VON NEUMANN’S SAMPLING TECHNIQUE OF THROWING POINTS ON SOME SPECIAL SURFACES UNIFORMLY IN AREA

In this paper, We established three theorems relating to Von Neumann’s sampling technique, and gave some methods to produce random points uniformly in area on certain particular n-dimensional surfaces, such as n-dimensional sphere x₁²+x₂²+…+x_n²=R²,n-dimensional cylinder x₁²+x₂²+…+x_n-1²=R², h₁≤x_n≤h₂ and n-dimensional surfare x_n= (x₁²+x₂²+…+x_n-1²)^1/2, 0≤x_n≤H, etc. And the results are particularly usefull in moute carlo method.