## Know anything special about numbers?

Posted by metaphorical on 22 February 2007

Now this is what make the Web special.

Erich Friedman, an Associate Professor of Mathematics at Stetson University, in DeLand, Florida, has a page called “What’s Special About This Number?” It has a list of numbers from 0 to 9999 and states for each one of them a unique property.

Here are a few examples:

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.

8 is the largest cube in the Fibonacci sequence.

Don’t know what a “perfect” number is? The site links to other pages around the Web that give detailed explanations. Mathematicians have tons of these technical terms (many of which use ordinary words, like “perfect”).

I had a major in math, and while I knew what a perfect number was, there are plenty of terms and ideas here that I didn’t learn in college, such as “hexomino.”

Friedman has an unfortunate tendency to link to Wolfram’s excellent MathWorld site, which gives extremely complicated, mathematically rigorous explanations (*“perfect numbers are positive integers n such that n==s(n), where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently sigma(n)==2n, where sigma(n) is the divisor function (i.e., the sum of divisors of n including n itself).”*)

But the Web is rife with simpler ones, and Google knows where they are. For practical purposes, a perfect number is any whose factors, not counting itself, add up to itself: 1+2+3=6. 1, 2, 4, 7, and 14 add up to 28, which is the second perfect number.

Anyway, Friedman’s page is delightful. He doesn’t find an interesting fact for every number between 0 and 9999, but he does for 2,849 of them, which is remarkable. For example, 35 is the number of hexominoes, which are structures made up of six squares. The Wolfram explanation is more helpful here and it has a diagram:

Did you know that 38 is the last Roman numeral when written lexicographically? Or that 40 is the only number whose letters are in alphabetical order? That 727 has the property that its square is the concatenation of two consecutive numbers? I sure didn’t.

The best thing about this site is that Friedman asks:

If you know a distinctive fact about a number not listed here, please e-mail me.

I’m sure that over time, each of the missing 7,151 factoids will be filled in, some of the existing ones will be improved, and the list will expand into the five-digit numbers and beyond. The Web can be the sum of all knowledge, assembled collaboratively, lovingly, in a way that’s never been possible before. We’ve put together a remarkable fraction of the world’s knowledge so far. Imagine what it will look like in a 100 years, if we don’t get in its way.

## Brooklynite said

I was going to post about this, but I wouldn’t have done it as well as you. So yay.

## Paul Tomblin said

I’m disappointed that he didn’t say that 1 was the loneliest number.