Table of Contents:
The Bridges of Konigsberg
The Value of Pi
Prime Numbers
Famous Paradoxes
The Problem of Points Proof of the Pythagorean Theorem

Squaring the circle is one of the three great problems of Classical Geometry, along with the trisection of the angle and the duplication of the cube. Since 1800 B.C. mathematicians have worked on the problem of constructing a square equal in area to that of a given circle. Whether or not this is possible depends, of course, on what tools you allow yourself. Plato insisted that the problem be solved with straightedge and compass only. To achieve this requires constructing a length equal to sqrt(pi) times the radius of the circle. Thus when Lindemann proved in 1882 that Pi is transcendental (not the root of any polynomial with rational coefficients) he effectively proved that the construction was impossible with only straightedge and compass.
This applet was created using a prototype of JavaSketchpad, a WorldWideWeb component of The Geometer's Sketchpad. Copyright ©19901998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work are being funded by the National Science Foundation (awards DMI 9561674 & 9623018).
to A Chronological Table of Values Attributed to Pi

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