Question

Projective Geomentry

Draw two coaxial triangles where the axis is ideal. Explain how you could use a perspectivity to map any pair of coaxial triangles to a pair of coaxial triangles where the axis is ideal.

Answer 1

If two or more three dimensional forms share a common axis , it is said to be linear.

A perspectivity is a projectivity fixing the points of a line called the axis of perspectivity and leaving invariant through all the points of the line called center of perspectivity.

To map a pair of coaxial triangles to another pair, the steps are:

1. Let ABC and CDE are two triangles.By Desargues theorem, the two triangles intersect at C1, C2, C3.

2. Line containing three points coincides with axis of perspectivity.

3.The three points are fixed of point F. This implies all the points are fixed of F.

4. Perspectivity is completely described by a line that has fixed points in it.