Professor Gilbert Strang
Massachusetts Institute of Technology
Are Most Triangles Acute or Obtuse?
This talk has two separate parts, both about shapes. First, we ask how a change from circle to polygon affects the solution to a differential equation inside. Key examples are the eigenvalue problem for Laplace's equation, and Poisson's equation u_xx + u_yy = 1. The area between the circle and polygon becomes a crucial quantity and we ask how this leading term in the error might be removed--to improve the accuracy of the eigenvalues and the solution.
Part 2 is about an innocent question--Is a random triangle acute or obtuse? Everything depends on the meaning of "random." Are the angles random or the sides? Is the distribution uniform or normal? New answers keep coming, and some are surprising.