Limit Pathology

thingiverse

This is a model of the graph of a function f(x,y) with the property that the limit as (x,y) -> (0,0) does not exist, despite the fact that limits along linear paths through the origin do exist. The formula for f(x,y) is given below: f(x,y) = cos(2*theta) = (x^2 - y^2) / (x^2 + y^2)