:35 am |
    • Rick

      And people wonder why and how our education system here in the USA has gone to hell!

      May 22, 2012 at 9:54 am |
    • indydave

      This quotation:
      "They've got these Lays Stax right next to the Pringles as though they are equivalent. How can they do that? One is a positive semi-definite quadratic form and the other is an indefinite quadratic form – they're not even the same definiteness!"
      ... I TOTALLY read in Sheldon's voice – an especially petulant version of it, in fact.

      I wonder if there's any similar snack device that illustrates a perfect inflection point,...

      May 22, 2012 at 10:11 pm |
  26. GF

    Unfortunately, having recently discovered that I have celiac disease, Pringles unlike Lays Stax have gluten. This is a very entertaining story that has succeeded in making me pine for Pringles but stuck with Stax.

    May 22, 2012 at 9:31 am |
    • jake

      Oh man... that sucks : /

      May 23, 2012 at 9:47 am |
  27. Curt

    What a loser.

    May 22, 2012 at 9:31 am |
  28. George

    Lays Stax are the best – for one reason alone. Lays are GLUTEN FREE, where as Pringles – are not. Pringles with all their wonderful varieties – are poisonous to anyone with Celiac Disease, a growing population throughout the world. Lays – are safe and delicious. Thank heavens for Staks!

    May 22, 2012 at 9:26 am |
    • Sun

      You shouldn't be eating chips AT ALL if you have celiac disease. Nor should you be eating processed foods. So you can claim Pringles have 'poison' for you, all you want, because you are a hypocrite.

      May 22, 2012 at 10:35 am |
    • basketcase

      @sun- Why not eat chips when you have celiac disease? The problem isn't processed foods, it's gluten. If it's gluten free there's no reason (in regards to the disease) not to eat it.

      May 22, 2012 at 10:47 am |
  29. Tr1Xen

    I think I would like this prof!

    May 22, 2012 at 9:21 am |
  30. Mike in NJ

    Great article. But please don't call the saddle "the taint" of critical points. Just don't. Seriously.

    May 22, 2012 at 9:19 am |
    • sosofresh


      May 22, 2012 at 9:51 am |
  31. Mendozian

    Awesome. Just awesome.

    May 22, 2012 at 9:12 am |
  32. KP

    Bending any material with a positive Poisson's ratio will result in a saddle shape, so they are incredibly common. The professor should be teaching his students about anticlastic bending and it's implications on sheet metal, beams, etc. instead of buying Pringles so he can listen to himself talk :-p

    May 22, 2012 at 8:58 am |
  33. rizzo

    Pringles taste like oily cardboard and they're always broken inside their awesome carton. Buy a bag of chips.

    May 22, 2012 at 8:29 am |
    • Mike

      Yes, because there are never any broken chips in bag... and usually are not greasy either.

      May 22, 2012 at 8:54 am |
    • Alex

      i have to agree...pringles are not the greatest tasting snack.

      May 22, 2012 at 9:08 am |
    • Hobo

      Bags of chips are 3/4 air, zero calories, zero fat, the new weight loss chip!

      May 22, 2012 at 9:13 am |
    • rizzo

      @Mike: Chip makers also don't brag about how awesome their bags are at stopping breakage. Plus chips taste, you know, good.

      May 22, 2012 at 11:42 am |
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