Duality and perpendicularity | Universal Hyperbolic Geometry 9 | NJ Wildberger
Perpendicularity in universal hyperbolic geometry is defined in terms of duality. One big difference with classical HG is that points can also be perpendicular, not just lines. Once we have perpendicularity, we can define altitudes. We also state the collinear points theorem and concurrent
From playlist Universal Hyperbolic Geometry
The circle and Cartesian coordinates | Universal Hyperbolic Geometry 5 | NJ Wildberger
This video introduces basic facts about points, lines and the unit circle in terms of Cartesian coordinates. A point is an ordered pair of (rational) numbers, a line is a proportion (a:b:c) representing the equation ax+by=c, and the unit circle is x^2+y^2=1. With this notation we determine
From playlist Universal Hyperbolic Geometry
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
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
What is a Tensor? Lesson 36: Other Notions of Duality
What is a Tensor? Lesson 36: Other Notions of Duality
From playlist What is a Tensor?
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
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
What is a Tensor? Lesson 33/34: Duality and Hodge Duality
What is a Tensor? Lesson 33/34: Duality and Hodge Duality This is a long lecture, so it should be split into two parts. The first part discusses "duality" in general and the second part discusses the most important duality: Hodge duality. This video has an annotation. Annotations are NOT
From playlist What is a Tensor?
Duality, polarity and projective linear algebra | Differential Geometry 10 | NJ Wildberger
Projective geometry is a fundamental subject in mathematics, which remarkably is little studied by undergraduates these days. But this situation is about to change---there are just too many places where a projective point of view illuminates mathematics. We will see that differential geome
From playlist Differential Geometry
Einstein's General Theory of Relativity | Lecture 12
Lecture 12 of Leonard Susskind's Modern Physics concentrating on General Relativity. Recorded December 9, 2008 at Stanford University. This Stanford Continuing Studies course is the fourth of a six-qarter sequence of classes exploring the essential theoretical foundations of modern phys
From playlist Lecture Collection | Modern Physics: Einstein's Theory
Kelly Bickel: Singular rational inner functions on the polydisk
This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the
From playlist Analysis and its Applications
algebraic geometry 34 Blowing up a point
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers blowing up a point of affine space, and gives some examples of using this to resolve singularities of plane curves.
From playlist Algebraic geometry I: Varieties
Geometric Approach to Invertibility of Random Matrices (Lecture 1) by Mark Rudelson
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY
Pre-recorded lecture 15: gl-regular Nijenhuis operators (part 4)
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Nijenhuis Geometry Chair's Talk 4 (Alexey Bolsinov)
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Chair's Talk 4 (Alexey Bolsinov) 10 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 February 2022 Wee
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Commutative algebra 34 Geometry of normalizations
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the geometric meaning of finite morphisms and normal rings. Finite morphisms have the property that in the map of
From playlist Commutative algebra
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships