By Serge Lang
Dieses Buch enthalt eine Sammlung von Dialogen des bekannten Mathematikers Serge Lang mit Schulern. Serge Lang behandelt die Schuler als seinesgleichen und zeigt ihnen mit dem ihm eigenen lebendigen Stil etwas vom Wesen des mathematischen Denkens. Die Begegnungen zwischen Lang und den Schulern sind nach Bandaufnahmen aufgezeichnet worden und daher authentisch und lebendig. Das Buch stellt einen frischen und neuartigen Ansatz fur Lehren, Lernen und Genuss von Mathematik vor. Das Buch ist von grossem Interesse fur Lehrer und Schule
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Extra info for Math!: Encounters with High School Students
Sample text
OK. You've got a circle, and [Laughter] and you divide it, OK, and the radius is r. And you divide it up n times. Here n is any number. So, then with those little ... when you divide it you have little triangles, and the area of the triangle is half base times height. SERGE LANG. Yes. MIKE. And the base of that triangle would be b n , the height would be h n, so the area is half bnh n. SERGE LANG. Right. MIKE. Then you times it by n, which is the number that you got. ] And then n times b n is the length, so that becomes Ln.
You don't know the relation between a,b, and c? You have never seen it? We have You've never seen this? THE TEACHER. Next year. A STUDENT (VANYA). Why the squares? SERGE LANG. It's not at all obvious why you need the squares. One has to prove it, but it's not what I wanted to do today. So I am asking you to accept it. Can you accept it? THE CLASS. Yes, OK. SERGE LANG. Good. Now I cut up the ball and I make cylindrical slices, like this. Actually, I took a half ball, and I cut it up. Does everybody see the slices?
The volume. SERGE LANG. That's right, the volume, What's your name? STUDENT. Ann. SERGE LANG. You know the formula for the volume of the ball of radius r? ANN. SERGE LANG. Who knows the formula? THE CLASS. SERGE LANG. All right. The length of the circle is 2m· and the area is 'lTr2. But for the ball, what is it going to be? A STUDENT. 'IT squared times r to the power 4. SERGE LANG. No. So let's go back to boxes. Suppose I have a square with sides equal to r. Then its area is equal to what? THE CLASS.