Euclidean geometry | Symmetry | Group theory

One-dimensional symmetry group

A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x. The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram . Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x). The reflections can be represented by the affine Coxeter group [∞], or Coxeter-Dynkin diagram representing two reflections, and the translational symmetry as [∞]+, or Coxeter-Dynkin diagram as the composite of two reflections. (Wikipedia).

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Group Theory II Symmetry Groups

Why are groups so popular? Well, in part it is because of their ability to characterise symmetries. This makes them a powerful tool in physics, where symmetry underlies our whole understanding of the fundamental forces. In this introduction to group theory, I explain the symmetry group of

From playlist Foundational Math

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Visual Group Theory, Lecture 2.2: Dihedral groups

Cyclic groups describe the symmetry of objects that exhibit only rotational symmetry, like a pinwheel. Dihedral groups describe the symmetry of objects that exhibit rotational and reflective symmetry, like a regular n-gon. The corresponding dihedral group D_n has 2n elements: half are rota

From playlist Visual Group Theory

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Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

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Symmetric groups

In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto

From playlist Abstract algebra

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Symmetric Groups (Abstract Algebra)

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in

From playlist Abstract Algebra

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Introduction to Group Theory

A more high brow video. An introduction to group theory - the mathematics of symmetry. This is what I really study.

From playlist My Maths Videos

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Group Theory: The Center of a Group G is a Subgroup of G Proof

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Group Theory: The Center of a Group G is a Subgroup of G Proof

From playlist Abstract Algebra

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Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger

This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk abou

From playlist MathHistory: A course in the History of Mathematics

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Symmetries in QFT and their Relationship with Category Theory (Lecture 3) by Lakshya Bhardwaj

INFOSYS-ICTS STRING THEORY LECTURES SYMMETRIES IN QFT AND THEIR RELATIONSHIP WITH CATEGORY THEORY SPEAKER: Lakshya Bhardwaj (Mathematical Institute, University of Oxford) DATE : 10 October 2022 to 12 October 2022 VENUE: Madhava Lecture Hall (Hybrid) Lecture 1: 10 October 2022 at 3:30 pm

From playlist Infosys-ICTS String Theory Lectures

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Group Theory Package (GTPack) and Symmetry Principles in Condensed Matter: Live with the R&D team

In this stream, we have Group Theory Package (GTPack) and Symmetry Principles in Condensed Matter with Wolfram R&D. Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.facebook.com/wolframresearch/ Instagram: https://

From playlist Live with the R&D Team

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Bridges 2014 talk: The quaternion group as a symmetry group

This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 18th August 2014, about my paper with Vi Hart with the same title. The slides are available at https://www.math.okstate.edu/~segerman/talks/quaternion_group_as_a_symmetry_group.pdf

From playlist 3D printing

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Dominic Else - Emergent Symmetries and Anomalies in Metals: Luttinger's Theorem and Beyond

Séminaire organisé le 23 novembre 2021 Metals are an interesting class of gapless quantum many-body systems. Many metals are described by the famous "Fermi liquid theory" at low temperatures, but there are also many metallic materials for which Fermi liquid theory is an inadequate descrip

From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory

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Strange Pattern in symmetries - Bott periodicity

A strange repeating pattern in the symmetries of circles, spheres and higher dimensional spheres called Bott periodicity. We will learn about symmetries of spheres, homotopy groups, the orthogonal groups and, finally, Bott periodicity. Produced by Connect films https://www.connectfi

From playlist Summer of Math Exposition Youtube Videos

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AMMI Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract group

From playlist AMMI Geometric Deep Learning Course - First Edition (2021)

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SQCD and Pairs of Pants by Shlomo Razamat

PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan

From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)

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AMMI 2022 Course "Geometric Deep Learning" - Lecture 3 (Geometric Priors I) - Taco Cohen

Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 3: Symmetries • Abstract groups • Symmetry groups • Gro

From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)

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Teach Astronomy - Symmetry

http://www.teachastronomy.com/ A lot of fundamental concepts in physics are based on the idea of symmetry. Symmetry is familiar to us in an aesthetic sense. It often means things that have pleasing proportion, or look the same from every direction, or have a harmonious nature about them.

From playlist 23. The Big Bang, Inflation, and General Cosmology 2

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Marcus du Sautoy: Symmetry explained

Marcus Peter Francis du Sautoy is a British mathematician, author, and populariser of science and mathematics. You can view more content of Marcus du Sautoy here: https://www.youtube.com/channel/UCYF21Xc9fSdqVWRxpBAOleQ/featured This video is a clip from the Abel Prize Announcement 2008.

From playlist Popular presentations

Related pages

Infinite dihedral group | Translation (geometry) | Point group | Point groups in two dimensions | Lattice (group) | Symmetry | Discrete symmetry | Level of measurement | Affine geometry | Index of a subgroup | Group (mathematics) | Discrete group | Trivial group | Group isomorphism | Space group | Frieze group | Torus | Coimage | Symmetry group | Dihedral group | Point reflection | Wallpaper group | Coxeter group | Semidirect product | Line group | Normal subgroup | Subset | Bijection | Function composition | Coxeter notation | Fundamental domain | Coset | Reflection (mathematics) | Image (mathematics)