M.C. Escher was a famous artist who used unique viewpoints in his drawings that moved beyond flat plane surfaces. In his drawings, there are an infinite number of lines parallel to a given line through a point not on the given line. Which geometry did he use as his model?

In hyperbolic geometry, through a point not on a given line, there are infinitely many lines that do not intersect the given line. This matches the description of Escher’s drawings, so the model is hyperbolic geometry. Euclidean geometry has exactly one parallel through the point, while elliptical geometry has none.

AI-written and checked against the verified answer.