Tutorial -- Construction with the Compass Alone with Cabri Java Applets

[[abstract]]Mascheroni dedicated one of his books Geometria del compasso (1797) to Napoleon in verse in which he proved that all Euclidean constructions can be made with compasses alone, so a straight edge in not needed. This theorem was (unknown to Mascheroni) proved in 1672 by a little known Danish mathematician Georg Mohr. In the setting of dynamic geometry, the Mohr-Mascheroni construction asks for specific procedures in which the figure is constructed using the compass alone. In this tutorial the participants are guided through this sort of constructions step-by-step using Cabri Java Applets as the tool. We shall concentrate the constructions of 1) the conics: hyperbola, parabola and ellipse. 2) the epicycloids (the cardioid and the nephroid), hypocycloids (the deltoid and the astroid) and their osculating circles. 3) the Lemniscate of Bernoulli. 4) the Bowditch curve.[[fileno]]2010225030005[[department]]數學