I’m away on vacation this week, taking my kids to Disney World. Since I’m not likely to have time to write while I’m away, I’m taking the opportunity to re-run an old classic series of posts on numbers, which were first posted in the summer of 2006. These posts are mildly revised.

One of the annoying things about how we write numbers is the fact that we generally write things one of two ways: as fractions, or as decimals.

You might want to ask, “Why is that annoying?” (And in fact, that’s what I want you to ask, or else there’s no point in my writing the rest of this!)

It’s annoying because both fractions and decimals can both only describe rational numbers – that is, numbers that are a perfect ratio of two integers. The problem with that is that most numbers aren’t rational. Our standard notations are incapable of representing the precise values of the overwhelming majority of numbers!

But it’s even more annoying than that: if you use decimals, then there are lots of rational numbers that you can’t represent exactly (i.e., 1/3); and if you use fractions, then it’s hard to express the idea that the fraction isn’t exact. (How do you write π as a fraction? 22/7 is a standard fractional approximation, but how do you say π, which is almost 22/7?)

So what do we do?

Continue reading →

I’m away on vacation this week, taking my kids to Disney World. Since I’m not likely to have time to write while I’m away, I’m taking the opportunity to re-run an old classic series of posts on numbers, which were first posted in the summer of 2006. These posts are mildly revised.

Anyway. Todays number is e, aka Euler’s constant, aka the natural log base. e is a very odd number, but very fundamental. It shows up constantly, in all sorts of strange places where you wouldn’t expect it.

Continue reading →

. I’m away on vacation this week, taking my kids to Disney World. Since I’m not likely to
have time to write while I’m away, I’m taking the opportunity to re-run an old classic series
of posts on numbers, which were first posted in the summer of 2006. These posts are mildly
revised.

I’ve always been perplexed by roman numerals.

First of all, they’re just weird. Why would anyone come up with something so strange as a
way of writing numbers?

And second, given that they’re so damned weird, hard to read, hard to work with, why do
we still use them for so many things today?

Continue reading →

I’m away on vacation this week, taking my kids to Disney World. Since I’m not likely to have time to write while I’m away, I’m taking the opportunity to re-run an old classic series of posts on numbers, which were first posted in the summer of 2006. These posts are mildly revised.

After the amazing response to my post about zero, I thought I’d do one about something that’s fascinated me for a long time: the number i, the square root of -1. Where’d this strange thing come from? Is it real (not in the sense of real numbers, but in the sense of representing something real and meaningful)? What’s it good for?

Continue reading →

This post originally came about as a result of the first time I participated in a DonorsChoose fundraiser. I offered to write articles on requested topics for anyone who donated above a certain amount. I only had one taker, who asked for an article about zero. I was initially a bit taken aback by the request – what could I write about zero? This article which resulted from it ended up turning out to be one of the all-time reader-favorites for this blog!

Continue reading →