Date of Award
Union College Only
Bachelor of Science
plane, define, gaussian, infinity, number
The following popular question from number theory motivated this paper: ”Can someone with finite step size walk to infinity while restricting his or her possible steps to prime numbers?” We will show the answer to be ”No,” before expanding the problem. If instead of looking at the real number line we look at the complex plane, the problem becomes much harder. First, we must define the ”Gaussian integers” of this plane and then define what makes a Gaussian integer prime. Next, we will prove that by limiting the walker’s range of motion to sectors of the plane, the walker can never reach infinity. We will also show that the union of these sectors is arbitrarily close to the entire plane.
Cohen, Steve, "A study of Gaussian integers" (2008). Honors Theses. 1518.