Projectively extended real line

Introduction to Projective Geometry (Part 1)

The first video in a series on projective geometry. We discuss the motivation for studying projective planes, and list the axioms of affine planes.

From playlist Introduction to Projective Geometry

Projective Coordinates for Points and Lines | Algebraic Calculus One | Wild Egg and Anna Tomskova

Dr Anna Tomskova explains a more modern framework for projective geometry where the extra coordinate often associated with infinity is the first coordinate in a projective vector. This gives us a uniform way to associate to affine points and lines projective points and lines, with the adva

From playlist Algebraic Calculus One

The extended rational numbers in practice | Real numbers and limits Math Foundations 105

We review the extended rational numbers, which extend the rational numbers to all expressions of the form a/b, where a and b are integers---even b=0. Then we give some examples of how these strange beasts might prove useful in mathematics. But first we give one example of where they are un

From playlist Math Foundations

algebraic geometry 15 Projective space

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry

From playlist Algebraic geometry I: Varieties

Extending arithmetic to infinity! | Real numbers and limits Math Foundations 103 | N J Wildberger

We are interested in investigating how to rigorously and carefully extend arithmetic with rational numbers to a wider domain involving the symbol 1/0, represented by a ``sideways 8''. First we have a look at the simpler case of natural number arithmetic, where extending to infinity is re

From playlist Math Foundations

Introduction to Projective Geometry (Part 2)

The second video in a series about projective geometry. We list the axioms for projective planes, give an examle of a projective plane with finitely many points, and define the real projective plane.

From playlist Introduction to Projective Geometry

Elliptic curves: point at infinity in the projective plane

This video depicts point addition and doubling on elliptic curve in simple Weierstrass form in the projective plane depicted using stereographic projection where the point at infinity can actually be seen. Explanation is in the accompanying article https://trustica.cz/2018/04/05/elliptic-

From playlist Elliptic Curves - Number Theory and Applications

The circle and projective homogeneous coordinates | Universal Hyperbolic Geometry 7a | NJ Wildberger

Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine

From playlist Universal Hyperbolic Geometry

The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b

Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine

From playlist Universal Hyperbolic Geometry

Tropical Geometry - Lecture 11 - Toric Varieties | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Stanford Seminar - From Haptic Illusions to Beyond Real Interactions in Virtual Reality

Parastoo Abtahi, Stanford University May 27, 2022 Advances in audiovisual rendering have led to the commercialization of virtual reality (VR) hardware; however, haptic technology has not kept up with these advances. While haptic devices aim to bridge this gap by simulating the sensation o

From playlist Stanford Seminars

Schemes 25: Proper morphisms and valuations

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We describe how to test a morphism for being proper using discrete valuation rings, and use this to show that projective morphisms are proper.

From playlist Algebraic geometry II: Schemes

Schemes 23: Valuations and separation

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We state a condition for morphisms of schemes to be separated in therms of discrete valuation rings, and apply this to the line with two origins and the proje

From playlist Algebraic geometry II: Schemes

p-Adic Analytic Continuation of Genus 2 Overconvergent... - Yichao Tian

Yichao Tian Princeton University; Member, School of Mathematics March 17, 2011 A well known result of Coleman says that p-adic overconvergent (ellitpic) eigenforms of small slope are actually classical modular forms. Now consider an overconvergent p-adic Hilbert eigenform F for a totally r

From playlist Mathematics

Totally nonparallel immersions - Michael Harrison

Seminar in Analysis and Geometry Topic: Totally nonparallel immersions Speaker: Michael Harrison Affiliation: Member, School of Mathematics Date: February 08, 2022 An immersion from a smooth n-dimensional manifold M into Rq is called totally nonparallel if, for every pair of distinct poi

From playlist Mathematics

Inheritance in Java | What is Inheritance | Types of Inheritance | Java OOPs Tutorial | Simplilearn

🔥Post Graduate Program In Full Stack Web Development: https://www.simplilearn.com/pgp-full-stack-web-development-certification-training-course?utm_campaign=InheritanceInJavaJun26-cC5ZgGSh-iU&utm_medium=DescriptionFirstFold&utm_source=youtube 🔥Caltech Coding Bootcamp (US Only): https://www

From playlist 🔥Java Tutorial For Beginners | Java Full Course | Java Interview Questions And Answers | Java Programming | Updated Java Playlist 2023 | Simplilearn

A brief history of Geometry III: The 19th century | Sociology and Pure Mathematics | N J Wildberger

The 19th century was a pivotal time in the development of modern geometry, actually a golden age for the subject, which then saw a precipitous decline in the 20th century. Why was that? To find out, let's first overview some of the main developments in geometry during the 1800's, includin

From playlist Sociology and Pure Mathematics

Beyond geometric invariant theory 2: Good moduli spaces, and applications by Daniel Halpern-Leistner

DISCUSSION MEETING: MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE: 10 February 2020 to 14 February 2020 VENUE: Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classifying

From playlist Moduli Of Bundles And Related Structures 2020

J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2)

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of section

From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

Algebraic structure on the Euclidean projective line | Rational Geometry Math Foundations 137

In this video we look at some pleasant consequences of imposing a Euclidean structure on the projective line. We give a proof of the fundamental projective Triple quad formula, talk about the equal p-quadrances theorem, and see how the logistic map of chaos theory makes its appearance as t

From playlist Math Foundations