Euclidean symmetries | Group theory
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d). Point groups are used to describe the symmetries of geometric figures and physical objects such as molecules. Each point group can be represented as sets of orthogonal matrices M that transform point x into point y according to y = Mx. Each element of a point group is either a rotation (determinant of M = 1), or it is a reflection or improper rotation (determinant of M = −1). The geometric symmetries of crystals are described by space groups, which allow translations and contain point groups as subgroups. Discrete point groups in more than one dimension come in infinite families, but from the crystallographic restriction theorem and one of Bieberbach's theorems, each number of dimensions has only a finite number of point groups that are symmetric over some lattice or grid with that number of dimensions. These are the crystallographic point groups. (Wikipedia).
Overview of points lines plans and their location
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
How to label points lines and planes from a figure ex 1
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Naming the rays in a given figure
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Name the opposite rays in the given figure
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
CCSS How to Label a Line, Line Segment and Ray
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
What is a point line and plane
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
How do we label a point line and plane
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Name the segments in the given figure
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Katrin Tent: Sharply 2-transitive groups
Katrin Tent: Sharply 2-transitive groups Abstract Finite sharply 2-transitive groups were classified by Zassenhaus in the 1930s and were shown to have regular abelian normal subgroups. While there were partial results in the infinite setting the question whether the same holds for infini
From playlist Talks of Mathematics Münster's reseachers
Chemistry 107. Inorganic Chemistry. Lecture 02
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 02. Inorganic Chemistry -- Symmetry and Point Groups View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/inf
From playlist Chem 107: Week 1
Lie Groups and Lie Algebras: Lesson 37 - The Fundamental Groups of SU(2) and SO(3)
Lie Groups and Lie Algebras: Lesson 37 - Homotopy Groups of SU(2) and SO(3) In this lesson we discover the Fundamental Group of SU(2) and S0(3) and learn the critical fact that they are not the same. That is, the Fundamental Group associated with the topological space SU(2) is simply conn
From playlist Lie Groups and Lie Algebras
Group theory 32: Subgroups of free groups
This lecture is part of an online mathematics course on group theory. We describe subgroups of free groups, show that they are free, calculate the number of generators, and give two examples.
From playlist Group theory
Emily Stark: The visual boundary of hyperbolic free-by-cyclic groups
Abstract: Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, th
From playlist Topology
Volodymyr Nekrashevych: Contracting self-similar groups and conformal dimension
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 20, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM'
From playlist Dynamical Systems and Ordinary Differential Equations
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
Algebraic topology: Calculating the fundamental group
This lecture is part of an online course on algebraic topology. We calculate the fundamental group of several spaces, such as a ficure 8, or the complement of a circle in R^3, or the group GL3(R). For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EF
From playlist Algebraic topology
Prerequisites I: Groups, Representations & Equivariance - Maurice Weiler
Video recording of the First Italian Summer School on Geometric Deep Learning, which took place in July 2022 in Pescara. Slides: https://www.sci.unich.it/geodeep2022/slides/Groups_Representations_and_Equivariance.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
What is a point a line and a plane
👉 Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
G. Walsh - Boundaries of Kleinian groups
We study the problem of classifying Kleinian groups via the topology of their limit sets. In particular, we are interested in one-ended convex-cocompact Kleinian groups where each piece in the JSJ decomposition is a free group, and we describe interesting examples in this situation. In ce
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie