Projective geometry | Linear algebra
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix. If homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infinity, the number of coordinates required to allow this extension is one more than the dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three homogeneous coordinates are required to specify a point in the projective plane. (Wikipedia).
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Ex: Identifying the Coordinates of Points on the Coordinate Plane
This video explains how to determine the coordinates of points on the coordinate plane. Complete Video List at http://www.mathispower4u.com Search by Topic at http://www.mathispower4u.wordpress.com
From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
Determine if a First-Order Differential Equation is Homogeneous - Part 1
This video explains how to determine if a given linear first order differential equation is homogeneous using the ratio definition. Website: http://mathispower4u.com
From playlist First Order Homogeneous Differential Equations
Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger
In this video we introduce projective geometry into the study of conics and quadrics. Our point of view follows Mobius and Plucker: the projective plane is considered as the space of one-dimensional subspaces of a three dimensional vector space, or in other words lines through the origin.
From playlist Differential Geometry
Introduction to Homogeneous Differential Equations
Introduction to Homogeneous Differential Equations A full introduction to homogeneous differential equations.
From playlist Differential Equations
Computations with homogeneous coordinates | Universal Hyperbolic Geometry 8 | NJ Wildberger
We discuss the two main objects in hyperbolic geometry: points and lines. In this video we give the official definitions of these two concepts: both defined purely algebraically using proportions of three numbers. This brings out the duality between points and lines, and connects with our
From playlist Universal Hyperbolic Geometry
Lecture 05: Spatial Transformations (CMU 15-462/662)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/
From playlist Computer Graphics (CMU 15-462/662)
12. Non-Euclidean Spaces: Open Universes and the Spacetime Metric
MIT 8.286 The Early Universe, Fall 2013 View the complete course: http://ocw.mit.edu/8-286F13 Instructor: Alan Guth In this lecture, the professor reviewed a closed three-dimensional space and implications of general relativity; and talked about open universe and the spacetime metric. Li
From playlist The Early Universe by Prof. Alan Guth
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Introduction to Spherical Coordinates
This video defines spherical coordinates and explains how to convert between spherical and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Fundamentals of Robotics - Part 1 : Combining Rotation and Translation #SoME2
First video in a multi-part introduction to Robotics. Time Stamps: 00:00 - Opening/Intro 00:12 - Chapter 1 : Joints 03:11 - Chapter 2 : Transformations 08:05 - Chapter 3 : Homogeneous Coordinates Animations: Manim: https://www.manim.community/ Blender: https://www.blender.org/ Thanks: G
From playlist Summer of Math Exposition 2 videos
Introduction to Cylindrical Coordinates
Introduction to Cylindrical Coordinates Definition of a cylindrical coordinate and all of the formulas used to convert from cylindrical to rectangular and from rectangular to cylindrical. Examples are also given.
From playlist Calculus 3
Cosmological Perturbation Theory - Lecture 1(Pedagogical Lecture) by Shiv Sethi
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From playlist LESS TRAVELLED PATH TO THE DARK UNIVERSE
Introduction to Elliptic Curves 1 by Anupam Saikia
PROGRAM : ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (ONLINE) ORGANIZERS : Ashay Burungale (California Institute of Technology, USA), Haruzo Hida (University of California, Los Angeles, USA), Somnath Jha (IIT - Kanpur, India) and Ye Tian (Chinese Academy of Sciences, China) DA
From playlist Elliptic Curves and the Special Values of L-functions (ONLINE)
CEB T2 2017 - Fraydoun Rezakhanlou - 3/3
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From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Introduction to Spherical Coordinates
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From playlist Calculus 3
4. The Kinematics of the Homogeneous Expanding Universe
MIT 8.286 The Early Universe, Fall 2013 View the complete course: http://ocw.mit.edu/8-286F13 Instructor: Alan Guth In this lecture, the professor first talked about the properties of the universe, then discussed Hubble's Law, gave an example of isotropy without homogeneity, etc. License
From playlist The Early Universe by Prof. Alan Guth
Determine if a First-Order Differential Equation is Homogeneous - Part 2
This video explains how to determine if a given linear first order differential equation is homogeneous. Website: http://mathispower4u.com
From playlist First Order Homogeneous Differential Equations