Pappus’s theorem (original) (raw)
Let A,B,C be points on a line (not necessarily in that order) and let D,E,F points on another line (not necessarily in that order). Then the intersection
points of AD with FC, DB with CE, and BF with EA, are collinear
.
Remark. Pappus’s theorem is a statement about the incidence relation between points and lines in any geometric structure
with points, lines, and an incidence relation between the points and the lines. Generally speaking, an incidence geometry is Pappian or satisfies the Pappian property if the statement of Pappus’s theorem is true. In both Euclidean and affine geometry
, Pappus theorem is true. In plane projective geometry
, both Pappian and non-Pappian planes exist. Furthermore, it can be shown that every Pappian plane is Desarguesian, and the converse
is true if the plane is finite (the result of Wedderburn’s theorem).
| Title | Pappus’s theorem |
|---|---|
| Canonical name | PappussTheorem |
| Date of creation | 2013-03-22 12:25:01 |
| Last modified on | 2013-03-22 12:25:01 |
| Owner | drini (3) |
| Last modified by | drini (3) |
| Numerical id | 9 |
| Author | drini (3) |
| Entry type | Theorem |
| Classification | msc 51A05 |
| Synonym | Pappus Theorem |
| Related topic | PascalsMysticHexagram |
| Related topic | Collinear |
| Related topic | Concurrent |
| Defines | Pappian |
| Defines | Pappian property |