Conway's topograph is a visual representation of the integer points of the projective line. Conway used his topograph to classify binary integer quadratic forms. I have used the topograph in a number theory class to visualize the Euclidean algorithm. During the summer of 2017, Jenna Allen, Jiahao Cao, Douglas Dipaola, Andre Davis, and I wrote a computer program that allows a user to explore Conway's topograph interactively.
Someday I hope to make this program run interactively inside a webpage. For now, you can look at the screenshots below or download the source code. The regions in the screenshots are labelled by the coordinate of an integer point of the projective line and the value of the quadratic form x2 + 2xy + y2 at that point.
