Non – Euclidean Geometry to impress the ladies
“Some of the men stood talking in this room, and at the right of the door a little knot had formed round a small table, the center of which was the mathematics student, who was eagerly talking. He had made the assertion that one could draw through a given point more than one parallel to a straight line; Frau Hagenström had cried out that this was impossible, and he had gone on to prove it so conclusively that his hearers were constrained to behave as though they understood.”
From the short story “Little Herr Friedemann” (1896) by Thomas Mann
A dinner party at von Rinnglingen’s gathers army officers, doctors, lawyers and “all those who had some importance in upper class society”. Among them a young student of Mathematics who employs his information of non – Euclidean Geometries to impress the ladies. According to Playfair’s axiom, which is equivalent to Euclid’s fifth postulate, only one parallel to a straight line can be drawn from a point outside this line. Negation of the postulate gives rise to non – Euclidean Geometries, such as the Hyperbolic Geometry described by Mann’s student, according to which infinite parallels to a straight line can be drawn from a point.