Playground

PG(2, q) explorer

The projective plane PG(2, q) has q² + q + 1 points [x : y : z] with coordinates in GF(q), and as many lines [a : b : c]; a point lies on a line when ax + by + cz = 0. One view lays the points out by coordinates, the other by Singer number: point i is the point of αⁱ in GF(q³). In the Singer numbering every line is a translate D + j of one difference set D. Click two points or two lines. The address bar keeps your choices, so you can share a view.

Background: Lesson 10 (vectors over GF(q)), Lesson 11 (coordinates), Lesson 12 (the Singer numbering), and Lesson 13 (the Singer cycle).