MathDB

1

Part of 1985 Spain Mathematical Olympiad

Problems(1)

bijective map where images of lines are lines, and preserve parallels

Source: Spanish Mathematical Olympiad 1985 P1

8/2/2018
Let f:Pā†’Pf : P\to P be a bijective map from a plane PP to itself such that: (i) f(r)f (r) is a line for every line rr, (ii) f(r)f (r) is parallel to rr for every line rr. What possible transformations can ff be?
geometric transformationgeometrytransformation