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[4] viXra:2112.0139 [pdf] submitted on 2021-12-25 21:29:24
Authors: James A. Smith
Comments: 5 Pages.
“You can’t add things that are of different types!” This objection to the “addition” of scalars and bivectors—which is voiced by physicists as well as students—has been a barrier to the adoption of Geometric Algebra. We suggest that the source of the objection is not the operation itself, but the expectations raised in critics’ minds by the term “addition”. Indeed, the ways in which this operation interacts with others are unlike those of other “additions”, and might well cause discomfort to the student. This document explores those potential sources of discomfort, and notes that no problems arise from this unusual “addition” because the developers of GA were careful in choosing the objects (e.g. vectors and bivectors) employed in this algebra, and also in defining not only the operations themselves, but their interactions with each other. The document finishes with an example of how this “addition” proves useful.
Category: Geometry
[3] viXra:2112.0108 [pdf] submitted on 2021-12-20 15:54:11
Authors: Saburou Saitoh
Comments: 6 Pages.
In this note, we would like to refer simply to the great history of Euclidean geometry and as a result we would like to state the great and essential development of Euclidean geometry by the new discovery of division by zero and division by zero calculus. We will be able to see the important and great new world of Euclidean geometry by Hiroshi Okumura.
Category: Geometry
[2] viXra:2112.0091 [pdf] submitted on 2021-12-16 21:03:01
Authors: Gerasimos T. Soldatos
Comments: 9 Pages.
This article tackles the problem of quadrature through reductio ad impossibile in the form of proof by contradiction. The general conclusion is that an irrational number is irrational on the real plane, but in the three-dimensional world, it is as a vector the image of one at least constructible position vector, and through the angle formed between them, constructible becomes the “irrational vector” too, as a right-triangle side.
Category: Geometry
[1] viXra:2112.0063 [pdf] submitted on 2021-12-12 05:24:55
Authors: Hiroshi Okumura
Comments: 3 Pages.
We show that there are seven Archimedean circles with 6-fold symmetry for the arbelos.
Category: Geometry
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