Triangle Point Picking -- from Wolfram MathWorld

Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by x=a_1v_1+(1-a_1)a_2v_2, (1) where A_1 and A_2 are uniform variates in the interval [0,1]. However, as can be seen in the plot above, this samples the triangle nonuniformly, concentrating points in the v_1 corner. Randomly picking each of the trilinear coordinates from a uniform distribution [0,1] also does not produce a uniform

ChatGPT and Wolfram Alpha

Triangle - Wikipedia

Recreational mathematics for MichMATYC 10 10

Computing Exact Closed-Form Distance Distributions in Arbitrarily

Line -- from Wolfram MathWorld, line

Will AIs Take All Our Jobs and End Human History—or Not? Well, It's Complicated…—Stephen Wolfram Writings

3.1: The Definite Integral - Mathematics LibreTexts

Mathematics, Free Full-Text

probability - Mean distance from origin of a random point in unit square - Mathematics Stack Exchange

Ternary Diagrams

Angle - Wikipedia

Easy” Excel Inverse Triangular Distribution for Monte Carlo Simulations Redux, by Dawn Wright

Triangle Line Picking -- from Wolfram MathWorld

Triangle Triangle Picking -- from Wolfram MathWorld

Posts Tagged with 'Mathematics'—Wolfram