During the summer of 2005 I carried out research into the geometry of the triangle, exploring consequences of a result on statics and barycentric coordinate systems first demonstrated by my supervisor Geoff Smith. This project was financed by a Nuffield Undergraduate Research Bursary, specifically URB/02196/G. More on that scheme can be found at The Nuffield Foundation site.
The main results of this work are contained in my report, Applications of the GPAT to Triangle Geometry, which you can access in [ps] or [pdf] formats according to preference.
The latter part of that work refers to conjectures based on experimentation with the Cinderella geometry package; from this a java applet has been generated which can be accessed here.
Additional applets demonstrating other geometric results are also available on: The Euler Line, The Brocard Points, The Fermat and Nagel points.
For reference, the original papers from which I was working are as follows (all via Forum Geometricorum):