Monday, March 01, 2010

Fun with mathematics

Steven Strogatz's series on Math: From Basic To Baffling is chugging along nicely. It presents interesting mathematical concepts, and appeals to your intuition in showing how they arise and why they work. It has an entertaining, easy-going pace, established right in the first article: From Fish To Infinity.

I think the best, so far, is the second article -- Rock Groups, which uses arrangements of rocks to prove theorems involving natural numbers. Since then, it has moved on to subtraction and negative numbers, and division and rational numbers.

This week, the series takes baby steps in basic algebra,with The Joy of x.

Working with formulas ... is a bit like art and science. Instead of dwelling on a particular x, you’re manipulating and massaging relationships that continue to hold, even as the numbers in them change. These changing numbers are called “variables,” and they are what truly distinguishes algebra from arithmetic.

The formulas in question might express elegant patterns about numbers for their own sake. This is where algebra meets art. Or they might express relationships between numbers in the real world, as they do in the laws of nature for falling objects or planetary orbits or genetic frequencies in a population. This is where algebra meets science.

This division of algebra into two grand activities is not standard (in fact, I just made it up), but it seems to work pretty well. [...]


  1. Rahul Siddharthan said...

    I'm late to this, but the Verizon conversation in the division article -- 0.002 dollars vs 0.002 cents -- goes some way to explaining something that always mystified me. Petrol bunks ("gas stations") in America show prices in terms like this: "$ 3.15 8/10", and I couldn't understand it until an Indian living in America explained it to me: it's $3.15 and 8/10 of a cent. So why not write 3.158? Because, apparently, Americans don't understand how the decimal system works. They just happen to use it in coinage -- where they take it to mean that the numbers following the dot indicate "cents", so 3.158 would mean 3 dollars 158 cents.

    In nearly everything other than money, Americans use non-decimal (Imperial) units, that even the British have largely given up on. But this is understandable. To most Americans, "How many centimetres in 4.5 metres?" is just as hard a problem as "how many inches in 4 1/2 yards?"