Circle and Hyperbola As Lighthouse Curves
A Mathematical Droodle

Two lines rotate with constant angular velocities around two points in a plane. (An apt metaphore of two lighthouses was invented by R. K. Guy of the University of Calgary.) The point illuminated by two beams traces a curve. What is it?

Equal angular velocities:


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

Opposite angular velocities


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

Explanation

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

For circles, the explanation is based on the equality of the inscribed angles subtended by the same arc.

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

71491755