Two curves, say y = f(x) and y = g(x) of degree m and nalways meet in mn points “counted properly.”

The recent ramblings are mainly for my friends and folks back in India. Life here in America is different. One major cultural difference I observe is that your profession, Mathematics is just a part of life not your life. There have been many interesting things that distracted over the months. But this is just a lame excuse. The fact is that recently, I have been learning only old stuff more thoroughly and not newer maths. The main purpose in blogging was not as much in writing expository articles as learning things more clearly for myself. And yes, I will definitely try posting math articles soon.

Coming back to our little problem of intersecting curves, I learnt recently that a lot of mathematics was studied to make this statement come true. For example, a circle (quadratic) meets a line (degree one) in two points. Except when it is not a tangent. So count properly! Sometimes, it meets in no “real” points. So work over complex numbers. It is interesting how definitions were modified over the centuries to make this statement (Bezout’s theorem) true in all cases. So much for now…

]]>