Euclidean geometry | Affine geometry | Linear algebra

Flat (geometry)

In geometry, a flat or Euclidean subspace is a subset of a Euclidean space that is itself a Euclidean space (of lower dimension). The flats in two-dimensional space are points and lines, and the flats in three-dimensional space are points, lines, and planes. In a n-dimensional space, there are flats of every dimension from 0 to n − 1; flats of dimension n − 1 are called hyperplanes. Flats are the affine subspaces of Euclidean spaces, which means that they are similar to linear subspaces, except that they need not pass through the origin. Flats occur in linear algebra, as geometric realizations of solution sets of systems of linear equations. A flat is a manifold and an algebraic variety, and is sometimes called a linear manifold or linear variety to distinguish it from other manifolds or varieties. (Wikipedia).

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Geometry (1-1) First Terms

Geometry lecture on points, lines, and planes.

From playlist Geometry

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Parallel Lines and Transversals (Geometry Made Easy)

Parallel lines and transversal form many angles in geometry. These angles include vertical angles, alternate interior angles, same side interior angles and corresponding angles.

From playlist Geometry

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Geometry: Ch 5 - Proofs in Geometry (2 of 58) Definitions

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of definitions. Next video in this series can be seen at: https://youtu.be/-Pmkhgec704

From playlist GEOMETRY 5 - PROOFS IN GEOMETRY

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Geometry - Ch. 1: Basic Concepts (28 of 49) What are Convex and Concave Angles?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how to identify convex and concave polygons. Convex polygon: When extending any line segment (side) it does NOT cut through any of the other sides. Concave polygon: When extending any line seg

From playlist THE "WHAT IS" PLAYLIST

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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

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What is a net

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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Holomorphic Cartan geometries on simply connected manifolds by Sorin Dumitrescu

Discussion Meeting Complex Algebraic Geometry ORGANIZERS: Indranil Biswas, Mahan Mj and A. J. Parameswaran DATE:01 October 2018 to 06 October 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore The discussion meeting on Complex Algebraic Geometry will be centered around the "Infosys-ICT

From playlist Complex Algebraic Geometry 2018

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Branched Holomorphic Cartan Geometries by Sorin Dumitrescu

DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be

From playlist Analytic and Algebraic Geometry-2018

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Cosmology Lecture 3

(January 28, 2013) Leonard Susskind presents three possible geometries of homogeneous space: flat, spherical, and hyperbolic, and develops the metric for these spatial geometries in spherical coordinates. Originally presented in the Stanford Continuing Studies Program. Stanford Universit

From playlist Lecture Collection | Cosmology

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Hao Xu (7/26/22): Frobenius algebra structure of statistical manifold

Abstract: In information geometry, a statistical manifold is a Riemannian manifold (M,g) equipped with a totally symmetric (0,3)-tensor. We show that the tangent bundle of a statistical manifold has a Frobenius algebra structure if and only if the sectional K-curvature vanishes. This gives

From playlist Applied Geometry for Data Sciences 2022

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The top-heavy conjecture for vectors and matroids - Tom Braden

Members’ Seminar Topic: The top-heavy conjecture for vectors and matroids Speaker: Tom Braden SPEAKER AFFILIATION Affiliation: University of Massachusetts, Amherst; Member, School of Mathematics Date: February 08, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Lecture 9 | String Theory and M-Theory

(November 23, 2010) Leonard Susskind gives a lecture on the constraints of string theory and gives a few examples that show how these work. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced

From playlist Lecture Collection | String Theory and M-Theory

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Zhaoting Wei: Determinant line bundles and cohesive modules

Talk by Zhaoting Wei in Global Noncommutative Geometry Seminar (Americas) https://www.math.wustl.edu/~xtang/NCG-Seminar on December 16, 2020

From playlist Global Noncommutative Geometry Seminar (Americas)

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S. Ghazouani - Isoholonomic foliations of moduli spaces of Riemann surfaces

In this talk, I will introduce families of foliations on the moduli space of Riemann surfaces M_{g,n} which we call Veech foliations. These foliations are defined by identifying M_{g,n} to certain moduli spaces of flat structures and were first defined by Bill Veech. I will try to expose t

From playlist Ecole d'été 2019 - Foliations and algebraic geometry

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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

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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

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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

Related pages

Linear subspace | Linear algebra | Angle | Heinrich Guggenheimer | Algebraic variety | Intersection (set theory) | Distance from a point to a plane | Coplanarity | Lattice (order) | Origin (mathematics) | Parallel (geometry) | Plücker coordinates | Distance from a point to a line | Angles between flats | Parameter | Dimension | Hyperplane | Three-dimensional space | Parametric equation | Empty set | Distributive lattice | Matroid | System of linear equations | Isometry | Right angle | Euclidean space | Manifold | Distributive property | Affine space | Euclidean distance | Geometry | Dihedral angle