Quadrics | Surfaces | Geometric shapes
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, an ellipsoid is characterized by either of the two following properties. Every planar cross section is either an ellipse, or is empty, or is reduced to a single point (this explains the name, meaning "ellipse-like"). It is bounded, which means that it may be enclosed in a sufficiently large sphere. An ellipsoid has three pairwise perpendicular axes of symmetry which intersect at a center of symmetry, called the center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the principal axes, or simply axes of the ellipsoid. If the three axes have different lengths, the figure is a triaxial ellipsoid (rarely scalene ellipsoid), and the axes are uniquely defined. If two of the axes have the same length, then the ellipsoid is an ellipsoid of revolution, also called a spheroid. In this case, the ellipsoid is invariant under a rotation around the third axis, and there are thus infinitely many ways of choosing the two perpendicular axes of the same length. If the third axis is shorter, the ellipsoid is an oblate spheroid; if it is longer, it is a prolate spheroid. If the three axes have the same length, the ellipsoid is a sphere. (Wikipedia).
Special Topics - GPS (65 of 100) What is Reference Ellipsoid
Visit http://ilectureonline.com for more math and science lectures! http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn The Reference Ellipsoid is a mathematically derived surface that approximates the shape of the globe. It includes undulations of t
From playlist SPECIAL TOPICS 2 - GPS
http://demonstrations.wolfram.com/Ellipsoid/ The Wolfram Demonstration Project contains thousands of free interactive visualizations with new entries added daily. An ellipsoid is a quadratic surface given by a^2/x^2+b^2/y^2+c^2/z^2=1 Contributed by Jeff Bryant
From playlist Wolfram Demonstrations Project
What is the definition of an ellipse for conic sections
Learn all about ellipses for conic sections. We will discuss all the essential definitions such as center, foci, vertices, co-vertices, major axis and minor axis. We will also discuss the essential processes such as how to graph and writing the equation based on if it has a horizontal or
From playlist The Ellipse in Conic Sections
What is the relationship and formula between a b and c of an ellipse
Learn all about ellipses for conic sections. We will discuss all the essential definitions such as center, foci, vertices, co-vertices, major axis and minor axis. We will also discuss the essential processes such as how to graph and writing the equation based on if it has a horizontal or
From playlist The Ellipse in Conic Sections
Alternative Locus Definition of an Ellipse (1 of 2: Algebraically finding Locus of an Ellipse)
More resources available at www.misterwootube.com
From playlist Further Work with Functions (related content)
What are the basic characteristics of an ellipse for conic sections
Learn all about ellipses for conic sections. We will discuss all the essential definitions such as center, foci, vertices, co-vertices, major axis and minor axis. We will also discuss the essential processes such as how to graph and writing the equation based on if it has a horizontal or
From playlist The Ellipse in Conic Sections
Find the foci vertices and center of an ellipse by completing the square
Learn how to graph horizontal ellipse which equation is in general form. A horizontal ellipse is an ellipse which major axis is horizontal. When the equation of an ellipse is written in the general form, we first rewrite it in standard form using completing the square. After the equation h
From playlist How to Graph Vertical Ellipse (General Form) #Conics
How to graph an ellipse with the center at the origin
Learn how to graph horizontal ellipse centered at the origin. A horizontal ellipse is an ellipse which major axis is horizontal. To graph a horizontal ellipse, we first identify some of the properties of the ellipse including the major radius (a) and the minor radius (b) and the center. Th
From playlist How to Graph Horizontal Ellipse (At Origin) #Conics
Ellipsoids and The Bizarre Behaviour of Rotating Bodies
Derek's video: The Bizarre Behavior of Rotating Bodies, Explained https://www.youtube.com/watch?v=1VPfZ_XzisU Based on this amazing footage: Dancing T-handle in zero-g https://www.youtube.com/watch?v=1n-HMSCDYtM Terence Tao's original answer, with update. https://mathoverflow.net/questio
From playlist Matt and Hugh play with a thing and then do some working out
Lecture 7 | Convex Optimization II (Stanford)
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd finishes his lecture on Analytic center cutting-plane method, and begins Ellipsoid methods. This course introduces topics such as subgradient, cutting
From playlist Lecture Collection | Convex Optimization
Lecture 12 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on geometric problems in the context of electrical engineering and convex optimization for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and so
From playlist Lecture Collection | Convex Optimization
Nearly Optimal Deterministic Algorithms Via M-Ellipsoids - Santosh Vempala
Santosh Vempala Georgia Institute of Technology January 30, 2011 Milman's ellipsoids play an important role in modern convex geometry. Here we show that their proofs of existence can be turned into efficient algorithms, and these in turn lead to improved deterministic algorithms for volume
From playlist Mathematics
Wolfgang Schief: A canonical discrete analogue of classical circular cross sections of ellipsoids
Abstract: Two classical but perhaps little known facts of "elementary" geometry are that an ellipsoid may be sliced into two one-parameter families of circles and that ellipsoids may be deformed into each other in such a manner that these circles are preserved. In fact, as an illustration
From playlist Integrable Systems 9th Workshop
Davorin Lešnik (9/9/20) Sampling smooth manifolds using ellipsoids
Title: Sampling smooth manifolds using ellipsoids Abstract: A common problem in data science is to determine properties of a space from a sample. For instance, under certain assumptions a subspace of a Euclidean space may be homotopy equivalent to the union of balls around sample points,
From playlist AATRN 2020
Aditya Tiwari: On the eigenvalues of the Laplacian on ellipsoids with curvature condition
Aditya Tiwari, Indian Institute of Science Education and Research Bhopal, MP, India Title: On the eigenvalues of the Laplacian on ellipsoids with curvature condition We study the eigenvalues of the Laplacian on ellipsoids that are obtained as analytic perturbations of the standard Euclidea
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
The stabilized symplectic embedding problem - Dusa McDuff [2017]
Name: Dusa McDuff Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: The stabilized symplectic embedding problem Date: 2017-10-25 @4:00 PM Location: 103 Abstract: I will describe some of what is known about the question of when one open subset of Euclidean space embeds
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Symplectic embeddings and infinite staircases - Ana Rita Pires
Princeton/IAS Symplectic Geometry Seminar Topic: Symplectic embeddings and infinite staircases Speaker: Ana Rita Pires Date: Friday, April 15 McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ba
From playlist Mathematics
How to determine the foci vertices and center of an ellipse in general form
Learn how to graph horizontal ellipse which equation is in general form. A horizontal ellipse is an ellipse which major axis is horizontal. When the equation of an ellipse is written in the general form, we first rewrite it in standard form using completing the square. After the equation h
From playlist How to Graph Vertical Ellipse (General Form) #Conics
Infinite staircases and reflexive polygons - Ana Rita Pires
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Infinite staircases and reflexive polygons Speakers: Ana Rita Pires Affiliation: University of Edinburgh Date: July 3, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics