Euclidean solid geometry | Theorems in geometry
In geometry, Bang's theorem on tetrahedra states that, if a sphere is inscribed within a tetrahedron, and segments are drawn from the points of tangency to each vertex on the same face of the tetrahedron, then all four points of tangency have the same triple of angles. In particular, it follows that the 12 triangles into which the segments subdivide the faces of the tetrahedron form congruent pairs across each edge of the tetrahedron. It is named after A. S. Bang, who posed it as a problem in 1897. (Wikipedia).
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Linear Equations in Primes and Nilpotent Groups - Tamar Ziegler
Tamar Ziegler Technion--Israel Institute of Technology January 30, 2011 A classical theorem of Dirichlet establishes the existence of infinitely many primes in arithmetic progressions, so long as there are no local obstructions. In 2006 Green and Tao set up a program for proving a vast gen
From playlist Mathematics
Theory of numbers: Fermat's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se
From playlist Theory of numbers
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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
Fourier series + Fourier's theorem
Free ebook http://tinyurl.com/EngMathYT A basic lecture on how to calculate Fourier series and a discussion of Fourier's theorem, which gives conditions under which a Fourier series will converge to a given function.
From playlist Engineering Mathematics
Oxford Mathematics Public Lectures : Roger Penrose - Eschermatics Roger Penrose's relationship with the artist M.C. Escher was not just one of mutual admiration. Roger's thinking was consistently influenced by Escher, from the famous Penrose tiling to his groundbreaking work in cosmology.
From playlist The Roger Penrose Playlist
Hyperbolic Knot Theory (Lecture - 2) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Number Theory | A very special case of Fermat's Last Theorem
We prove a very simple case of Fermat's Last Theorem. Interestingly, this case is fairly easy to prove which highlights the allure of the theorem as a whole -- especially given the fact that much of modern number theory was developed as part of the program that ended in the full proof. ht
From playlist Number Theory
Hyperbolic Knot Theory (Lecture - 1) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Tetrahedral hyperbolic 3-manifolds and links by Andrei Vesnin
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Barbara Nimershiem: Geometric Triangulations of a Family of Hyperbolic 3-Braids
Barbara Nimershiem, Franklin & Marshall College Title: Geometric Triangulations of a Family of Hyperbolic 3-Braids We construct topological triangulations for complements of $(-2, 3, n)$-pretzel knots and links with $n \geq 7$. Following a procedure outlined by Futer and Gueritaud, we use
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Cascading Principles - Conrad Shawcross, Martin Bridson and James Sparks with Fatos Ustek
Whether a mathematician or an artist, when you begin you often don't know where you'll end up. In this fascinating discussion, artist Conrad Shawcross and mathematicians Martin Bridson and James Sparks explore connections between mathematics and art. An exhibition of Conrad's mathematical
From playlist Oxford Mathematics Public Lectures
Number Theory - Fundamental Theorem of Arithmetic
Fundamental Theorem of Arithmetic and Proof. Building Block of further mathematics. Very important theorem in number theory and mathematics.
From playlist Proofs
10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX In this first half of this lecture, Prof. Zhao shows how
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Veering Dehn surgery - Saul Schleimer
Geometric Structures on 3-manifolds Topic: Veering Dehn surgery Speaker: Saul Schleimer Date: Tuesday, April 12 (Joint with Henry Segerman.) It is a theorem of Moise that every three-manifold admits a triangulation, and thus infinitely many. Thus, it can be difficult to learn anything
From playlist Mathematics
Number Theory | Fermat's Little Theorem
We state and prove Fermat's Little Theorem. www.michael-penn.net
From playlist Number Theory
The Signature and Natural Slope of Hyperbolic Knots - Marc Lackenby
DeepMind Workshop Topic: The Signature and Natural Slope of Hyperbolic Knots Speaker: Marc Lackenby Affiliation: University of Oxford Date: March 30, 2022 Andras Juhasz has explained in his talk how machine learning was used to discover a previously unknown relationship between invariant
From playlist DeepMind Workshop
Proof of Pythagoras' theorem - GCSE Maths
Support me on Patreon: https://www.patreon.com/mathsaurus A simple and elegant proof of Pythagoras' Theorem. Visit http://www.mathsaurus.com/ for more free GCSE and A-level maths videos and resources Visit the Mathsaurus Amazon shop at https://www.amazon.co.uk/shop/mathsaurus to see so
From playlist GCSE IGCSE Trigonometry