In discrete and computational geometry, a set of points in the Euclidean plane or a higher-dimensional Euclidean space is said to be in convex position or convex independent if none of the points can be represented as a convex combination of the others. A finite set of points is in convex position if all of the points are vertices of their convex hull. More generally, a family of convex sets is said to be in convex position if they are pairwise disjoint and none of them is contained in the convex hull of the others. An assumption of convex position can make certain computational problems easier to solve. For instance, the traveling salesman problem, NP-hard for arbitrary sets of points in the plane, is trivial for points in convex position: the optimal tour is the convex hull. Similarly, the minimum-weight triangulation of planar point sets is NP-hard for arbitrary point sets, but solvable in polynomial time by dynamic programming for points in convex position. The ErdลsโSzekeres theorem guarantees that every set of points in general position (no three in a line) in two or more dimensions has at least a logarithmic number of points in convex position. If points are chosen uniformly at random in a unit square, the probability that they are in convex position is The McMullen problem asks for the maximum number such that every set of points in general position in a -dimensional projective space has a projective transformation to a set in convex position. Known bounds are . (Wikipedia).
What is the difference between convex and concave
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between convex and concave polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are the names of different types of polygons based on the number of sides
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Geometry - Ch. 1: Basic Concepts (28 of 49) What are Convex and Concave Angles?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how to identify convex and concave polygons. Convex polygon: When extending any line segment (side) it does NOT cut through any of the other sides. Concave polygon: When extending any line seg
From playlist THE "WHAT IS" PLAYLIST
Determine if a polygon is concave or convex ex 2
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between concave and convex polygons
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Lecture 3 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on convex and concave functions for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engine
From playlist Lecture Collection | Convex Optimization
Lecture 4 | Convex Optimization I (Stanford)
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, continues his lecture on convex functions in electrical engineering for the course, Convex Optimization I (EE 364A). Complete Playlist for the Course: http://www.youtube.com/view_play_list?p=3940DD956
From playlist Lecture Collection | Convex Optimization
Lecture 2 | Convex Optimization I (Stanford)
Guest Lecturer Jacob Mattingley covers convex sets and their applications in electrical engineering and beyond for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex se
From playlist Lecture Collection | Convex Optimization
An Introduction to Geodesic Convexity - Nisheeth Vishnoi
Optimization, Complexity and Invariant Theory Topic: An Introduction to Geodesic Convexity Speaker: Nisheeth Vishnoi Affiliation: EPFL Date: June 7. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Jean-Bernard Lasserre: The moment-LP and moment-SOS approaches
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Control Theory and Optimization
(IC 3.2) Entropy as a lower bound on expected length (part 2)
The expected codeword length of a symbol code is bounded below by the entropy of the source. A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F
From playlist Information theory and Coding
3D convex contact forms and the Ruelle invariant - Oliver Edtmair
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: 3D convex contact forms and the Ruelle invariant Speaker: Oliver Edtmair Affiliation: Berkeley Date: January 29, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Using Excel to check convexity for splines | Algebraic Calculus One | Anna Tomskova
In this video, Dr Anna Tomskova explains how to use Excel to create a worksheet to check convexity of a given COPS (cyclic oriented polygonal spline), using the framework of signed areas. Anna demonstrates the use of the program also view a GeoGebra visualization. Besides reviewing basic a
From playlist Algebraic Calculus One
Fixed Income: Bullet versus Barbell Bond Portfolio (FRM T4-40)
The bullet portfolio invests in a single medium-term bond. The corresponding barbell portfolio invests the same amount of capital and achieves the same duration, but invests in a mix of the short-term plus long-term bond. But the barbell portfolio will have greater convexity. Tuckman expla
From playlist Valuation and RIsk Models (FRM Topic 4)
Yakov Eliashberg - Interplay between notions of convexity in complex, symplectic and contact (...)
The classical notions of holomorphic, polynomial, rational convexity, and pseudo-convexity in complex geometry have their counterparts in symplectic and contact geometries. Understanding the relationship between these notions is important for all these fields. Yakov Eliashberg (Stanford)
From playlist Not Only Scalar Curvature Seminar
๐ Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons