MathHistory8: Projective geometry

Projective geometry began with the work of Pappus, but was developed primarily by Desargues, with an important contribution by Pascal. Projective geometry is the geometry of the straightedge, and it is the simplest and most fundamental geometry. We describe the important insights of the 19th century geometers that connected the subject to 3 dimensional space.

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Education

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• MathHistory8
• History
• of
• mathematics
• projective
• geometry
• history
• Pappus
• Desargues
• Pascal
• Poncelet
• von
• Staudt
• Chasles
• Plucker
• Mobius
• Klein
• cross
• ratio
• three
• dimensional
• space
• plane
• Wildberger
• UNSW
• course
• education
• MATH3560
• GENS2005

[madier1000]

I enjoyed this lecture very much and look forward to the whole serie.

[njwildberger]

@madier1000 You might like to know that in my WildTrig series there is a 8-10 part segment on projective geometry, if you are particularly interested in that topic.

[EmanT777]

Hello Professor Wildberger. If my understanding is good, Euclidean, elliptic and hyperbolic geometries are all subgeometries of projective geometry. I've also read somewhere that those same geometries are all subgeometries of Mobius geometry. Are projective geometry and Mobius geometry also somehow related? Thanks.

[njwildberger]

@EmanT777 Yes projective geometry is indeed a unifying framework for other geometries. This is not properly appreciated these days, one of the reasons students often miss out on this important geometry. Projective geometry and Mobius geometry are also closely related. I will discuss such topics in my Universal Hyperbolic Geometry series.

[QuantumMaths]

The girl that walks in at 9:02-9:06 is pretty cute.

[water0heaven]

Epic! This video should be the first ingredients for persons like me, who have never come across projective planes before. Nice work!

[IronHuge]

The alien metaphor is so great, it makes me very happy! Thank you.

[mathofphys]

Hi,would you like to give some comment about the relationship between particle-wave duality in physics and the line-point duality.haha

[EmanT777]

@njwildberger Thanks.

[d3modawid]

Thank you very much for posting these online, Professor! I'm watching them all and I have to say this particular lecture simply blew my mind. I wish I had been introduced to these concepts earlier.