Conic sections | Elliptic curves

Poncelet's closure theorem

In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. It is named after French engineer and mathematician Jean-Victor Poncelet, who wrote about it in 1822; however, the triangular case was discovered significantly earlier, in 1746 by William Chapple. Poncelet's porism can be proved by an argument using an elliptic curve, whose points represent a combination of a line tangent to one conic and a crossing point of that line with the other conic. (Wikipedia).

Poncelet's closure theorem
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Galois theory: Algebraic closure

This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically

From playlist Galois theory

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Umberto Zannier - The games of Steiner and Poncelet and algebraic group schemes

November 13, 2017 - This is the first of three Fall 2017 Minerva Lectures We shall briefly present in very elementary terms the 'games' of Steiner and Poncelet, amusing mathematical solitaires of the XIX Century, also related to elliptic billiards. We shall recall that the finiteness of t

From playlist Minerva Lectures Umberto Zannier

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Multivariable Calculus | The Squeeze Theorem

We calculate a limit using a multivariable version of the squeeze theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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Existence and Uniqueness of Solutions (Differential Equations 11)

https://www.patreon.com/ProfessorLeonard THIS VIDEO CAN SEEM VERY DECEIVING REGARDING CONTINUITY. As I watched this back, after I edited it of course, I noticed that I mentioned continuity is not possible at Endpoints. This is NOT true, as we can consider one-sided limits. What I MEANT

From playlist Differential Equations

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Rolle's Theorem

This calculus video tutorial provides a basic introduction into rolle's theorem. It contains plenty of examples and practice problems on how to find the value of c that will satisfy the conclusion of rolle's theorem on the closed interval [a, b]. For rolle's theorem to apply to a funct

From playlist New Calculus Video Playlist

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Compasses are overrated #some2

This video is about the Poncelet-Steiner Theorem

From playlist Summer of Math Exposition 2 videos

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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

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Bayes' Theorem - The Simplest Case

►Second Bayes' Theorem example: https://www.youtube.com/watch?v=k6Dw0on6NtM ►Third Bayes' Theorem example: https://www.youtube.com/watch?v=HaYbxQC61pw ►FULL Discrete Math Playlist: https://www.youtube.com/watch?v=rdXw7Ps9vxc&list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS Bayes' Theorem is an inc

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

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Proof of Rolle's Theorem

This video proves Rolle's Theorem. http://mathispower4u.com

From playlist Rolle’s Theorem and the Mean Value Theorem

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Alex Wright - Minicourse - Lecture 5

Alex Wright Dynamics, geometry, and the moduli space of Riemann surfaces We will discuss the GL(2,R) action on the Hodge bundle over the moduli space of Riemann surfaces. This is a very friendly action, because it can be explained using the usual action of GL(2,R) on polygons in the plane

From playlist Maryland Analysis and Geometry Atelier

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Real Analysis Ep 15: Closure of a set

Episode 15 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about the closure of a set. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.f

From playlist Math 3371 (Real analysis) Fall 2020

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Non-Rigidity of Horocycle Orbit Closures in Geometrically Infinite Surfaces - Or Landesberg

Special Year Research Seminar [DO NOT PUBLICLY POST] Topic: Non-Rigidity of Horocycle Orbit Closures in Geometrically Infinite Surfaces Speaker: Or Landesberg Affiliation: Yale University Date: January 31, 2023 Horospherical group actions on homogeneous spaces are famously known to be ext

From playlist Mathematics

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Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=G3mAXHuoDSw&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

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What is the Mordell-Lang problem?

It is my intention to eventually explain some things about the Mordell-Lang problem and the higher dimensional versions of these. The presentation in this video is due to Mazur and can be found in an MSRI article he wrote that introduces these things.

From playlist Mordell-Lang

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P. Apisa - Marked points in genus two and beyond

In the principal stratum in genus two, McMullen observed that something odd happens - there is only one nonarithmetic Teichmuller curve - the one generated by the decagon. This strange phenomenon begets another - a primitive translation surface in genus two admits a periodic point that is

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

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Math 031 030617 Sequences continued

Additional examples of using the Squeeze Theorem to prove limits of sequences; of using L'Hopital's Rule on sequences. Showing that the limit of a sequence is 0 if and only if the limit of its absolute value is zero. Limits and continuous functions. What it means for the limit of a sequ

From playlist Course 3: Calculus II (Spring 2017)

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Yoshinori Namikawa: Symplectic singularities and nilpotent orbits

Abstract: I will characterzize, among conical symplectic varieties, the nilpotent orbit closures of a complex semisimple Lie algebra and their finite coverings. Recording during the meeting "Symplectic Representation Theory" the April 3, 2019 at the Centre International de Rencontres Math

From playlist Algebraic and Complex Geometry

Related pages

Bézout's theorem | Bicentric polygon | Elliptic curve | Conic section | Geometry | Polygon | Tangent lines to circles | Hartshorne ellipse | Circle | Complex projective plane | Tangent | Inscribed figure