Why do people denote this center by G? Interestingly, it, in fact, is the center of Gravity of a triangle made by homogeneous material. In other words, if we put of tiny pivot at this center G, the homogeneous triangle will keep balance on this pivot. Mathematically, it is because the six small triangles formed by the three medians have the same area, i.e., the medians of a triangle separate that triangle into 6 smaller triangles of equal area. I searched for this proof online. I think Karl Mealor did a good job in this proof: http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/writeup4/assignment4.html

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