Numb3rs Season 3 Episode 10: Brutus

In this episode several different mathematical topics are mentioned including network valuation theory and area filling problems, but we're going to focus on Euclid's Orchard.

Euclid's Orchard

Euclid's Orchard is a thought experiment involving an imaginary forest of trees. Each tree is an idealized line segment, having length 1, no width or depth, and standing straight up. This forest is on the two-dimensional coordinate plane, and there is a tree standing up at every integer lattice point on this coordinate plane.

Activity 1: Looking into Euclid's Orchard

Imagine that you cut away the tree at the origin and stand at the origin at a height of zero, looking at the trees in the first quadrant (the trees whose x and y coordinates are both non-negative). If one tree is on the line of sight between you and another tree, then the tree in the middle obviously blocks your view of the farther tree.

Dirichlet's Function

Dirichlet's function, which we will denote by f, is a function from the interval to the real numbers. Dirichlet's function is defined by the following:

Activity 2: Graphing

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