Moments of Distance from a Vertex to a Uniformly Distributed Random Point within Arbitrary Triangles

Table 1

Error of the simulation results and the theory results. Here IsosRight means the isosceles right triangle case. All error rates are reported here in percentiles. In each round of simulation studies, points are sampled within each triangle, and the summary statistics reported in this table are calculated from repetitions.

Triangle
Acute	0.405	0.693	0.952	1.199	0.657	1.181	2.135	2.925	3.591	1.741
Obtuse	0.543	1.013	1.482	1.916	0.718	1.867	3.536	5.363	7.008	2.217
Isosceles	0.303	0.526	0.712	0.868	0.674	1.055	1.715	2.277	2.694	2.131
Right	0.452	0.851	1.233	1.627	0.683	1.606	3.042	4.568	6.099	2.438
IsosRight	0.382	0.657	0.906	1.154	0.622	1.373	2.228	2.887	3.608	2.287