made by unbread on Jan 8, 2008

Oh, I just thought of another problem/interesting thing. My geologist …

Oh, I just thought of another problem/interesting thing.

My geologist friend what over and looking at some publishings on minerals. I asked here what all the triangles with dots in them represented. See said they showed the percentage(placement) of each of 3 minerals for a rock(dot). I'm sure I have the geology part of it wrong but the math part I understood. Each vertex represented a mineral. The closer the dot to the vertex the more the percentage of that mineral, and the closer to the opposite line the less of that mineral (an therefore more of the others). I was curious if the middle (33.3% of each) really was at a height 1/3rd of the altitude. With some simple geometry you can see that it is. I asked if they ever have 4 minerals. She said yes, but then it has to be a pyramid shape. I asked if she meant a tetrahedron, and she said yes (after I made one out of string with my fingers holding the vertices). I was curious then if the center of the polyhedral was really 1/4th the height of the altitude. After even more geometry i found it was. Where I get stuck is when I try to see if it works for a 4-dimensional tetrahedron (is it a hyper tetrahedron?), i.e. the center is 1/5th the altitude.