Geometry

Laguerre plane

In mathematics, a Laguerre plane is one of the three types of Benz plane, which are the Möbius plane, Laguerre plane and Minkowski plane. Laguerre planes are named after the French mathematician Edmond Nicolas Laguerre. The classical Laguerre plane is an incidence structure that describes the incidence behaviour of the curves , i.e. parabolas and lines, in the real affine plane. In order to simplify the structure, to any curve the point is added. A further advantage of this completion is that the plane geometry of the completed parabolas/lines is isomorphic to the geometry of the plane sections of a cylinder (see below). (Wikipedia).

Laguerre plane
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Distance point and plane the Lagrange way

In this video, I derive the formula for the distance between a point and a plane, but this time using Lagrange multipliers. This not only gives us a neater way of solving the problem, but also gives another illustration of the method of Lagrange multipliers. Enjoy! Note: Check out this vi

From playlist Partial Derivatives

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Lagrange Bicentenary - Cédric Villani's conference

From the stability of the Solar system to the stability of plasmas

From playlist Bicentenaire Joseph-Louis Lagrange

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Lagrange Bicentenary - Jacques Laskar's conference

Lagrange and the stability of the Solar System

From playlist Bicentenaire Joseph-Louis Lagrange

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Laguerre's Method

Laguerre's method for finding real and complex roots of polynomials. Includes history, derivation, examples, and discussion of the order of convergence as well as visualizations of convergence behavior. Example code available on github https://www.github.com/osveliz/numerical-veliz Chapte

From playlist Root Finding

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A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

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Ch04n2: Integrals over Infinite Intervals, Gauss Laguerre, Gauss Hermite

Integrals over Infinite Intervals. Gauss Laguerre, Gauss Hermite Numerical Computation, chapter 4, additional video no 2. To be viewed after the video ch04n1. Wen Shen, Penn State University, 2018.

From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

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Aberth-Ehrlich Method

The Aberth-Ehrlich Method for solving all roots of a polynomial simultaneously including history, methodology, examples, and order as well as comparison to Durand-Kerner. Example code github: http://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:19 History 0:41 Methodology 0:59

From playlist Root Finding

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Halley's Method

Halley's Method (the method of tangent hyperbolas) for finding roots including history, derivation, examples, and fractals. Also discusses Taylor's Theorem relating to Halley's Method as well as Halley's Comet. Sample code and images available on GitHub https://www.github.com/osveliz/numer

From playlist Root Finding

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Newton Fractals

Using Newton's Method to create Fractals by plotting convergence behavior on the complex plane. Functions used in this video include arctan(z), z^3-1, sin(z), z^8-15z^4+16. Example code and images available at https://github.com/osveliz/numerical-veliz Correction: The derivative of arctan

From playlist Root Finding

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Francesco Mezzadri: Moments of Random Matrices and Hypergeometric Orthogonal Polynomials

We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely

From playlist Jean-Morlet Chair - Grava/Bufetov

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Lagrange Multipliers

Some problems using Lagrange Multipliers for optimization. In this video there are some technical problems beginning at about 9:10. The first problem is worked entirely, but the 2nd problem is interrupted.

From playlist Calc3Exam3Fall2013

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Lagrange Bicentenary - Luigi Pepe's conference

Scientific biography of Joseph Louis Lagrange Part one, Lagrange in Turin : calculus of variation and vibrating sring Part two, Lagrange in Paris : didactical works and Dean for Scientific activities at the National Institute

From playlist Bicentenaire Joseph-Louis Lagrange

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A Tour Of The Lagrange Points. Part 1 - Past And Future Missions To L1

Thanks to gravity, there are places across the Solar System which are nicely balanced. They’re called Lagrange Points and they give us the perfect vantage points for a range of spacecraft missions, from observing the Sun to studying asteroids, and more. Various spacecraft have already vis

From playlist Guide to Space

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Complex numbers and curves | Math History | NJ Wildberger

In the 19th century, the study of algebraic curves entered a new era with the introduction of homogeneous coordinates and ideas from projective geometry, the use of complex numbers both on the curve and at infinity, and the discovery by the great German mathematician B. Riemann that topolo

From playlist MathHistory: A course in the History of Mathematics

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The Nature of War | WILDxRED

After 52 years of war between the FARC guerrillas and the Colombian government, this short film explores the tricky relationship between conflict and conservation. Did war unexpectedly benefit nature? ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographi

From playlist News | National Geographic

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The Curse of Oak Island: CANNONBALL DISCOVERY Linked to Treasure Defenses (Season 8) | History

While sifting through borehole remains, the team makes the significant discovery of a cannonball, in this clip from Season 8, "A Loose Cannonball." #OakIsland Watch all new episodes of The Curse of Oak Island, Tuesdays at 9/8c, and stay up to date on all of your favorite The HISTORY Ch

From playlist The Curse of Oak Island: Season: 8 | New Episodes Tuesdays at 9/8c | History

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Lagrange multipliers example

Download the free PDF from http://tinyurl.com/EngMathYT This video shows how to apply the method of Lagrange multipliers to a max/min problem. Such ideas are seen in university mathematics.

From playlist Lagrange multipliers

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Statistical aspects of stochastic algorithms for entropic (...) - Bigot - Workshop 2 - CEB T1 2019

Jérémie Bigot (Univ. Bordeaux) / 12.03.2019 Statistical aspects of stochastic algorithms for entropic optimal transportation between probability measures. This talk is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measu

From playlist 2019 - T1 - The Mathematics of Imaging

Related pages

Laguerre transformations | Quadratic set | Equivalence relation | Minkowski plane | Mathematics | Field (mathematics) | Benz plane | Möbius plane | Real number | Cylinder | Stereographic projection | Incidence structure | Affine plane