## Archive for August 31, 2012

### A Muppet You Can Count On

A big MJ4MF thanks to Lindsey Witcosky, who directed me to a wonderful BBC article about one of my favorite Sesame Street characters, the Count! The link to the article is provided below, but first a quiz based on some trivia in the article.

**1.** What was the Count’s full name?

**2.** What was the Count’s favorite number?

**3.** Who was the voice of the Count from 1970 until 2011?

Answers are below, but you can also find them in the BBC article:

http://www.bbc.co.uk/news/magazine-19409960

The Count’s favorite number is equal to 187^{2}, and BBC Radio asked listeners of the show *More or Less* to speculate why. One listener noted that 187 = 94^{2} ‑ 93^{2} and, of course, 187 = 94 + 93. The BBC article referred to this coincidence as, “An embarrassment of riches!” But I prefer to think of it as, “An embarassment of algebra!”

Algebra can be used to show why this is true. The *n*th square number is equal to the sum of the first *n* positive odd integers. That is,

*n*^{2} = 1 + 3 + 5 + 7 + … + (2*n* ‑ 1)

From this it follows that

94^{2} = 1 + 3 + 5 + 7 + … + (2 × 94 – 1)

and

93^{2} = 1 + 3 + 5 + 7 + … + (2 × 93 – 1)

so of course

94^{2} – 93^{2} = 2 × 94 – 1 = 187

Moreover, the difference of two squares is equal to the product of the sum and difference of the two numbers. That is,

a^{2} ‑ b^{2} = (a + b)(a ‑ b)

Consequently,

187 = 94^{2} ‑ 93^{2} = (94 + 93)(94 ‑ 93) = (94 + 93)(1)

So, saying that 187 = 94^{2} ‑ 93^{2} = 94 + 93 is kind of like saying the same thing twice, just in different ways.

**Answers**

**1.** Count von Count

**2.** 34,969

**3.** Jerry Nelson, who passed away on August 23. R. I. P.

### Pringles: The Edible Hyperbolic Paraboloid

My wife forwarded an email with a link to a CNN article and subject line, “Your husband will love this.” Uh-oh. Even my closest friends cannot correctly predict what I will and will not love, so how would a colleague of my wife — who only knows me from an introduction at a professional reception — be able to make such a prediction?

But the article did not disappoint. The author wrote about the mathematically satisfying shape of Pringles^{®}, and she quoted her husband thus:

They [Lays Stax] set themselves up as a Pringles competitor, but it’s an entirely different curvature!

I have never met the author, but her last name was familiar. As luck would have it, her math professor husband and I taught together at a gifted camp for several summers. Small world, eh?

My favorite line of the article was from the last paragraph.

Flavor is subjective. Math is irrefutable.

Fact.

What I enjoyed most about this occurrence was the intersection of several math topics. The article discusses parabolic cylinders and hyperbolic paraboloids, which are topics in **multivariable calculus**; a colleague of my wife forwarded a link about an article written by the wife of a former colleague, which demonstrates **social network theory**; and, a colleague of my wife is not equivalent to the wife of my colleague, which shows **non‑commutativity**.

My two cents? Pringles^{®} rule.