Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Math 131 Fall 2018 100318 Heine Borel Theorem
Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
More identities involving the Riemann-Zeta function!
By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
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
A Beautiful Proof of Ptolemy's Theorem.
Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool. In fact, the Pythagorean Theorem follows directly from it. Ptolemy used this theorem in his astronomical work. Google for the historical details. Thanks to this video for the idea of this visual
From playlist Mathy Videos
Riemann Sum Defined w/ 2 Limit of Sums Examples Calculus 1
I show how the Definition of Area of a Plane is a special case of the Riemann Sum. When finding the area of a plane bound by a function and an axis on a closed interval, the width of the partitions (probably rectangles) does not have to be equal. I work through two examples that are rela
From playlist Calculus
Paulo Carrillo Rouse: Chern assembly map for discrete groups and index theory
Talk by Paulo Carrillo Rouse in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on April 14, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
In this video, we present a geometric proof of the Pythagorean theorem. This famous theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Our proof utilizes the prin
From playlist Shorts
Alex Rampell, founder and CEO of Trialpay, discusses distribution channels and partnerships. Concepts such as bidirectional relevance and channel conflict are discussed. Take the quizzes and find the rest of the course at http://eesley.blogspot.com Stanford University: http://www.stanfor
From playlist Lecture Collection | Technology Entrepreneurship
Lie Algebras and Homotopy Theory - Jacob Lurie
Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
James Stasheff (8/31/22): Homotopy coherence - theme and variations
This survey will be semi-historical and idiosyncratic with the topics covered determined by the knowledge and taste of the authors, but we hope it will provide some links that may not be common knowledge between the various aspects of the theory of homotopy coherence and, in particular, to
From playlist AATRN 2022
Lionel Pournin - Distance, Strong Convexity, Flagness, and Associahedra
One can always transform a triangulation of a convex polygon into another by performing a sequence of edge flips, which amounts to follow a path in the graph G of the associahedron. The least number of flips required to do so is then a distance in that graph whose estimation is instrumenta
From playlist Combinatorics and Arithmetic for Physics: special days
How Platforms Like Airbnb and Uber are Inspiring Traditional Business Models| Big Think
How Platforms Like Airbnb and Uber are Inspiring Traditional Business Models Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ---------------------------------------------------------------------------------
From playlist Best Videos | Big Think
Philippe Eyssidieux: Examples of Kähler groups
Abstract : Malgré les succès de la théorie de Hodge non abélienne de Corlette-Simpson pour exclure que de nombreux groupes de présentation finie soient groupes fondamentaux de variétés projectives lisses (ou des groupes Kähleriens), les techniques de construction manquent. La construction
From playlist Analysis and its Applications
Conformal Dynamics in Pseudo-Riemannian Geometry: a Question of A. Lichnerowicz - Charles Frances
Charles Frances Universite Paris-Sud 11; Member, School of Mathematics April 1, 2013 In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The
From playlist Mathematics
HAR 2009: The Censoring Mob 4/7
Clip 4/7 Speaker: Annalee Newitz How Social Media Destroy Freedom of Expression - And Why That Might Be a Good Thing Social media is supposed to foster free speech by creating user-friendly web applications that let people talk, share ideas, and organize online. Instead it has cre
From playlist Hacking at Random (HAR) 2009
Pythagorean Theorem II (visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using a dissection of a square in two different ways. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #mathshort
From playlist Pythagorean Theorem
How the Sharing Economy Is Changing the World | HowStuffWorks NOW
If you’ve ever taken a ride sharing service such as Uber or booked a room with AirBnB, you’ve already participated in the sharing economy. But you may not realize how sharing has extended to many different parts of our lives already, including health care, utilities and travel. Chief Con
From playlist The Sharing Economy