Posts tagged ‘Euclid’

The Girl With the Dragon Tattoo

The Girl Who Played with Fire is the second volume in the late Stieg Larsson‘s The Millenium Trilogy. (Of course, you probably already knew that, since virtually everyone in North America has read this book. I mean, someone had to buy those 20 million copies, right?)

In this book the heroine, Lisbeth Salander, gets absorbed in recreational mathematics. She stumbles across a theorem about perfect numbers that, surprisingly, was proved by Euclid. (This is surprising because Euclid did most of his work in geometry, and a proof of his theorem about perfect numbers would rely on algebra and number theory.) The theorem appeared as Proposition IX.36 of Euclid’s Elements.

Stieg Larsson writes:

…a perfect number is always a multiple of two numbers, in which one number is a power of 2, and the second consists of the difference between the next power of 2 and 1. This was a refinement of Pythagoras’ equation, and [Lisbeth] could see the endless combinations:

6 = 21(22 – 1)

28 = 22(23 – 1)

496 = 24(25 – 1)

8128 = 26(27 – 1)

She could go on indefinitely without finding any numbers that would break the rule.

What Lisbeth does not state, but what is required for Euclid’s theorem to hold, is that 2k(2k – 1 – 1) is a perfect number if and only if 2k – 1 is prime. She doesn’t state this — but her list of “endless combinations” only includes examples for which this is the case.

I don’t begrudge Larsson for this omission. After all, how can you be mad at the first author to sell more than one-million e-books on Amazon, especially when his most popular works were published posthumously? Besides, adding too much math to a popular fiction novel might make it a little less popular. I’m just happy that so many readers will be exposed to a little of the mathematical beauty that makes me love numbers.

Here’s a perfect quote from Descartes:

Perfect numbers, like perfect individuals, are very rare.

And a perfect joke:

Teacher: What is 14 + 14?
Student: 28.
Teacher: That’s good!
Student: Good? It’s perfect!

August 26, 2010 at 12:39 am Leave a comment

Twin Pi Day

Today (June 23) around 7:41 a.m. and 8:05 a.m., respectively, my twin boys passed 3.1415926 years! My wife didn’t think it was a milestone worthy of celebration, but 154 days ago, I missed the chance to celebrate their e birthday, and I wasn’t going to let another opportunity slip away. This morning, we celebrated with circular pancakes for breakfast, and we had pizza for lunch. Which reminds me of a joke…

What is the volume of a disk with radius z and height a? pi · z · z · a

At lunch, I planned to explain pi to the boys. I wrote the letters p and i on a piece of paper and set the paper on the table, and Eli asked, “Daddy, why did you put pee on the table?” That was the end of the lesson. (It was funny to me that he’d pronounce it this way, since the i at the end of his name makes a long i sound. But then I thought of some other words he knows — such as ski, mi (Spanish for my), and his friend Ani (pronounced ahnee) from school — and realized his mistake was completely understandable.

In regards to mispronunciation, here’s a thought to ponder.

Ya ever wonder how Euler pronounced Euclid?

June 23, 2010 at 6:45 pm Leave a comment


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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