Aside from the centroid, the ancient Greeks also were fascinated by three other triangle centers: the triangle's incenter, circumcenter, and orthocenter.  Centuries passed before a fifth triangle center surfaced: the Fermat point.  During the nineteenth century, more triangle centers entered the literature, and then the people didn't talk much about them for a period of time.  New triangle centers are once again popping out, often with the help of computers. In the 1980s, it seemed that all these special points shared some general properties that should form the basis for a formal definition of triangle center.

For extra credit:
(You may do as many as five different constructions – only 3 can be classical centers – the other two must be 20^th century centers.  Each completed construction (as described below) is worth 5 points.  Only two constructions can be placed in any one grade category!)

1.       Pick a triangle center from the ones above. 

2.     Open a Word document, put your name at the top, and title your extra  credit the name of the triangle center that you plan to create.

3.     In the Word document, describe the triangle center that you will create- how it is to be constructed, any special properties that it has, and any interesting things about that center.

4.      Using Geometer's Sketchpad, construct a triangle and the center that you have chosen.  When you know how to make the sketch, record a script for your construction and save it to your disk.

5.      Copy your triangle center construction into your Word document.

6.      At the bottom of the document identify  :

• the script's file name
• the name of the file where the actual  construction can be found, and
• the grade category that you want to put the points in.

7.    Hand in your print-out and your disk.