Two 'clocks' - one turning at k revolutions/unit time, the other turning at n revolutions per unit time[br][br] - The BLUE point tracks the vertical position of the hand on one clock and the horizontal position of the hand on the other. [br][br]Use the ORANGE dots to set the initial positions of the hands. Can you make the BLUE dot trace a - [br]- circle [br]- ellipse [br]- straight line w/ positive slope [br]- straight line w/ negative slope [br]- parabola [br]- more complex figures [br][br][i][b]conjectures ? [br][br]proofs? [br][br]extensions ? [/b][/i][br][br][color=#ff0000][i][b]What questions could/would you pose to your students based on this applet ?[/b][/i][/color]

[i][b][size=85]N.B. To hear the notes made by the two oscillators, please download this applet and run it on a version of GeoGebra that runs on your computer.[/size][/b][/i]