Buffon's Needle An Analysis and Simulation by George Reese Run the simulation using a Java applet Introduction to the problem. The simplest case The other cases An estimate that is very close Questions References Download a graphical simulation program (Macintosh, binhexed) An interesting extension posed by p. ganguly. Send me an email if you think you have an answer. Introduction Buffon's ...

Buffon's Needle refers to a simple Monte Carlo method for the estimation of the value of pi, 3.14159265... The idea is very simple. Suppose you have a tabletop with a number of parallel lines drawn on it, which are equally spaced (say the spacing is 1 inch, for example). Suppose you also have a pin or needle, which is also an inch long.

A formula for Pi which involves just the Fibonacci numbers. It explains from first principles how to use the idea of slope, expressed as tangents of angles, and Gregory's formula for finding angles given' a tangent. Several beautiful and siple formula re derived on the page with investigatory questions to find more formulae. Suitable for 12-15 year olds.

Biography and links to information about Archimedes.

Archimedes' Approximation of Pi One of the major contributions Archimedes made to mathematics was his method for approximating the value of pi. It had long been recognized that the ratio of the circumference of a circle to its diameter was constant, and a number of approximations had been given up to that point in time by the Babylonians, Egyptians, and even the Chinese. There are some authors ...

Highly detailed information about calculating Pi, with enumerations of pertinent formulas.

Information about approximations of Pi using various formulas.