Tangents are used to find the slope of a curve at a certain point, while normals are used to find the equation of a curve at a certain point. Understanding the difference between these two concepts is …
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scala...
We develop the Lorentzian geometry of a crooked halfspace in 2+1-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types, giving an expl...
The Petty projection inequality is a fundamental affine isoperimetric principle for convex sets. It has shaped several directions of research in convex geometry which forged new connections between projection bodies, centroid bodies, and mixed volume...
The classical Petty projection inequality is an affine isoperimetric inequality which constitutes a cornerstone in the affine geometry of convex bodies. By extending the polar projection body to an inter-dimensional operator, Petty's inequality was g...
Line-of-sight (LoS) multiple-input multiple-output (MIMO) gives full spatial-multiplexing gain when the antenna array geometry and orientation are designed based on the inter-terminal distance. These known design methodologies, that hold for antenna...
The torus, a shape as familiar as a donut yet as rich in complexity as the most intricate mathematical concepts, holds a unique place in the study of mathematics.
Aug 3, 2023 · What is a torus in geometry. Learn how to find its surface area and volume with solved examples and diagrams.
We present a natural proof of Kepler's law of ellipses in the spirit of Euclidean geometry. Moreover we discuss two existing Euclidean geometric proofs, one by Feynman in hist Lost Lecture from 1964 and the other by Newton in the Principia of 1687....
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In computational geometry, the minimum bounding rectangle (MBR), also known as bounding box (BBOX) or envelope, is an expression of the maximum extents
Oct 8, 2025 · Adjective bounding (not comparable) (geometry) Containing all points of a given set within it.
computational geometry, a bounding sphere is a special type of bounding volume. There are several fast and simple bounding sphere construction algorithms
In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in
In this paper, we consider whether existence of a sums-of-squares formula depends on the base field. We reformulate the question of existence as a question in algebraic geometry. We show that, for large enough p, existence of sums-of-squares formulas...
Eighteenth century Japan was a time of isolation and peace, where education and the arts blossomed. Originally posted before 1749 by an unknown author, the sangaku (mathematical tablet) that became known as the Gion Shrine problem, has puzzled people...
A distributed graph database architecture that co-exists with the distributed relational DB for I/O and at-scale OLAP expression support with hundreds of PostGIS compatible geometry functions will be discussed in this article. The uniqueness of this...
across geodatabases. The following are a few of the functions built into PostGIS, a free geodatabase which is a PostgreSQL extension (the term 'geometry'
The embedding of finite metrics in $\ell_1$ has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems in which there is close relation between max-flow min-c...
The radio source 18P87, previously thought to be a point source, has been serendipitously found to be resolved into a core-jet geometry in VLA maps. HI absorption of continuum emission (in data from the Canadian Galactic Plane Survey) appears in gas...