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Random Triangles in the Unit Square

Newbie

Random Triangles in the Unit Square

By Patrice LeConte

random_triangles_intheunitsquare.png

  • Determines the probability that a triangle is obtuse if the points are independently and uniformly chosen in a unit square 
  • Academic in nature but various approaches can be used in other fields 
  • Performs using the marginal density function, derivation, integration, symbolic integration, etc.

     This worksheet using PTC Mathcad supposed that three points are independently and uniformly chose in a unit square to determine a unique triangle. This worksheet answers two questions:

  1. What can be said about the probability distribution governing the size of the largest angle in the triangle? 
  2. What is the probability that the triangle is obtuse?

     This worksheet takes you through the math to determine these answers. To solve you must define the region of integration, and then verify them. It shows you how to graph integration of specific members and integrating bounds. All formulas, calculations, and graphs are provided to aid you in your own calculations.

     Download and explore this worksheet yourself! You can download a free lifetime copy of PTC Mathcad Express and get 30 days of full functionality.