Construct an n-gon (polygon with n sides) for which n given points serve as midpoints of its sides.

Below there is a Java applet that may help you gain insight into the problem. The applet can be in two modes: "Place points" and "Drag mouse", depending on which of the two boxes at the bottom of the applet is checked.

  • In the "Place points" mode you should define n points - midpoints of the sides of a polygon. Just click the mouse anywhere inside the applet's rectangle.
  • Next you can experiment with the points you thus defined. Change the mode and start dragging the mouse.

If, for whatever reason, you decide to work with a different set of points - press the Reset button and start again.

A word of advice. First of all, start with a simple case. Try just a few points, say, 3, 4, 5. Secondly, attempt to visualize a polygon and then place the points approximately at the middle of its sides. Thirdly, pay attention to the blue circle.

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, download and install Java VM and enjoy the applet.

What if applet does not run?


[an error occurred while processing this directive]

|Activities| |Contact| |Front page| |Contents| |Eye opener| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny
[an error occurred while processing this directive]
[an error occurred while processing this directive]