Category Archives: Math on the web

Pringles

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This article about the saddle-shape of Pringles is a joy to read [ht: Prisca Chase]. I’ll give you an excerpt, but I encourage you to read the whole thing. It’s both mathematically stimulating and extremely funny:

Saddle up for maximum snack satisfaction (mathematically speaking)

Stephanie V.W. Lucianovic

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.

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Later in the article, the fact that a Pringle can’t be made from a sheet of paper is mentioned. For a normal sheet of paper, this is true. But you can fold paper in such a way as to approximate a hyperbolic parabaloid. I’ve mentioned this before here and here. So go try it!

Coursera.org

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File this under “flipping the classroom.”

Here’s a recent piece from NY Times columnist and best-selling author, Thomas Friedman [ht: Gene Chase]:

Thomas L. Friedman: Come the education revolution

By Thomas L. Friedman

PALO ALTO — Andrew Ng is an associate professor of computer science at Stanford, and he has a rather charming way of explaining how the new interactive online education company that he cofounded, Coursera, hopes to revolutionize higher education by allowing students from all over the world to not only hear his lectures, but to do homework assignments, be graded, receive a certificate for completing the course and use that to get a better job or gain admission to a better school.

“I normally teach 400 students,” Ng explained, but last semester he taught 100,000 in an online course on machine learning. “To reach that many students before,” he said, “I would have had to teach my normal Stanford class for 250 years.”

…

The combination of all these factors gave birth to Coursera.org, which launched April 18 with the backing of Silicon Valley venture funds, as my colleague John Markoff first reported.

…

When you consider how many problems around the world are attributable to lack of education, that is very good news. Let the revolution begin.

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Awesome Math Baby Gear

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Here is some awesome baby gear that you’ll get a kick out of, whether you have a little baby (like I do) or not. [ht: Carrie Gaffney]

Check out this one, for instance, perfect for the little Fermat in your life:

Or this one, with a slightly more ‘physics’ flavor–perfect for your little one that is constantly gaining momentum:

For the baby that’s two standard deviations above the mean:

Or how about this …

And here are some more for you:

By the way, the perfect place to collect random photos and other things you love is on Pinterest. I’ve been collecting pins for the last year or so, and you may want to check out these two boards of mine, at least:

Happy pinning!

Math paper contains no math

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I feel like I need to post about this too–just to get the word out.

At first I thought it was funny, but now it just makes me angry. I first heard about this paper thanks to my brother, Tim Chase, who shared this news via Retraction Watch. Then today I learned a bit more information by way of Alexander Bogomolny and his blog.

Okay, what’s going on? Authors M. Sivasubramanian and S. Kalimuthu have published this completely nonsensical math paper, and here’s what Retraction Watch had to say:

Have a seat, this one’s a howler.

According to a retraction notice for “Computer application in mathematics,” published in Computers & Mathematics with Applications:

This article has been retracted at the request of the Publisher, as the article contains no scientific content and was accepted because of an administrative error. Apologies are offered to readers of the journal that this was not detected during the submission process.

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Go read the whole paper in full text available here. At the very least, this paper has been retracted. That’s good.

But sadly, S. Kalimuthu and his coauthors are responsible for many other terrible papers too (seriously, go check them out!). How does this happen? Can anyone explain it? And why hasn’t he been stopped?

In one paper in particular, he has completely plagiarized Alexander Bogomolny’s site–as one commenter noticed. Check out Alexander’s blog CTK Insights for his coverage.

Like I said, this man needs to be stopped.

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Using math to get out of a ticket

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By now perhaps you’ve seen this floating around the internet. It was reported here and here and here and here, at least.

Physicist Dmitri Krioukov got a $400 ticket for not making a full stop at at stop sign. He wrote a paper explaining why the police officer could have been wrong, went to court, and got the fine lifted.

If you haven’t read the paper, I encourage you to do it. It’s fairly short and only requires knowledge of a Calculus. Here is a direct link to the pdf. Here’s the abstract:

We show that if a car stops at a stop sign, an observer, e.g., a police officer, located at a certain distance perpendicular to the car trajectory, must have an illusion that the car does not stop, if the following three conditions are satisfi ed: (1) the observer measures not the linear but angular speed of the car; (2) the car decelerates and subsequently accelerates relatively fast; and (3) there is a short-time obstruction of the observer’s view of the car by an external object, e.g., another car, at the moment when both cars are near the stop sign.

What do you think? Is Professor Krioukov just trying to buffalo the court, or does he have a legitimate case? I guess if there’s any doubt at all about his guilt, then he should be forgiven the fine. And that’s what the court did rule.

However, there is one particular assumption that he makes which is absolutely way-off (look at the paper and notice the key on Figure 3, labeling the blue curve). But the court certainly didn’t catch that. Like I said, he may have been trying to pull the wool over the eyes of the court with lots of math and physics.

Despite the fact that he published his paper on April 1st, I do think this story is true. Like I said, though, the paper does contain an error. So despite all of his good effort, I think he should have been given the ticket. The court didn’t notice it, but he pulled a fast one on them! (pun intended!)

Math Carnival #85 and other recent gems

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Math Carnival

The math carnivals are in full swing. I’ll be hosting one here at Random Walks in June, so get excited for that! 🙂 If you haven’t had a chance to check out Math Carnival #85 hosted by Aperiodical, go do it now. I especially like the idea of Math Busking, since I’ve done plenty of street performing as a juggler. Maybe I need to try adding math to my show!

Also found around the web

  • Awesome article about correct hangman strategy which touches on cryptography and conditional probability. Very good stuff, and possibly of good use in the classroom too.
  • Did you know a knight can visit every space on a chess board? I’m sure you did, but you may not have ever seen it actually happen:

  • I don’t have an iPad, but if I did I would definitely get this app from IBM which presents 1000 years of math history in an interactive way. Looks great!
  • These recent math videos that parody pop songs are funny.

An article from J. Michael Shaughnessy

Here’s another article from NCTM president, J. Michael Shaughnessy. He makes a point that Art Benjamin has made before, that Calculus should not be the goal of high school mathematics. I think I agree too. In general I agree with his article, but there are a few points on which I disagree.

In particular, he says, “If calculus is to be taught in high school, it should be taught at a college level.” I don’t think it hurts to teach non-AP Calculus. I say this because “Calc with Apps” is a course I teach, and I find the students really benefit from the more relaxed pace. There’s no pressure from an AP test at the end. Many come to my class lacking confidence, and leave having their confidence restored.

Shaughnessy goes on to say, “Whenever students enroll in calculus, they should have a solid mastery of algebra, geometry, and trigonometry.” I only agree with this in part. My kids have already taken Algebra 1 and 2, and Precalculus. There are definitely some algebraic rough spots that need to be smoothed out as we go through the course. But again, I find my course the perfect place to do it–since those algebraic skills are routinely needed for the Calculus. And in the end, they say they like math again.

I’ve heard from lots of kids who have gone on to take more Calculus in either high school (AP) or college and have really appreciated the informal foundation that we provided in our lower-key course.

This is Shaughnessy’s final president’s message. President-Elect Linda Gojak will be taking over. I’ll be sure to highlight some of her articles, too!