Pringles

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

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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A math carnival here??

Yes, that’s right!

In just a few weeks, I’ll be hosting the 87th Carnival of Mathematics. Please submit articles here, sometime before June 1st. I look forward to curating the submissions, and of course, sharing some great mathematics with the math blogging community!

And if you haven’t done so yet, please go check out the current carnival at the Math Less Traveled.

To get you in the carnival mood, here’s a juggling video. See if you can spot Mr. Chase :-).

In fact, today, I just gave the “Mathematics of Juggling” lecture three times. I try to give this lecture as a fun-day at the end of the year in my Precalculus classes. So, needless to say, I’m in the juggling mood!

I’m Perfect!

Happy Birthday to Mr. Chase, today!

Today, I think I can safely say, is the last time my age will be a perfect number. The last time my age was perfect was when I was 6 years old. For those that forget the definition of a perfect number:

A number is perfect if it is the sum of its proper divisors (that is, the sum of its divisors, excluding itself).

For example, 6 is perfect because 1+2+3=6.

I’m not 6. How old *am* I?

So, how old am I?

If you’re a consummate mathematician, you have the first couple perfect numbers memorized, and this is an easy question. If you’ve never thought about perfect numbers, or you forget what the next one is, I challenge you to figure it out for yourself. I challenged my students today to figure out my age, and two of them got it out without my help.

For a real challenge, prove that there are infinitely many perfect numbers. (open problem!)

Awesome Math Baby Gear

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!

Microsoft Equation Editor vs LaTeX

I have posted twice about Microsoft Equation Editor recently, and made comparisons to \LaTeX, claiming that those who like \LaTeX will be pleased that many beloved shortcuts work in Microsoft Equation Editor as well. If you couldn’t tell, I’ve been becoming a bigger and bigger fan of Microsoft Equation Editor, especially now that I’ve learned that  everything is possible from the keyboard.

I was talking with my good friend (and math professor) Matthew Wright, and I echoed the above sentiment. I said that I’m seeing less and less advantage to doing things in \LaTeX, when it’s so easy and fast in Microsoft Equation Editor. His reply, in defense of \LaTeX, was clear and helpful (published here with permission):

As much as I appreciate the improvements to Equation Editor, I can think of many reasons to use LaTeX. Here are some:

1. Math fonts: I like to use Palatino, but Word doesn’t support Palatino as a math font. Equation Editor defaults to some particular font, and I don’t know how to change the default setting. In order to use Palatino in equations, I have to convert my equations to “normal text”, but that removes the italics and some other equation formatting, so I then have to manually set the variables to be italics. I like to use a sans-serif font for presentations in PowerPoint, but that also requires a lot of manual font changes. LaTeX can specify all the fonts in the document by loading a single package.

2. LaTeX provides more symbols. The Equation Editor cheat sheet provides an impressive list of symbols, but it doesn’t come close to the amount of symbols available in LaTeX. The Comprehensive LaTeX Symbol List has 100 pages of symbols:

http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-letter.pdf

3. LaTeX supports some programming constructs, such as conditional statements and the ability to create new commands. For instance, if you use some expression repeatedly, you can define a new command so that you can easily insert your expression whenever you need it. Conditional formatting is useful to hide or print solutions in a worksheet, for example.

4. LaTeX numbers theorems and equations and lets you refer to them in your document. If you insert a theorem or equation, it automatically renumbers everything. The same applies for lemmas, definitions, chapters, sections, references, etc. (I know that Word has tools for cross-references, table of contents, and such, but I think consistent numbering of theorems and equations is easier in LaTeX.)

5. There are many special packages in LaTeX for a variety of tasks. For example, I use a schedule package to print my schedule each semester. Granted, this did not save time the first time I made a schedule, but saves me time now, since creating a schedule is really easy. I have attached my schedule.

6. Finally, I think that math looks better in LaTeX than in Word. This is subjective, but I like Donald Knuth’s Computer Modern font family.

I guess I knew all of that, but I was glad for his reminders of why \LaTeX is still a very, very powerful tool. I’ve been using it for all my math grad school assignments, and I think Matthew has convinced me to continue doing that. There’s also the obvious additional benefit of \LaTeX:

7. Geek cred 🙂

Do you have any to add?

More on Microsoft Equation Editor

As some of you know, I recently posted about Microsoft Equation Editor (here) and the way it’s been totally upgraded. I’ve been using Microsoft’s Equation Editor more and more, and I’ve learned a lot of new things, but I also still have questions (for instance, how do you force it to do display or in-line mode?).

Before, when I had questions, it seemed like Microsoft had no answers. I searched their website and found minimal help. I found help from third-parties, like this wonderful cheat-sheet which I still highly recommend. But today when I went searching for some more answers, I found this page on Microsoft’s website, which I swear wasn’t online two months ago.

The most interesting thing is that they mention their use of Unicode Nearly Plain-text Encoding of Mathematics and they claim that the Microsoft Equation editor adheres to the standards set forth in Unicode Technical Note 28.  I’ve now completely read this Unicode guide and it was very helpful.

I think I can finally use the new Microsoft Equation Editor without ever leaving the keyboard.

In particular, here are a few things I learned how to do. Hopefully this will save you the time of having to read through it all yourself:

Tips & Tricks with the new Microsoft Equation Editor

To start with, here are a handful of things I didn’t know how to do without visiting the toolbar. Now I can do them just by typing.

Boxed formula:   \rect(a/b) produces

boxed formula

Matrix:   (\matrix(a&b@&c&d))   produces

matrix

Radicals:  \sqrt(5&a^2)    produces

radical

Equation arrays are something I found hard to do in Microsoft Equation Editor. In their documentation, I learned you can type “Shift+Enter” to keep the next line as part of the same equation array. But here’s the more finely-grained method:

\eqarray(x+1&=2@1+2+3+y&=z@3/x&=6)

resolves to this:

equation array

A more complicated example of alignment, and a description of how it is interpreted comes from the Unicode page:

3.19 Equation Arrays
To align one equation relative to another vertically, one can use an equation array, such as

system of equationswhich has the linear format █(10&x+&3&y=2@3&x+&13&y=4), where █ is U+2588. Here the meaning of the ampersands alternate between align and spacer, with an implied spacer at the start of the line. So every odd & is an alignment point and every even & is a place where space may be added to align the equations. This convention is used in AmSTeX.

Instead of █, one can type \eqarray in Microsoft office. Also, to include a numbered equation is simple:  E=mc^2#(30).

Another nice thing I learned is how to quickly include text in your equations, without having to visit the toolbar (in retrospect, it’s somewhat obvious):

 “rate”=”distance”/”time”

resolves to

\text{rate}=\frac{\text{distance}}{\text{time}}

Like I said, one unresolved issue I still have is how to force math to be displayed in ‘in-line’ or ‘display’ mode. This is very easy in \LaTeX with the use of $ or $$. Section 3.20 of the Unicode notes isn’t very satisfying:

Note that although there’s no way to specify display versus inline  modes (TeX ‘s $ versus $$), a useful convention for systems that mark math zones is that a paragraph a paragraph consisting of a math zone is in display mode.  If any part of the paragraph isn’t in a math zone including a possible terminating period, then inline rendering is used.

So there you have it–more of what I’ve learned about the Microsoft Equation Editor. Please do share if you have other useful information.