Points and Lines in the Affine Plane | Algebraic Calculus One | Wild Egg

This is the first lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and high school algebra. The course will be carefully framed on careful definitions, explicit examples and concrete computations.

In this first rather introductory lecture, we introduce the basic geometric framework of the affine grid plane, or Cartesian coordinate geometry, and review what hopefully should be familiar concepts around points and lines. But we will also introduce a perhaps novel point of view coming from projective geometry, employing the important ideas of proportions.

This first lecture has two parts. The second part is given by Anna Tomskova and is Projective Points and Lines.

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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.

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Video Contents:
0:00 Intro
0:13 Algebraic Calculus and Linear Algebra
3:28 An affine point
5:58 An affine line
8:28 The point lies on the line
11:10 Collinear points and concurrent lines
12:39 Proportions
16:40 Proposition

Видео Points and Lines in the Affine Plane | Algebraic Calculus One | Wild Egg канала Wild Egg Maths