Topology of Numbers · Problem 4.2.2

Classification of Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · topograph-separator-line

Problem

For the following quadratic forms, draw enough of the topograph, starting with the edge separating the

^1\!/_0

and

^0\!/_1

regions, to locate the periodic separator line, and include the separator line itself in your topograph. (a)

x^2 + 3xy + y^2

(b)

6x^2 + 18xy + 13y^2

(c)

37x^2 - 104xy + 73y^2