The cross ratio | 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.
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Видео The cross ratio | WildTrig: Intro to Rational Trigonometry | N J Wildberger канала Insights into Mathematics