Numbers

I've been wanting to write a topic or two about math since I started this blog, but I was unsure of how to do it without turning off completely any of the two or three people who actually read it. I like numbers, I don't know why. I always did well in math in school; it just came naturally to me. At a college level I've taken probably a dozen mathematics courses - a couple of calculi (is that a real word?), statistics, probabilty, physics-related applications. Since this goes back fifteen or twenty years, and I don't use it everyday, I've forgotten much of it. But it still interests me, and every now and then my wife looks at me with incredulous disbelief when she sees me "wasting" my time reading a math book.

Oh, and words like "nerd" and "geek" are often thrown my way.

Anyway, the past two years or so I've read a half-dozen books on number theory. That interests me. Funny, I never took a course in it (actually, in my late teens and early twenties it didn't even occur to me to do something with math as a career). My family was lucky to get a paid week vacation to Puerto Rico last year, and what was my poolside reading down there? The Riemann Hypothesis book Prime Obsession by John Derbyshire.

So I really don't know how to write about this stuff in a way that will convey what makes it so interesting and enjoyable. Then, I realized, why not just throw out some trivia and the like, stuff I would claim to be "neat," for your consideration? Very well. In the field of number theory, how 'bout this?

Did you know every even number can be written as the sum of two prime numbers? It's called Goldbach's Conjecture, and though it's not technically proven, math geeks have confirmed it up to something like a gazillion or two. Some random examples? 2 = 1 + 1. 66 = 23 + 43. 102 = 5 + 97.

How can you tell if a number is divisible by 3? (This is handy in finding prime factors of a number.) Add up all the digits in the number, and if that number is divisible by 3, the original number is. Example? 128. 1 + 2 + 8 = 11, 11 is not divisible by 3, so 128 ain't, either. 129. 1 + 2 + 9 = 12, which is divisible by 3, so 129 is (the answer is, of course, 43).

Palindrome numbers are just like palindrome words. What's a palindrome word? A word spelled the same backwards and forwards, such as racecar. See? So what's an example of a palindrome number? I don't know, how about 5,487,845. Got it? Now for some trivia. The number 11 is, technically, a palindrome number. Raising it to some powers yields the following results:

11 ^ 0 = 1
11 ^ 1 = 11
11 ^ 2 = 121
11 ^ 3 = 1,331
11 ^ 4 = 14,641

The palindrome pattern breaks down when 11 is raised to the fifth power.

What's special about the number 17? Well, it's a prime number, true, but there's an (unproven but assumed) infinite number of primes. It's the only prime that's the sum of four consecutive primes (because the number 2, technically also a prime, is involved). 17 = 2 + 3 + 5 + 7.

A little interesting equation with a bunch of squares:

10 ^ 2 + 11 ^ 2 + 12 ^ 2 = 13 ^ 2 + 14 ^ 2

A "myriad" is actually a definite number; it's Greek for 10,000. Sven faces a myriad of problems means that Sven is really confronting 10,000 difficult situations.

There's a mathematical oddity called the Collatz Problem (also called Ulam's Problem, the Hailstone Sequence, the Haase Algorithm and the Kakutani Problem). Take any positive integer. If it's even, divide it by 2. If it's odd, multiply it by 3, add 1, and divide that by 2. Keep going until you reach the number 1 as a solution. No matter what positive original integer you start with, you will eventually end with the number 1. Why? No one knows.

There's a really cool proof of the Pythagorean Theorem, some interesting facts about pi and e, and the most beautiful equation ever discovered (see the diagram at the top of the post) that I'd love to post further about, but I think I need to figure out how to get math notation into blogger so it's easier on the eyes.

To hold you math lovers over, here's a neat little exercise. By using four 4s and any mathematical notation you wish (addition, subtraction, multiplication, division, exponents, roots) arrange them into simple equations that solve for the numbers 1 through 20. Example: 4 / 4 - 4 / 4 = 0. Now find answers for 1 to 20. Time limit: 20 minutes. GO!!!