Articles containing proofs | Theorems about circles | Euclidean plane geometry
In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is completely inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear. For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of circles always lie in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents. In other words, if the two external tangents are considered to intersect at the point at infinity, then the other two intersection points must be on a line passing through the same point at infinity, so the line between them takes the same angle as the external tangent. (Wikipedia).
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Number Theory | Lagrange's Theorem of Polynomials
We prove Lagrange's Theorem of Polynomials which is related to the number of solutions to polynomial congruences modulo a prime.
From playlist Number Theory
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
Differential Equations | The solution of a Cauchy-Euler Differential Equation
We prove a general theorem regarding the form of a solution of a Cauchy-Euler Differential Equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Mathematics named after Leonhard Euler
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
This video proves Rolle's Theorem. http://mathispower4u.com
From playlist Rolle’s Theorem and the Mean Value Theorem
Eleonora Di Nezza: Complex Monge-Ampere equations with prescribed singularities
Abstract: Since the proof of the Calabi conjecture given by Yau, complex Monge-Ampère equations on compact Kähler manifolds have been intensively studied. In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show e
From playlist Analysis and its Applications
Calculus 5.3 The Fundamental Theorem of Calculus
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
A brief history of geometry II: The European epoch | Sociology and Pure Mathematics | N J Wildberger
Let's have a quick overview of some of the developments in the European story of geometry -- at least up to the 19th century. We'll discuss Cartesian geometry, Projective geometry, Descriptive geometry, Algebraic geometry and Differential geometry. This is meant for people from outside m
From playlist Sociology and Pure Mathematics
Meusnier, Monge and Dupin II | Differential Geometry 32 | NJ Wildberger
Here we continue our study of the works of three important French differential geometers. Today we discuss G. Monge, who is sometimes called the father of the subject. He was the inventor of descriptive geometry (which he developed for military applications), and various theorems in Euclid
From playlist Differential Geometry
Oriented circles and relativistic geometry II | Wild Linear Algebra 35 | NJ Wildberger
We continue our discussion of oriented, or signed, or directed circles in the plane, which are also called cycles, and the intimate connection with relativistic geometry in three dimensions. This correspondence makes it easier for us to apply linear algebraic ideas to the geometry of circl
From playlist WildLinAlg: A geometric course in Linear Algebra
Images in Math - Pascal's Theorem
This video is about Pascal's Theorem.
From playlist Images in Math
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
From the Monge transportation problem to Einstein's gravitation through Euler's Hy... - Yann Brenier
Workshop on Recent developments in incompressible fluid dynamics Topic: From the Monge transportation problem to Einstein's gravitation through Euler's Hydrodynamics Speaker: Yann Brenier Affiliation: CNRS-Laboratoire de Mathematiques d'Orsay, Universite Paris-Saclay Date: April 04, 2022
From playlist Mathematics
Max Jensen: Convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids
The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (15.02.2017) In this presentation I will discuss a semi-Lagrangian discretisation of the Monge-Ampère operator on P1 finite elemen
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
The Monge - Ampère equations, the Bergman kernel... (Lecture 3)by Kengo Hirachi
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Tobias Ried - Optimal Transportation, Monge–Ampère, and the Matching Problem
We present a fully variational approach to the regularity theory for the Monge-Ampère equation, or rather of optimal transportation, with interesting applications to the problem of optimally matching a realisation of a Poisson point process to the Lebesgue measure. Following De Giorgi’s st
From playlist Research Spotlight
IGA: Duc Viet Vu - Complex Monge Ampere Equations with Solutions in Finite Energy Classes
Abstract: The notion of pluricomplex energy was introduced by U. Cegrell in 1988. Since then it has played an important role in complex Monge-Ampere equations. I present a recent joint work with Do Duc Thai in which we characterize the class of probability measures on a compact Kahler mani
From playlist Informal Geometric Analysis Seminar
Ex 2: Rolle's Theorem with Product Rule
This video provides an example of how to apply Rolle's Theorem. http://mathispower4u.com
From playlist Rolle’s Theorem and the Mean Value Theorem
Weil-Petersson currents by Georg Schumacher
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