Projective geometry

Projective harmonic conjugate

In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction: Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM meet at K, and LK meets AB at D, then D is called the harmonic conjugate of C with respect to A, B. The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem. In real projective geometry, harmonic conjugacy can also be defined in terms of the cross-ratio as (A, B; C, D) = −1. (Wikipedia).

Projective harmonic conjugate
Video thumbnail

How to find a Harmonic Conjugate Complex Analysis

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to find a Harmonic Conjugate Complex Analysis

From playlist Complex Analysis

Video thumbnail

How to Find a Harmonic Conjugate for a Complex Valued Function

How to Find a Harmonic Conjugate for a Complex Valued Function Nice example of finding a harmonic conjugate for u(x, y) = x^2 - y^2 - x + y. I did this the shortest/fastest/easiest way possible. Hope this helps:)

From playlist Complex Analysis

Video thumbnail

Find a Harmonic Conjugate of u(x, y) = sin(x)*cosh(y)

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Find a Harmonic Conjugate of u(x, y) = sin(x)*cosh(y)

From playlist Complex Analysis

Video thumbnail

Find a Harmonic Conjugate of u(x, y) = y

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Find a Harmonic Conjugate of u(x, y) = y

From playlist Complex Analysis

Video thumbnail

What is the complex conjugate?

What is the complex conjugate of a complex number? Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook

From playlist Intro to Complex Numbers

Video thumbnail

Apollonius and harmonic conjugates | Universal Hyperbolic Geometry 2 | NJ Wildberger

Apollonius introduced the important idea of harmonic conjugates, concerning four points on a line. He showed that the pole polar duality associated with a circle produces a family of such harmonic ranges, one for every line through the pole of a line. Harmonic ranges also occur in the cont

From playlist Universal Hyperbolic Geometry

Video thumbnail

The projective Quadruple quad formula | Rational Geometry Math Foundations 148 | NJ Wildberger

In this video we introduce the projective version of the Quadruple quad formula, which not only controls the relationship between four projective points, but has a surprising connection with the geometry of the cyclic quadrilateral. The projective quadruple quad function is called R(a,b,

From playlist Math Foundations

Video thumbnail

Duality, polarity and projective linear algebra | Differential Geometry 10 | NJ Wildberger

Projective geometry is a fundamental subject in mathematics, which remarkably is little studied by undergraduates these days. But this situation is about to change---there are just too many places where a projective point of view illuminates mathematics. We will see that differential geome

From playlist Differential Geometry

Video thumbnail

Supersymmetry and Superspace, Part 3 - Jon Bagger

Supersymmetry and Superspace, Part 3 Jon Bagger Johns Hopkins University July 21, 2010

From playlist PiTP 2010

Video thumbnail

Harmonic maps for surface group representations (Lecture 01) by Qiongling Li

DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o

From playlist Surface group representations and Projective Structures (2018)

Video thumbnail

Spherical Tensor Operators | Wigner D-Matrices | Clebsch–Gordan & Wigner–Eckart

In this video, we will explain spherical tensor operators. They are defined like this: A spherical tensor operator T^(k)_q with rank k is a collection of 2k+1 operators that are numbered by the index q, which transform under rotations in the same way as spherical harmonics do. They are als

From playlist Quantum Mechanics, Quantum Field Theory

Video thumbnail

Saskia Roos: The twist of the free fermion

Talk by Saskia Roos in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on December 8, 2020

From playlist Global Noncommutative Geometry Seminar (Europe)

Video thumbnail

Higher solutions of Hitchin’s selfduality equations and real sections by Sebastian Heller

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

Video thumbnail

Commensurators of thin Subgroups by Mahan M. J.

PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.

From playlist Smooth And Homogeneous Dynamics

Video thumbnail

Nicolás Matte Bon: On actions on the real line of some finitely generated groups

CONFERENCE Recording during the thematic meeting : "Big Mapping Class Group and Diffeomorphism Groups " the October 13, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mat

From playlist Dynamical Systems and Ordinary Differential Equations

Video thumbnail

S. Hersonsky - Electrical Networks and Stephenson's Conjecture

The Riemann Mapping Theorem asserts that any simply connected planar domain which is not the whole of it, can be mapped by a conformal homeomorphism onto the open unit disk. After normalization, this map is unique and is called the Riemann mapping. In the 90's, Ken Stephenson, motivated by

From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie

Video thumbnail

Math 135 Complex Analysis Lecture 08 021215: Harmonic Functions, Differentiation, Contour Integrals

Inverse function theorem (for analytic functions); harmonic functions; harmonic conjugates; (example of) non-existence of a harmonic conjugate; differentiating the exponential function, the principal branch of the logarithm; contours; contour integrals; examples of contour integration

From playlist Course 8: Complex Analysis

Video thumbnail

Sebastian Hurtado Salazar: Irreducible lattices in semi-simple Lie groups of higher rank are not...

CONFERENCE Recording during the thematic meeting : "Big Mapping Class Group and Diffeomorphism Groups " the October 13, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mat

From playlist Dynamical Systems and Ordinary Differential Equations

Video thumbnail

Boundary First Flattening

Project page: https://geometrycollective.github.io/boundary-first-flattening/ App Tutorial: https://www.youtube.com/watch?v=h_iJFQEb-_A

From playlist Research

Video thumbnail

Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger

In this video we introduce projective geometry into the study of conics and quadrics. Our point of view follows Mobius and Plucker: the projective plane is considered as the space of one-dimensional subspaces of a three dimensional vector space, or in other words lines through the origin.

From playlist Differential Geometry

Related pages

Real projective line | Midpoint | Projective geometry | Complete quadrangle | Jean Dieudonné | Apollonian circles | Point at infinity | Additive inverse | Bertrand Russell | Projective linear group | Projective range | Skew lines | Golden ratio | Galois geometry | Inversive geometry | Cross-ratio | Pole and polar