Monday Mornings are for Math

I missed linking to last week's installment of Steven Strogatz's series -- Math: From Basic to Baffling. Here, then, are two links:

1. Power Tools: In math, the function of functions is to transform.

   A mathematician needs functions for the same reason that a builder needs hammers and drills. Tools transform things. So do functions. In fact, mathematicians often refer to them as “transformations” because of this. But instead of wood or steel, functions pound away on numbers and shapes and, sometimes, even on other functions.

2. Take It To The Limit -- Archimedes recognized the power of the infinite, and in the process laid the groundwork for calculus.

   The key to thinking mathematically about curved shapes is to pretend they’re made up of lots of little straight pieces. That’s not really true, but it works … as long as you take it to the limit and imagine infinitely many pieces, each infinitesimally small. That’s the crucial idea behind all of calculus.

   Following the excellent tradition he has established in this series, Strogatz then goes on to provide an intuitive proof for the well known relation between a circle's area (A) and its radius (r): A = π r².

Kalid Azad's Better Explained is the best resource for simple explanations of math concepts (and business concepts, programming concepts, ... ;-). So I checked to see if Azad has covered the Problem of Pi, and sure enough, he has. So, here are a couple of links:

1. Prehistoric Calculus: Discovering Pi describes the logic behind Archimedes's method of calculating π .

2. A Gentle Introduction To Learning Calculus has a different -- but equally intuitive -- proof for the relationship between a circle's area and its radius: A = π r²