Summary

A pseudosphere is a surface with constant negative curvature. This model is half of a surface of revolution obtained by revolving the tractrix y=a*ln((a+sqrt(a^2-x^2))/x)-sqrt(a^2-x^2) about the y-axis. To complete the model, print two and glue them together along the flat disk bases. https://en.wikipedia.org/wiki/Pseudosphere
https://en.wikipedia.org/wiki/Tractrix