This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and high school algebra, and avoiding all "infinite processes", "real numbers" and other modern fantasies. The course will be carefully framed on careful definitions, explicit examples and concrete computations.
In this lecture, we continue to introduce the fundamental definition for signed area. We begin by discussing the differences between different levels of geometry, and then also introduce important terminology for oriented objects in planar geometry. And we introduce the single most important definition in the algebraic integral calculus.
************************
Screenshot PDFs for my videos are available at the website [ Ссылка ]. 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 [ Ссылка ]
My blog is at [ Ссылка ], 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 [ Ссылка ] Please join us for an exciting new approach to one of mathematics' most important subjects!
************************
Video Contents:
0:00 Intro
0:13 Affine geometry and Projective geometry
4:50 Area is an affine concept
8:47 Sides and triangles
14:50 A triangle
17:41 An oriented triangle
20:59 The really crucial formula
************************
Here are the Wild Egg Maths Playlists (some available only to Members!)
Algebraic Calculus One (for the Open Learning Course) : [ Ссылка ]
Algebraic Calculus Two (for the Open Learning Course in preparation): [ Ссылка ]-
Advice for Mathematics Exploration (for Members only): [ Ссылка ]
Solving Polynomial Equations (Members only): [ Ссылка ]
Hexagrammum Mysticum (Members only): [ Ссылка ]_
Algebraic Calculus and de Casteljau Bezier curves (Members only): [ Ссылка ]
Exceptional Structures in Maths and Physics via Dynamics on Graphs (Members only): [ Ссылка ]
Maxel Inverses and Orthogonal Polynomials (for Members only): [ Ссылка ]
Triangle Centres: [ Ссылка ]
Six: An elementary course in pure mathematics: [ Ссылка ]
***********************
Here are the Insights into Mathematics Playlists:
Maths and Music: [ Ссылка ]
Diffusion Symmetry: [ Ссылка ]
Elementary Mathematics (K-6) Explained: [ Ссылка ]?
list=PL8403C2F0C89B1333
Playing Go: [ Ссылка ]
Year 9 Maths: [ Ссылка ]
Ancient Mathematics: [ Ссылка ]
Wild West Banking: [ Ссылка ]
Sociology and Pure Mathematics: [ Ссылка ]
Math History: [ Ссылка ]
Wild Trig: Intro to Rational Trigonometry: [ Ссылка ]
MathFoundations: [ Ссылка ]
Wild Linear Algebra: [ Ссылка ]
Famous Math Problems: [ Ссылка ]
Probability and Statistics: An Introduction: [ Ссылка ]
Boole's Logic and Circuit Analysis: [ Ссылка ]
Universal Hyperbolic Geometry: [ Ссылка ]
Differential Geometry: [ Ссылка ]
Algebraic Topology: [ Ссылка ]
Math Seminars: [ Ссылка ]
