Half-full and Half-empty

A thought experiment: Suppose you had a container with a rectangular base whose length runs from x = a to x = b, with a width of one-inch. The container has four vertical rectangular sides. You put a piece of, say, plastic into the container which fits snugly along the bottom and four sides. The…

Most Triangles Are Obtuse!

What is the probability that a triangle picked at random will be acute? An average value problem. The thing here is to define what you mean by picking a triangle “at random.” You could open a Geometry book and take the first triangle you come to, but are the triangles in a Geometry book really…