proof of Pappus’s theorem
Pappus’s theorem says that if the six vertices of a hexagon lie alternately on two lines, then the three points of intersection of opposite sides are collinear. In the figure, the given lines are and , but we have omitted the letter .
The appearance of the diagram will depend on the order in which the given points appear on the two lines; two possibilities are shown.
No three of the four points , , , and are collinear, and therefore we can choose homogeneous coordinates such that
That gives us equations for three of the lines in the figure:
These lines contain , , and respectively, so
for some scalars . So, we get equations for six more lines:
|Title||proof of Pappus’s theorem|
|Date of creation||2013-03-22 13:47:40|
|Last modified on||2013-03-22 13:47:40|
|Last modified by||mathcam (2727)|