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Internal Organs of a Triangle

by Dr Peter Woo
Assoc. Prof., Biola University

The following interactive applet is done by me, and we teach you how to make applets using the language Java. If you don't see a picture, perhaps you are not using a browser such as Netscape 3.0 running on Windows95 that can run Java applets. Sorry. If you see misbehavior, that is a bug. Tell me how I can fix it. If you are interested in my Java code, because you want to modify it, Email me to convince me you are a geometry nut, and I may give it to you.

Please move cursor into the picture, and click the button anywhere, then try the button "Motion", as well as other buttons. What you see is not just art, but geometric truths. Took me many hours to achieve this.

This chapter in geometry exemplifies many interesting things which we teach math students at Biola. In high school they teach you 4 internal centers of any triangle: the centroid, circumcenter, incenter, orthocenter. We at Biola teach you Fermat center, 9-point circle center, Napoleon center, Feuerbach point, Gergonne point, Nagel center, Lemoigne center, Sotty center, Mixtilinear center, and others. Dr Kimberling of Evansville Indiana told me he has collected over 400 such centers.

You notice when the triangle is isosceles, most of the centers are alligned in the line of symmetry. When the triangle is obtuse, the centers are scattered apart. Each center represents a number of theorems, which math majors have to know their proofs.

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