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.
|What if applet does not run?|