Geometry, Volume 1, Issue 1 (December 2024) – 2 articles

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13 pages, 303 KiB  
Article
Unary Operations on Homogeneous Coordinates in the Plane of a Triangle
by Peter J. C. Moses and Clark Kimberling
Geometry 2024, 1(1), 3-15; https://doi.org/10.3390/geometry1010002 - 8 Jul 2024
Viewed by 175
Abstract
Suppose that X is a triangle center with homogeneous coordinates (barycentric or trilinear) x:y:z. Eight unary operations discussed in this paper include [...] Read more.
Suppose that X is a triangle center with homogeneous coordinates (barycentric or trilinear) x:y:z. Eight unary operations discussed in this paper include u1(X)=(yz)/x:(zx)/y:(xy)/z. For each ui, there exist, formally, two points, P and U, such that ui(P)=ui(U)=X. To such pairs of inverses are applied nine binary operations, each resulting in a triangle center. If L is a line, then formally, ui(L) is a cubic curve that passes through the vertices A,B,C. If L passes through the point 1:1:1 (the centroid or incenter, assuming that the coordinates are barycentric or trilinear), then the cubic is degenerate as the union of a parabola and the line at infinity. The methods in this work are largely algebraic and computer-dependent. Full article
2 pages, 297 KiB  
Editorial
Geometry: A Bridge Connecting All Things
by Yang-Hui He
Geometry 2024, 1(1), 1-2; https://doi.org/10.3390/geometry1010001 - 29 May 2024
Viewed by 357
Abstract
In the ancient realm of geometry, we have witnessed the ultimate display of mathematical abstract thought [...] Full article
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