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
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
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
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
Duality, polarity and projective linear algebra (II) | Differential Geometry 11 | NJ Wildberger
We review the simple algebraic set-up for projective points and projective lines, expressed as row and column 3-vectors. Transformations via projective geometry are introduced, along with an introduction to quadratic forms, associated symmetrix bilinear forms, and associated projective 3x3
From playlist Differential Geometry
Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
The projective line can be given a Euclidean structure, just as the affine line can, but it is a bit more complicated. The algebraic structure of this projective line supports some symmetries. Symmetry in mathematics is often most efficiently encoded with the idea of a group--a technical t
From playlist Math Foundations
Projective geometry | Math History | NJ Wildberger
Projective geometry began with the work of Pappus, but was developed primarily by Desargues, with an important contribution by Pascal. Projective geometry is the geometry of the straightedge, and it is the simplest and most fundamental geometry. We describe the important insights of the 19
From playlist MathHistory: A course in the History of Mathematics
Introduction to Signed Area b) | Algebraic Calculus One | Wild Egg
This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and high school algebra, and avoiding all "infinite processes", "real numbers" and other modern fantasies. The course will be carefully framed on
From playlist Algebraic Calculus One from Wild Egg
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
History of Geometry IV: The emergence of higher dimensions | Sociology and Pure Maths| NJ Wildberger
In this history of mathematics, the 19th century stands out as an especially important chapter in the story of geometry. One of the key developments here is the move to understanding and studying higher dimensions. Here we touch on some of these advances, with an aim to explaining: where d
From playlist Sociology and Pure Mathematics
Lecture 5: Recent research: Retrographic Sensing for the Measurement of Surface Texture and Shape
MIT MAS.531 Computational Camera and Photography, Fall 2009 View the complete course: https://ocw.mit.edu/courses/mas-531-computational-camera-and-photography-fall-2009/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61pwA6paIRZ30q1sjLE8b6c Lecture 5: Recent research:
From playlist MIT MAS.531 Computational Camera and Photography, Fall 2009
Maciej Dołęga: Bijections for maps on non-oriented surfaces
HYBRID EVENT Recorded during the meeting "Random Geometry" the January 17, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
Lecture 4: k-Forms (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Hyperbolic Geometry is Projective Relativistic Geometry (full lecture)
This is the full lecture of a seminar on a new way of thinking about Hyperbolic Geometry, basically viewing it as relativistic geometry projectivized, that I gave a few years ago at UNSW. We discuss three dimensional relativistic space and its quadratic/bilinear form, particularly the uppe
From playlist MathSeminars
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 1
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Why Hyperbolic Geometry? | A Case Study in Linear Fractional Transformations
Animations at 14:38. Visualizing certain linear fractional transformations (ax+b)/(cx+d) as rotations of the hyperbolic plane! A huge thank you to my friend Alex Mallen for giving me this problem and helping with the video. Mercator Visualization used: https://mrgris.com/projects/merc-ext
From playlist Summer of Math Exposition Youtube Videos
Stable Homotopy without Homotopy - Toni Mikael Annala
IAS/Princeton Arithmetic Geometry Seminar Topic: Stable Homotopy without Homotopy Speaker: Toni Mikael Annala Affiliation: Member, School of Mathematics Date: January 30, 2023 Many cohomology theories in algebraic geometry, such as crystalline and syntomic cohomology, are not homotopy in
From playlist Mathematics
algebraic geometry 17 Affine and projective varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.
From playlist Algebraic geometry I: Varieties
algebraic geometry 35 More on blow ups
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It continues the discussion of blowing up in the previous video, with examples, of blowing up the real affine plane, blowing up an ideal, and regularizing a ration map fro
From playlist Algebraic geometry I: Varieties