problem0():
  mean and std of random triangle area.

  mean area is    0.44346288406706585
  std of area is  0.40013380234910445

problem1():
  likelihood that random triangle is obtuse..

  number of tests          100
  obtuse triangles         76
  estimated probability =  0.76

problem2():
  draw the polygon graph.
  Graphics saved as "polygon_graph.png"

problem3():
  triangulate polygon graph, compute areas, sum.
  Triangle areas: [2.  2.  2.5 2. ]
  Polygon area  8.500000000000002

problem4():
  triangulate polygon graph, compute centroids,
  compute centroid of polygon by weighted sum.
  Triangle centroids: [[2.66666667 1.66666667]
 [2.         3.33333333]
 [1.         2.33333333]
 [1.33333333 1.        ]]
  Polygon centroid  [1.70588235 2.09803922]

problem5():
  Estimate area of example triangle by random sampling.
  Estimated area of triangle is  19.6736
  Actual area is 20.

problem6():
  estimate integral of f(x,y) over example triangle
  using Monte Carlo method.
  Integral estimate is  6161.939780350342

problem7():
  estimate integral of f(x,y) over example triangle
  using six-point rule.
  Integral estimate is  6053.333333333338

problem8():
  Compute distance from point to triangle.
  Triangle distance for  [2 5]  is  9.930136612989092e-16
  Triangle distance for  [10  3]  is  2.0
  Triangle distance for  [4 5]  is  0.8000000000000007

problem9():
  find intersection of two lines.
  Computed intersection is  [4. 1.]
  Expected intersection is (4,1).