WT40: The fundamental theorem of projective geometry

The fundamental theorem of projective geometry states that any four planar non-collinear points (a quadrangle) can be sent to any quadrangle via a projectivity, that is a sequence of perspectivities. We prove this by first establishing the simpler one-dimensional case of three points on a projective line.

This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry.

Category:

Science & Technology

Tags:

• Mathematics
• geometry
• projective
• foundations
• fundamental
• theorem
• quadrangle
• projectivity
• perspectivity
• Wildberger

[MrFunatabi]

In the diagram that was explained around 5:00, if I exchange B" and C", it seems I need an extra line through A'' for another intermediate perspectivity. Is there a way to do it in less steps?

[jakbarzel]

thank you, these videos are very helpful .

[786HKHM]

Thanks you. I think this one more time to get it.