VISIBLES PROJECT

 

  1. Give the definition and examples of visible points.

 

  1. Include the proof that a lattice point (x,y) is visible if and only if  gcd(x,y) = 1.

 

  1. Include an m-file that figures out how may visible points there are in a user-specified rectangle and then calculates the ratio of visibles to lattice points in that rectangle. This program should also have a graphical output showing the actual visible points in some nice way.

 

  1. Point out and explain some of the patterns in the graphical (printed) display of visibles.

 

  1. For extra credit, see me about calculating the limiting ratio of visibles to lattice points in large rectangles. This is more challenging and is not required. Even more technical information can be found in

 

http://www.math.neu.edu/~zelevinsky/bridgzel.pdf