Euclidean geometry

Plane symmetry

A plane symmetry is a symmetry of a pattern in the Euclidean plane: that is, a transformation of the plane that carries any direction lines to lines and preserves many different distances. If one has a pattern in the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of considerable mathematical interest. A symmetry plane is a three-dimensional object's symmetry axe. There are several kinds of plane symmetry groups: * Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through the origin. * Rotation groups. These groups consist of rotations around a point. * Translation groups. * Symmetries of geometrical figures. Some of these are reflection groups, e.g., the group of symmetries of the square or the rectangle. The symmetry group of a swastika or any similar figure without an axis of symmetry is a rotation group. (Wikipedia).

Video thumbnail

What are opposite rays

👉 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

Video thumbnail

What are opposite rays

👉 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

Video thumbnail

What are opposite Rays

👉 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

Video thumbnail

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

Video thumbnail

What is a line segment and ray

👉 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

Video thumbnail

What is a Ray and how do we label one

👉 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

Video thumbnail

What is the definition of a ray

👉 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

Video thumbnail

What is a ray

👉 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

Video thumbnail

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

Video thumbnail

What is a segment

👉 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

Video thumbnail

Mod-01 Lec-2 Symmetry in Perfect Solids

Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course

Video thumbnail

MIT 3.60 | Lec 7a: Symmetry, Structure, Tensor Properties of Materials

Part 1: 2D Plane Groups, Lattices (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material

Video thumbnail

Chemistry 107. Inorganic Chemistry. Lecture 01

UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 01. Inorganic Chemistry -- Course Introduction & Symmetry of Nature 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://

From playlist Chem 107: Week 1

Video thumbnail

MIT 3.60 | Lec 4a: Symmetry, Structure, Tensor Properties of Materials

Part 1: 2D Symmetries View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material

Video thumbnail

Chemistry 107. Inorganic Chemistry. Lecture 03

UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 03. Inorganic Chemistry -- Representations and Character Tables 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.

From playlist Chem 107: Week 1

Video thumbnail

MIT 3.60 | Lec 6a: Symmetry, Structure, Tensor Properties of Materials

Part 1: 2D Plane Groups, Lattices (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material

Video thumbnail

11. Mass Moment of Inertia of Rigid Bodies

MIT 2.003SC Engineering Dynamics, Fall 2011 View the complete course: http://ocw.mit.edu/2-003SCF11 Instructor: J. Kim Vandiver License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 2.003SC Engineering Dynamics, Fall 2011

Video thumbnail

MIT 3.60 | Lec 6b: Symmetry, Structure, Tensor Properties of Materials

Part 2: 2D Plane Groups, Lattices (cont.) View the complete course at: http://ocw.mit.edu/3-60F05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 3.60 Symmetry, Structure & Tensor Properties of Material

Video thumbnail

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

Video thumbnail

Mod-01 Lec-3 Symmetry in Perfect Solids (Continued)

Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course

Related pages

Rectangle | Reflection group | Swastika | Euclidean plane | Circle group | Group (mathematics)