古人(中國or西方)如何找到和計算圓周率?

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle. The word "diameter" derives from Greek διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure"[1]).

In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.

For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the width is defined to be the smallest such distance. For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. See also Tangent lines to circles.

The diameter of a connected graph is the distance between the two vertices which are furthest from each other. The distance between two vertices a and b is the length of the shortest path connecting them (for the length of a path, see Graph theory).

Drawing a big circle and measuring the diameter and radius is the way to go, Chinese or others. The one that my instructor mentioned was the one used by Archimedes. He would used a lot of regular polygons to represent a circle. It is very easy to get the length of the side of a polygon and if one fixes the radius, it is possible to add up all the sides of all polygons that makes up the circle. This is also described in detail in the following link (wiki) in the Mathematics section. It is called the method of exhaustion.

http://en.wikipedia.org/wiki/Archimedes#Mathematics