Present, Greek Mathematics

I've been reading a book entitled 'The Archimedes Codex'. In case you don't know who Archimedes is, well let's just say he was the one who, while watching water splash out of his bath, suddenly ran out naked and shouted 'Eureka'. He had discovered a way to determine whether his king's crown was made of pure gold. His discovery was perhaps the beginning of science.

The Archimedes Principle states that a body immersed in a fluid experiences an upthrust of magnitude equal to the weight of fluid displaced. What I find so fascinating is that he had lived at least 1800 years before Newton studied on forces. In fact, most scientists living in the so-called Golden Age of science referred to Archimedes', or more specifically, Greek knowledge.

I admired the Greek, they were most probably the first superpower in the world. They were the founders of so many areas of human society, be it in religion (Zeus is now so famous in computer games), warfare, literature, mathematics and sciences, philosophy, and even politics (they were the first to practice voting). How did the Greeks figured out so many wonderful things is something I can never understand. Picture 2500 years ago, they already have a whole city built using precise calculations. There were no schools and letters took months to circulate. Yet, they have produced so many geniuses that could have still been geniuses if they lived in our time.

There's one brand of Greek mathematics that I particularly like a lot. I think the MOE should add this into the maths syllabus. It's so easy to understand yet in all my years of study, I've never really looked at area this way. Suppose you needed to find the area of a polygon. An average person will try to divide that polygon into smaller parts like triangles and rectangles and calculating the individual areas before summing them up. But the problem is you often get stuck on where to draw the dividing lines. A primary school student will find it less humiliating to draw unit squares and try to approximate the area.

Well, the Greeks did something quite similar to the primary student but at a deeper level. You see, Greek mathematicians from very early on came up with 3 important discoveries that solved this problem:
1. Every area bound by straight lines can be divided up into triangles.
2. Every triangle can be made equal to half a rectangle.
3. Every rectangle can be made into a square.
The first 2 are easy to understand, but the last one needs a bit of thinking. See, if you can make a square into a rectangle then the reverse can be done as well.

Neat. Next time just divide any shape into triangles since they are the simplest of shapes. Perhaps this is how contractors determine how large an apartment is.