Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Hyperbolic Geometry (2)
- Abstract Algebra (1)
- Algebraic Geometry (1)
- Algorithms (1)
- Bipartite graphs (1)
-
- Graph methods (1)
- Graph theory (1)
- Gröbner bases (1)
- Henri Poincaré (1)
- Henri Poincaré 1854-1912 (1)
- Hermitian structures (1)
- Hyperbolic Differential equations (1)
- Ideals (Algebra) (1)
- Leonhard Euler (1)
- Matrices (1)
- Möbius transformations (1)
- Non-Euclidean Geometry (1)
- Parameter estimation (1)
- Polynomial rings (1)
- Varieties (Universal algebra) (1)
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
The Euler Line In Non-Euclidean Geometry, Elena Strzheletska
The Euler Line In Non-Euclidean Geometry, Elena Strzheletska
Theses Digitization Project
The main purpose of this thesis is to explore the conditions of the existence and properties of the Euler line of a triangle in the hyperbolic plane. Poincaré's conformal disk model and Hermitian matrices were used in the analysis.ʹ
Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren
Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren
Theses Digitization Project
The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.
The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha
The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha
Theses Digitization Project
Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.
Hyperbolic Transformations On Cubics In H², Frank S. Marfai
Hyperbolic Transformations On Cubics In H², Frank S. Marfai
Theses Digitization Project
The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).