Скачать или смотреть The group of blue planar isometries | WildTrig: Intro to Rational Trigonometry | N J Wildberger

[This is a reposting of an earlier video which had some technical problems.]

In this video we examine Euclidean (blue) isometries from a rational point of view, concentrating on grounded isometries which fix the origin. We derive basic formulas for projections and reflections with respect to a symmetric bilinear form.

The we introduce reflections in a line through the origin., described or labelled by the rational point on the circle which is the image of the point [1,0], and associated to the rational parameter h, which is the slope of the reflecting line.

This gives us an important interpretation of the famous Weierstrass subsitution in calculus. We end with the formula for the composition of two reflections.

************************
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/...

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/... 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   / njwildberger   Your support would be much appreciated.

Here are the Insights into Mathematics Playlists:

   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  

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

   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
   • Плейлист  
************************