Insights into Mathematics | The perspective image of a square II -- more Projective Geometry! | FMP 18b | N J Wildberger @njwildberger | Uploaded 4 years ago | Updated 2 hours ago
We delve further in Projective Geometry in pursuit of the problem of showing that a general quadrilateral is the perspective image of a square. To prepare the scene, we investigate the role of vanishing points and lines at infinity, first in the two-dimensional case when we project one line onto another, and the in the three-dimensional case when we project one plane onto another.

We also discuss the important situation when a perspectivity becomes a parallel projection, and actually use this to show how to accurately represent the image of a perspectivity, This naturally meets the three-dimensional version of Desargues famous theorem.

Video Contents:
00:00 The perspective image of a square
01:22 Planar perspectivity
05:02 The relative positions of P,__ are flexible
0645 Parallel projections and the point of perspectivity
07:39 Mathematical diagrams with 3D co-ordinate systems and parallel projections
10:39 Three dimensional perspectivity
20:34 Desargues' configuration in space
25:54 Desargues' theorem in the plane

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at researchgate.net/profile/Norman_Wildberger

My blog is at http://njwildberger.com, where I will discuss lots of foundational issues, along with other things.

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Here are the Insights into Mathematics Playlists:

youtube.com/playlist?list=PL55C7C83781CF4316
youtube.com/playlist?list=PL3C58498718451C47
youtube.com/playlist?list=PL5A714C94D40392AB
youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw
youtube.com/playlist?list=PL8403C2F0C89B1333
youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa
youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
youtube.com/playlist?list=PL6763F57A61FE6FE8
youtube.com/playlist?list=PLBF39AFBBC3FB30AF
youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW
youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7

Here are the Wild Egg Maths Playlists (some available only to Members!)

youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
youtube.com/playlist?list=PLzdiPTrEWyz4VlOppC5CN0D0GjrjvBGKy
youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
youtube.com/playlist?list=PLzdiPTrEWyz6zpIZ4Y_RK9zyJ9OufqNJv
youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6
youtube.com/playlist?list=PLzdiPTrEWyz5j1BJdXBw1MFst_nQAqzZ_
youtube.com/playlist?list=PLzdiPTrEWyz5HWgaVkhIwpGVKi6fciRxW
youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM
youtube.com/playlist?list=PLzdiPTrEWyz7LKbuJAHaXAhRj2ylD0OoX
youtube.com/playlist?list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
youtube.com/playlist?list=PLzdiPTrEWyz6MwUTOHRgC0oIxVtaHGQBd
youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C
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