In topological graph theory, the Petrie dual of an embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie polygons of the first embedding as its faces. The Petrie dual is also called the Petrial, and the Petrie dual of an embedded graph may be denoted .It can be obtained from a signed rotation system or ribbon graph representation of the embedding by twisting every edge of the embedding. (Wikipedia).
necklace,two way,Torus by Villarceau circles,mobius ball
From playlist Handmade geometric toys
Definition of V** (double dual) and an amazing miracle Dual Space Definition: https://youtu.be/OGO3HGlOQO4 Dual Spaces Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCs0fJDQnXgeuyFR8iQDwLV Subscribe to my channel: https://www.youtube.com/c/drpeyam
From playlist Dual Spaces
Dual-Clutch Transmission / Double-Clutch Gearbox (Animation)
http://www.bring-knowledge-to-the-world.com/ Do you want to know how dual-clutch transmissions work? Then, this is the right video for you! Dual-clutch transmissions, which are also known as twin-clutch gearboxes or double-clutch transmissions, are automatic transmissions. The complexity b
From playlist Automotive Engineering
In this video, I show a very neat result about dual spaces: Namely, any basis of V* is automatically a dual basis of some basis of V. Even though this result is very interesting, it's the proof that makes this very exciting, by simply using the fact that V and V** are 'very' isomorphic. En
From playlist Dual Spaces
What is the dot product of two vectors? How is it useful? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/2SGI5Kvpk9
From playlist Introduction to Vectors
Michael Groechenig - Complex K-theory of Dual Hitchin Systems
Let G and G’ be Langlands dual reductive groups (e.g. SL(n) and PGL(n)). According to a theorem by Donagi-Pantev, the generic fibres of the moduli spaces of G-Higgs bundles and G’-Higgs bundles are dual abelian varieties and are therefore derived-equivalent. It is an interesting open probl
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Geometry - Basic Terminology (15 of 34) What Are Trapezoids?
Visit http://ilectureonline.com for more math and science lectures! In this video I will define the trapezoid and the difference between the trapezoid and quadrilateral. Next video in the Basic Terminology series can be seen at: http://youtu.be/fqTPIILZieE
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
The QCD Axion (Lecture 1) by David Marsh
PROGRAM LESS TRAVELLED PATH OF DARK MATTER: AXIONS AND PRIMORDIAL BLACK HOLES (ONLINE) ORGANIZERS: Subinoy Das (IIA, Bangalore), Koushik Dutta (IISER, Kolkata / SINP, Kolkata), Raghavan Rangarajan (Ahmedabad University) and Vikram Rentala (IIT Bombay) DATE: 09 November 2020 to 13 Novemb
From playlist Less Travelled Path of Dark Matter: Axions and Primordial Black Holes (Online)
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra
Wolfram Physics Project: Relations to Category Theory
Stephen Wolfram and special guests discuss the Wolfram Physics Project and its relations to Category Theory. Begins at 9:50 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announc
From playlist Wolfram Physics Project Livestream Archive
Algebraic curves, tropical geometry, and moduli - Sam Payne
Sam Payne Yale University February 11, 2015 Tropical geometry gives a new approach to understanding old questions about algebraic curves and their moduli spaces, synthesizing techniques that range from Berkovich spaces to elementary combinatorics. I will discuss an outline of this method,
From playlist Mathematics
In this video, I present a very classical example of a duality argument: Namely, I show that T^T is one-to-one if and only if T is onto and use that to show that T is one-to-one if and only if T^T is onto. This illustrates the beautiful interplay between a vector space and its dual space,
From playlist Dual Spaces
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
Equivariant principal bundles on toric varieties- Part 1 by Mainak Poddar
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
AlgTop8: Polyhedra and Euler's formula
We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's
From playlist Algebraic Topology: a beginner's course - N J Wildberger
A conversation between Jonathan Gorard and Stephen Wolfram at the Wolfram Summer School 2022
Stephen Wolfram plays the role of Salonnière in an on-going series of intellectual explorations with special guests. In this episode, Jonathan Gorard joins Stephen at the 20th annual Wolfram Summer School. Watch all of the conversations here: https://wolfr.am/youtube-sw-conversations Foll
From playlist Conversations with Special Guests
In this video, I prove quite a shocking result: Even though for matrices, we have A^TT = A, for linear transformations, we do not have T^TT = T. However, I also show that if we identify V^** with V, then in some sense, we do have T^TT = T. Enjoy this double duality extravaganza! Transpose
From playlist Dual Spaces
Clinton Young: The Wrong Man on Death Row? | Real Stories True Crime Documentary
Innocent on Death Row: Clinton Young's Story (Crime Documentary) | Real Stories At just 19 years old, Clinton Young was charged with the murder of two men and sentenced to death. Now, 14 years later, he is still awaiting execution and continues to plead he was not the real killer. With th
From playlist Prison Stories
Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016)
Computer Musings 2016 Donald Knuth's 23rd Annual Christmas Tree Lecture: "Hamiltonian Paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its steps.
From playlist Donald Knuth Lectures
In this video, I show how to explicitly calculate dual bases. More specifically, I find the dual basis corresponding to the basis (2,1) and (3,1) of R^2. Hopefully this will give you a better idea of how dual bases work. Subscribe to my channel: https://www.youtube.com/c/drpeyam What is
From playlist Dual Spaces