Look Who it Was Random video

Parallels and the double triangle | Universal Hyperbolic Geometry 18 | NJ Wildberger

4,879 views · Published 20 June 2011 · 29:35 · Indexed 3 October 2026

Channel: Insights into Mathematics · 2011 · Education

Watch on YouTube

We discuss Euclid's parallel postulate and the confusion it led to in the history of hyperbolic geometry. In Universal Hyperbolic Geometry we define the parallel to a line through a point, NOT the notion of parallel lines. This leads us to the useful construction of the double triangle of a triangle, and various perspective centers associated to it, the x, y and z points of a triangle. The x and z point lie on the ortho-axis, the y point generally does not.

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

Thanks to EmptySpaceEnterprise for help with contents.

Video Content:
00:00 Introduction and parallels
5:54 Better definitions of parallel lines
9:29 Construction of the parallel
12:57 Double triangle in Euclidean geometry
16:33 Construction of double triangle algebraically
22:41 Second double triangle perspective theorem
24:44 Double dual triangle perspective theorem
26:57 zbhs harmonic range theorem

************
Research Gate page: https://www.researchgate.net/profile/Norman_Wildberger

Blog: http://njwildberger.com/

Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!

Patreon: https://www.patreon.com/njwildberger Your support would be much appreciated.

Wild Egg Maths YT channel:  https://www.youtube.com/channel/UCriFv3G22iOUidUhkIGXuh 

Insights into Mathematics Playlists:

https://www.youtube.com/playlist?list=PLIljB45xT85CL0-5wO4P-OwuH7SzBUyC0 (31 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85B0aMG-G9oqj-NPIuBMnq8z (18 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85DHcleY93bd2WlywQYxHv7H (6 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85AZjh2GUdwsMuAWTEHXCLb- (4 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85DeX148Q2T2elycnIYHTxdP (44 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85A6D0eylgAM4Xc1b_dDTgHW (8 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85DGxj1x_dyaSggbauAgrB6R (226 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85A_VZD126sND3XECDSI-qGs (26 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85DfokRNdx5eQ_qA43BwyM-_ (45 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85CvrEUnhS4dkTm9Lci5JTYS (43 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85D7wczwyUQdwDe2duZ7wPTf (40 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85Ar_tuHmRDI2Xr5tWOTI1oW (55 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85DPSrQpExd2L870ggxd2KEB (34 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85C3-5f6-qQS3YhgygZgnGYs (8 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85D7hfVLKyEJbQxOJ4yYm1-9 (9 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85BtiJIcDF2uuFc7_ndd1UL6 ( 46 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85B6MYBrWldlJ3w-Q1LaEdoy (40 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85DIpzaWggqJDIK8m2u09dQL (7 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85Ag6ragdmHaxUOKcQsIsrXZ (7 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85A5w_vZ5BB1IQAxAMhz5o5S (19 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85BjhYV7QswANMF3gKPx9BqT (21 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85Bi7PvrTkAaAswTwsfsR5HV (10 videos)
https://www.youtube.com/playlist?list=PLIljB45xT85CyF_7bKd6y36VArOy3p2oh (94 videos)

Wild Egg Maths Playlists:

https://www.youtube.com/playlist?list=PLzdiPTrEWyz5m3XKK0OPc31l-GTqDiAjs (4 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz4CVqTYS1fwInPOZxBxDaQf (64 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz7PpsRFHuGb3EhwZtEOdRjV (45 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz6HqaFPB4HTZOQ8jgDAVnuz (20 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz71VHhAIUN-7Y6-JVcwF-xA (8 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz75-t4UaYvHwPe5AHGA_EWe (9 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz5W25vaXSreTMTwpPhWs1w2 (52 videos)
https://www.youtube.com/playlist?list=PLzdiPTrEWyz4DCenuIAr9R2kXLq4ywRAm (9 videos)

More from this channel