Barycentric coordinates and subtractive arithmetic of vectors | Algebraic Calculus and dCB Curves 9

We introduce a consistent arithmetic of affine points and vectors, following a recent paper of J. C. Ho and myself, entitled A case study in Universal Geometry: extending Apollonian circles to relativistic geometry and finite fields (2020). You can have a look at the full paper at https://www.researchgate.net/publicat... Then we show how this arithmetic provides a useful tool for understanding the geometry of de Casteljau Bezier polygons and their associated dCB curves. This video is part of the Algebraic Calculus and the geometry of de Casteljau Bezier curves series of videos, whose Playlist is    • Playlist   Please consider becoming a Member of the Wild Egg Maths (YouTube) channel at    / @wildeggmathematicscourses   to access all the videos that will be posted in this series, along with many others. These include how to solve general polynomial equations, and how to create exceptional structures in mathematics and physics through dynamics on graphs, along with advice on being an amateur mathematician / graduate student in the subject. Also extra pdf and worksheet resources will be available to Members there. Lots to learn and do, so please join us. :) And the exciting Algebraic Calculus One online course is now open at https://www.openlearning.com/courses/... Join us for an exciting new approach to one of mathematics' most important subjects. Dozens of rich hours or learning and activity await you with this novel, powerful and beautiful treatment. ************************ 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 discuss lots of foundational issues, along with other things. 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 all the Insights into Mathematics Playlists: Sociology and Pure Mathematics:    • Playlist   MathFoundations:    • Playlist   Year 9 Maths:    • Playlist   Wild West Banking:    • Playlist   Wild Linear Algebra:    • Playlist   Famous Math Problems:    • Playlist   Elementary Mathematics (K-6) Explained:    / playlist   list=PL8403C2F0C89B1333 Ancient Mathematics:    • Playlist   Boole's Logic and Circuit Analysis:    • Playlist   Math History:    • Playlist   Wild Trig: Intro to Rational Trigonometry:    • Playlist   Universal Hyperbolic Geometry:    • Playlist   Old Babylonian Mathematics (with Daniel Mansfield):    / playlist   list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov Differential Geometry:    • Playlist   Algebraic Topology:    • Playlist   Probability and Statistics: An Introduction:    • Playlist   Math Seminars:    • Playlist