In plane geometry, a Jacobi point is a point in the Euclidean plane determined by a triangle ABC and a triple of angles α, β, and γ. This information is sufficient to determine three points X, Y, and Z such that ∠ZAB = ∠YAC = α, ∠XBC = ∠ZBA = β, and ∠YCA = ∠XCB = γ. Then, by a theorem of , the lines AX, BY, and CZ are concurrent, at a point N called the Jacobi point. The Jacobi point is a generalization of the Fermat point, which is obtained by letting α = β = γ = 60° and triangle ABC having no angle being greater or equal to 120°. If the three angles above are equal, then N lies on the rectangular hyperbola given in areal coordinates by which is Kiepert's hyperbola. Each choice of three equal angles determines a triangle center. (Wikipedia).
Theory of numbers: Jacobi symbol
This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t
From playlist Theory of numbers
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
The J function, sl(2) and the Jacobi identity | Universal Hyperbolic Geometry 19 | NJ Wildberger
We review the basic connection between hyperbolic points and matrices, and connect the J function, which computes the joins of points or the meets of lines, with the Lie bracket of 2x2 matrices. This connects with the Lie algebra called sl(2) in the projective setting. The Jacobi identity
From playlist Universal Hyperbolic Geometry
Introduction to number theory lecture 35 Jacobi symbol
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We define the Jacobi symbol and prove its basic properties, and show how to calculate it fa
From playlist Introduction to number theory (Berkeley Math 115)
Jacobian chain rule and inverse function theorem
A lecture that discusses: the general chain rule for the Jacobian derivative; and the inverse function theorem. The concepts are illustrated via examples and are seen in university mathematics.
From playlist Several Variable Calculus / Vector Calculus
Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function
In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL
From playlist Etale Theta
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Brent Pym: Holomorphic Poisson structures - lecture 1
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the April 28, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on
From playlist Virtual Conference
Jim Bryan : Curve counting on abelian surfaces and threefolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
CEB T2 2017 - Fraydoun Rezakhanlou - 3/3
Fraydoun Rezakhanlou (Berkeley) - 09/06/2017 The lectures will discuss the following topics: 1. Scalar Conservation Laws and theirs Markovian solutions 2. Conservation laws with stochastic external force 3. Hamilton-Jacobi PDE, Hamiltonian ODEs and Mather Theory 4. Homogenization for
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Mohamed Boucetta: On the geometry of noncommutative deformations
Recording during the meeting "Workshop on Differential Geometry and Nonassociative Algebras" the November 12, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Geometry
Pre-recorded lecture 1: Introduction. What is Nijenhuis Geometry?
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Hodge theory and algebraic cycles - Phillip Griffiths
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Phillip Griffiths Institute for Advanced Study October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a f
From playlist Pierre Deligne 61st Birthday
Sinh-Gordon equation and application to the geometry of CMC surfaces - Laurent Hauswirth
Workshop on Mean Curvature and Regularity Topic: Sinh-Gordon equation and application to the geometry of CMC surfaces. Speaker: Laurent Hauswirth Affiliation: Université de Marne-la-Vallée Date: November 7, 2018 For more video please visit http://video.ias.edu
From playlist Workshop on Mean Curvature and Regularity
Intro to Jacobian + differentiability
A lecture that introduces the Jacobian matrix and its determinant. Such ideas may be thought of as a general derivative of a vector-valued function of many variables and find uses in integration theory.
From playlist Several Variable Calculus / Vector Calculus
Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
8ECM Invited Lecture: Emmanuel Kowalski
From playlist 8ECM Invited Lectures
Parallel session 8 by Dave Constantine
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
Gentle example explaining how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
I give a proof of the Cartan-Hadamard theorem on non-positively curved complete Riemannian manifolds. For more details see Chapter 7 of do Carmo's "Riemannian geomety". If you find any typos or mistakes, please point them out in the comments.
From playlist Differential geometry