A Coxeter decomposition of a polygon is a decomposition into a finite number of polygons in which any two sharing a side are reflections of each other along that side. Hyperbolic polygons are the analogues of Euclidean polygons in hyperbolic geometry. A hyperbolic n-gon is an area bounded by n segments, rays, or entire straight lines. The standard model for this geometry is the Poincaré disk model. A major difference between Euclidean and hyperbolic polygons is that the sum of internal angles of a hyperbolic polygon is not the same as Euclidean polygons. In particular, the sum of the angles of a hyperbolic triangle is less than 180 degrees. Coxeter decompositions are named after Harold Scott MacDonald Coxeter, an accomplished 20th century geometer. He introduced the Coxeter group, an abstract group generated by reflections. These groups have many uses, including producing the rotations of Platonic solids and tessellating the plane. (Wikipedia).
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation of Hyperbolic Functions
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions.
From playlist Using the Properties of Hyperbolic Functions
Diophantine analysis in thin orbits - Alex Kontorovich
Special Seminar Topic: Diophantine analysis in thin orbits Speaker: Alex Kontorovich Affiliation: Rutgers University; von Neumann Fellow, School of Mathematics Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Graph coloring problem and fibering right angled Coxeter groups - Kasia Jankiewicz
Women and Mathematics Title: Graph coloring problem and fibering right angled Coxeter groups Speaker: Kasia Jankiewicz Affiliation: McGill University Date: May 19, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Homological Algebra(Homo Alg) 5 by Graham Ellis
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Petrie polygons of a polyhedron | Universal Hyperbolic Geometry 52
John Flinders Petrie was the son of the famed Egyptologist Flinders Petrie, and a good friend of Donald Coxeter. He discovered lovely polygonal paths on polytopes or polyhedra, that in the case of the Platonic solids have remarkable properties when we project these solids orthogonally onto
From playlist Universal Hyperbolic Geometry
Sophie Morel - Intersection cohomology of Shimura varieties and pizza
Correction: The affiliation of Lei Fu is Tsinghua University. Given a disc in the plane select any point in the disc and cut the disc by four lines through this point that are equally spaced. We obtain eight slices of the disc, each having angle π/4 at the point. The pizza theorem says th
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
Using composition of inverses using triangles
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Composition of inverses using a triangle with variables
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Hyperbolic trigonometric functions
Definition of the hyperbolic sine and cosine functions from solving second-order differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differe
From playlist Differential Equations
Null points and null lines | Universal Hyperbolic Geometry 12 | NJ Wildberger
Null points and null lines are central in universal hyperbolic geometry. By definition a null point is just a point which lies on its dual line, and dually a null line is just a line which passes through its dual point. We extend the rational parametrization of the unit circle to the proj
From playlist Universal Hyperbolic Geometry
Converting the Rectangular Equation x^2 + y^2 = 4 into Polar Form
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Converting the Rectangular Equation x^2 + y^2 = 4 into Polar Form
From playlist Trigonometry
Representation theory and geometry – Geordie Williamson – ICM2018
Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor
From playlist Plenary Lectures
Jeff Erickson - Lecture 2 - Two-dimensional computational topology - 19/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Jeff Erickson (University of Illinois at Urbana-Champaign, USA) Two-dimensional computational topology - Lecture 2 Abstract: This series of lectures will describe recent
From playlist Jeff Erickson - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Using triangles to evaluate for compositions of inverse functions
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
How to find all the solutions to a trigonometric equation
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Taking the Square Root
Evaluate the composition of sine and sine inverse
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Geometric graph theory: Weyl Groups, Root Systems and Quadratic Forms
In this video we explore the geometry of a graph coming from a combinatorial game. By playing the Mutation Game on populations on a graph, i.e. integer valued functions on the vertices, we can generate special populations which form a root system. In the ADE cases these are well-studied, f
From playlist MathSeminars