This is the full lecture of a seminar on a new way of thinking about Hyperbolic Geometry, basically viewing it as relativistic geometry projectivized, that I gave a few years ago at UNSW. We discuss three dimensional relativistic space and its quadratic/bilinear form, particularly the upper sheet of the two sheeted hyperbola, which is a Riemannian manifold under the induced metric from the Lorentzian quadratic form x^2+y^2-z^2. Two views give the Poincare and Klein models (both due to Beltrami!) and it is the latter that we extend to include the entire projective plane.
We discuss some related projective geometry, harmonic ranges and cross ratio, introduce the main metrical notions of quadrance and spread, illustrate with diagrams of circles, connect with classical notions of distance and angle, and state the main laws of trigonometry as well as some important secondary results, such as the Parallax theorem.
We explain the Null perspective theorem and related null trigonometric results, the 48/64 theorem and finish with the remarkable Jumping Jack theorem---my personal favourite theorem in mathematics.
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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 https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
Here are the Insights into Mathematics Playlists:
https://www.youtube.com/playlist?list=PL55C7C83781CF4316
https://www.youtube.com/playlist?list=PL3C58498718451C47
https://www.youtube.com/playlist?list=PL5A714C94D40392AB
https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
https://www.youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw
https://www.youtube.com/playlist?list=PL8403C2F0C89B1333
https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
https://www.youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa
https://www.youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
https://www.youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW
https://www.youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7
Here are the Wild Egg Maths Playlists (some available only to Members!)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
https://www.youtube.com/playlist?list=PLzdiPTrEWyz4VlOppC5CN0D0GjrjvBGKy
https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
https://www.youtube.com/playlist?list=PLzdiPTrEWyz6zpIZ4Y_RK9zyJ9OufqNJv
https://www.youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6
https://www.youtube.com/playlist?list=PLzdiPTrEWyz5j1BJdXBw1MFst_nQAqzZ_
https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HWgaVkhIwpGVKi6fciRxW
https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM
https://www.youtube.com/playlist?list=PLzdiPTrEWyz7LKbuJAHaXAhRj2ylD0OoX
https://www.youtube.com/playlist?list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
https://www.youtube.com/playlist?list=PLzdiPTrEWyz6MwUTOHRgC0oIxVtaHGQBd
https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
https://www.youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C
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