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Articles 1 - 5 of 5
Full-Text Articles in Mathematics
Integrating Non-Euclidean Geometry Into High School, John Buda
Integrating Non-Euclidean Geometry Into High School, John Buda
Honors Thesis
The purpose of this project is to provide the framework for integrating the study of non-Euclidean geometry into a high school math class in such a way that both aligns with the Common Core State Standards and makes use of research-based practices to enhance the learning of traditional geometry. Traditionally, Euclidean geometry has been the only strand of geometry taught in high schools, even though mathematicians have developed several other strands. The non-Euclidean geometry that I focus on in this project is what is known as taxicab geometry. With the Common Core Standards for Math Practice pushing students to “model …
Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden
Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden
Journal of Catholic Education
Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical piazza of Saint Peter's Basilica at Vatican City within Rome, Italy.
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Mathematics Faculty Works
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.
Epimorphisms And Boundary Slopes Of 2–Bridge Knots, Jim Hoste, Patrick D. Shanahan
Epimorphisms And Boundary Slopes Of 2–Bridge Knots, Jim Hoste, Patrick D. Shanahan
Mathematics Faculty Works
In this article we study a partial ordering on knots in S3 where K1≥K2 if there is an epimorphism from the knot group of K1 onto the knot group of K2 which preserves peripheral structure. If K1 is a 2–bridge knot and K1≥K2, then it is known that K2 must also be 2–bridge. Furthermore, Ohtsuki, Riley and Sakuma give a construction which, for a given 2–bridge knot Kp∕q, produces infinitely many 2–bridge knots Kp′/q′ with Kp′∕q′≥Kp∕q. After characterizing all 2–bridge knots …
Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg
Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg
Mathematics Faculty Works
We introduce a new formalism of exact triples of triangulated categories arranged in certain types of diagrams. We prove that these arrangements are well-behaved relative to the process of gluing and ungluing t-structures defined on the indicated categories and we connect our con. structs to· a problem (from number theory) involving derived categories. We also briefly address a possible connection with a result of R. Thomason.