Investigation for an Alternate Construction of a Projectivity
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
—
Felix Klein (1849–1925)
4.6
Interactive Diagram for the
Investigation for an Alternate
Construction of a Projectivity
Thus, in a sense, mathematics has been most
advanced by those who distinguished themselves by intuition rather than by
rigorous proofs.
—Felix Klein (1849–1925)
In the given diagram, the two pencils of points are projectively related. Consider the points AB' · BA', AC' · CA', AD' · DA', BC' · CB', BD' · DB', and CD' · DC'. (The pairs of lines, such as AB' and BA', are called cross joins.) How are the points they related to each other?
How are the intersections of each pair of cross joins related?
Drag the points A, B,
C, D, A',
B', and C'. How are the points related to each other? State your result as a conjecture.
Timothy Peil, 6 February 2013, Created with GeoGebra |
4.6 Investigation Activity
4.6
Alternate Construction
of a Projectivity
© Copyright 2013 -
Timothy Peil