In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional, then a half-space is called a half-plane (open or closed). A half-space in a one-dimensional space is called a half-line or ray. More generally, a half-space is either of the two parts into which a hyperplane divides an affine space. That is, the points that are not incident to the hyperplane are partitioned into two convex sets (i.e., half-spaces), such that any subspace connecting a point in one set to a point in the other must intersect the hyperplane. A half-space can be either open or closed. An open half-space is either of the two open sets produced by the subtraction of a hyperplane from the affine space. A closed half-space is the union of an open half-space and the hyperplane that defines it. A half-space may be specified by a linear inequality, derived from the linear equation that specifies the defining hyperplane.A strict linear inequality specifies an open half-space: A non-strict one specifies a closed half-space: Here, one assumes that not all of the real numbers a1, a2, ..., an are zero. (Wikipedia).
Geometry - Basic Terminology (3 of 34) Definition of Line Segments
Visit http://ilectureonline.com for more math and science lectures! In this video I will define and give examples of line segments. Next video in the Basic Terminology series can be seen at: http://youtu.be/O-2HNIXve6o
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
Teach Astronomy - The Shape of Space
http://www.teachastronomy.com/ According to the theory of general relativity, the universe and the space we live in may actually have a shape, and the shape need not be the flat infinite space described by Euclidean geometry. Infinite space will be flat, but curved space could be finite o
From playlist 22. The Big Bang, Inflation, and General Cosmology
Dimensions (2 of 3: A More Flexible Definition - Scale Factor)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
Cornelia Drutu - Connections between hyperbolic geometry and median geometry
The interest of median geometry comes from its connections with property (T) and a-T-menability and, in its discrete version, with the solution to the virtual Haken conjecture. In this talk I shall explain how groups endowed with various forms of hyperbolic geometry, from lattices in rank
From playlist Geometry in non-positive curvature and Kähler groups
Introduction to Projective Geometry (Part 1)
The first video in a series on projective geometry. We discuss the motivation for studying projective planes, and list the axioms of affine planes.
From playlist Introduction to Projective Geometry
Hyperbolic Knot Theory (Lecture - 1) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 1) by Subhojoy Gupta
ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME: 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This wi
From playlist Geometry and Topology for Lecturers
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
Weakly Modular Functions | The Geometry of SL2,Z, Section 1.4
We provide an alternative motivation for the definition of weakly modular functions. My Twitter: https://twitter.com/KristapsBalodi3 Weakly Modular Functions (0:00) Boring Functions on Compact Riemann Surfaces (2:06) Transforming the Transformation Property (9:15)
From playlist The Geometry of SL(2,Z)
Euclidean and Algebraic Geometry, David Cox [2014]
Slides for this talk: https://drive.google.com/file/d/1s87shlFPPVolx1dV7H4CBc1DjDrh0piR/view?usp=sharing David Cox Amherst College This talk will survey some examples, mostly geometric questions about Euclidean space, where the methods of algebraic geometry can offer some insight. I wil
From playlist Mathematics
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
Guo Chuang Thiang: What is a Coarse Index, physically?
Talk in Global Noncommutative Geometry Seminar, May 4, 2022
From playlist Global Noncommutative Geometry Seminar (Europe)
Lisa Glaser: A picture of a spectral triple
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: A compact manifold can be described through a spectral triple, consisting of a Hilbert space H, an algebra of functions A and a Dirac operator D. But what if we are g
From playlist Noncommutative geometry meets topological recursion 2021
Aspects of Eternal Inflation, part 3 - Leonard Susskind
Aspects of Eternal Inflation, part 3 Leonard Susskind Stanford University July 20, 2011
From playlist PiTP 2011
Tropical Geometry - Lecture 2 - Curve Counting | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
A Group Theoretic Description | The Geometry of SL(2,Z), Section 2.1
Expressing the complex upper half plane as a quotient of topological (in fact, Lie) groups. Twitter: https://twitter.com/KristapsBalodi3 Topological Groups (0:00) A Lemma on Stabilization (7:19) Connecting Geometry and Algebra (9:55)
From playlist The Geometry of SL(2,Z)