classics
goodmath | December 31, 2008I'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.
Ω is my own personal favorite transcendental number. Ω isn't really a specific number, but rather a family of related numbers with bizarre properties. It's the one real transcendental number that I know of that comes from the theory of computation, that is important, and that expresses meaningful fundamental…
goodmath | December 30, 2008 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…
goodmath | December 29, 2008I'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 some old classic posts which were first posted in the summer of 2006. These posts are mildly revised.
Back when I first wrote this post, I was taking a break from some puzzling debugging.
Since I was already a bit frazzled, and I felt like I needed some comic relief, I decided to
hit one of my favorite comedy sites, Answers in Genesis. I can pretty much always find
something sufficiently stupid to amuse me on their site. On that…
goodmath | December 27, 2008 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.
What is e?
e is a transcendental irrational number. It's roughly 2.718281828459045. It's also the base of…
goodmath | December 26, 2008. 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?
The Roman Numeral…
goodmath | December 25, 2008 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 ze ro, 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)?…
goodmath | December 24, 2008 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.
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 -…
goodmath | October 5, 2006A few months ago, I wrote about the Poincare conjecture, and the fact that it appeared to finally have been solved by a reclusive russian mathematician named Grisha Perelman. Now there's news that *another* classic problem may have been solved. This time, it's the Navier-Stokes equation, apparently solved by [Professor Penny Smith](http://comet.lehman.cuny.edu/sormani/others/smith.html) of Lehigh University. She's published the steps leading up to her solution in top peer-reviewed journals, and a [preprint of the final paper is now available via arxiv](http://arxiv.org/abs/math/0609740).…
goodmath | June 21, 2006Harald Hanche-Olsen, in the comments on my earlier post about the Principia Mathematica, has pointed out that this months issue of the Notices of the American Mathematical Society is a special issue in honor of the 100th anniversary of Kurt Gödels birth. The entire issue is available for free online
I haven't read much of the journal yet; but Martin Davis's article The Incompleteness Theorem is a really great overview of the theorem abnd the proof, how it works, and what it means.
goodmath | June 17, 2006Finally, I have found online, a copy of the magnificent culmination of the 20th century's most ambitious work of mathematics. The last page of Russel and Whitehead's proof that 1+1=2. On page 378 (yes, three hundred and seventy eight!) of the Principia Mathematica.. Yes, it's there. The whole thing: the entire Principia, in all of its hideous glory, scanned and made available for all of us to utterly fail to comprehend.
For those who are fortunate enough not to know about this, the Principia was, basically, an attempt to create the perfect mathematics: a complete formalization of all things…