In convex geometry, the projection body of a convex body in n-dimensional Euclidean space is the convex body such that for any vector , the support function of in the direction u is the (n – 1)-dimensional volume of the projection of K onto the hyperplane orthogonal to u. Minkowski showed that the projection body of a convex body is convex. and used projection bodies in their solution to Shephard's problem. For a convex body, let denote the polar body of its projection body. There are two remarkable affine isoperimetric inequality for this body. proved that for all convex bodies , where denotes the n-dimensional unit ball and is n-dimensional volume, and there is equality precisely for ellipsoids. proved that for all convex bodies , where denotes any -dimensional simplex, and there is equality precisely for such simplices. The intersection body IK of K is defined similarly, as the star body such that for any vector u the radial function of IK from the origin in direction u is the (n – 1)-dimensional volume of the intersection of K with the hyperplane u⊥.Equivalently, the radial function of the intersection body IK is the Funk transform of the radial function of K.Intersection bodies were introduced by . showed that a centrally symmetric star-shaped body is an intersection body if and only if the function 1/||x|| is a positive definite distribution, where ||x|| is the homogeneous function of degree 1 that is 1 on the boundary of the body, and used this to show that the unit balls lpn, 2 < p ≤ ∞ in n-dimensional space with the lp norm are intersection bodies for n=4 but are not intersection bodies for n ≥ 5. (Wikipedia).
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From playlist 3D Printing
THE FIGURE: Foreshortening & The Head
Marc takes you through two common viewpoints to solve in foreshortening of the head.
From playlist THE FIGURE
This object is transformable hyperboloid,you can transform from cylinder to various hyperboloids.See video. Buy at http://www.shapeways.com/shops/GeometricToy Copyright (c) 2014,AkiraNishihara
From playlist 3D printed toys
LIGHT shadow (stereographic projection)
Stereographic projection spheres available at https://www.shapeways.com/shops/henryseg?section=Stereographic+Projection
From playlist 3D printing
THE FIGURE: Head Proportions and Landmarks Demonstrations
Marc demonstrates in varied drawing media, head structure demonstrations to help you find proportions and landmarks of the human head.
From playlist THE FIGURE
How To Model Articulated Action Figurine For 3D Printing | Session 03 | #gamedev
Don’t forget to subscribe! In this project series, you will learn how to model articulated action figurines for 3D printing. In this tutorial, we will be designing Futurama's Bender articulated figurine for 3D printing. It will have fully articulated arms and legs (these will utilize mu
From playlist Model Articulated Action Figurine For 3D Printing
How To Model Articulated Action Figurine For 3D Printing | Introduction | #gamedev
Don’t forget to subscribe! In this project series, you will learn how to model articulated action figurines for 3D printing. In this tutorial, we will be designing Futurama's Bender articulated figurine for 3D printing. It will have fully articulated arms and legs (these will utilize mu
From playlist Model Articulated Action Figurine For 3D Printing
How To Model Articulated Action Figurine For 3D Printing | Session 06 | #gamedev
Don’t forget to subscribe! In this project series, you will learn how to model articulated action figurines for 3D printing. In this tutorial, we will be designing Futurama's Bender articulated figurine for 3D printing. It will have fully articulated arms and legs (these will utilize mu
From playlist Model Articulated Action Figurine For 3D Printing
How To Model Articulated Action Figurine For 3D Printing | Session 02 | #gamedev
Don’t forget to subscribe! In this project series, you will learn how to model articulated action figurines for 3D printing. In this tutorial, we will be designing Futurama's Bender articulated figurine for 3D printing. It will have fully articulated arms and legs (these will utilize mu
From playlist Model Articulated Action Figurine For 3D Printing
New isoperimetric inequalities for convex bodies - Amir Yehudayoff
Computer Science/Discrete Mathematics Seminar I Topic: New isoperimetric inequalities for convex bodies Speaker: Amir Yehudayoff Affiliation: Technion - Israel Institute of Technology Date: November 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Franz Schuster: Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms
The Blaschke–Santaló inequality is one of the best known and most powerful affine isoperimetric inequalities in convex geometric analysis. In particular, it is significantly stronger than the classical Euclidean Urysohn inequality. In this talk, we present new isoperimetric inequalities fo
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality
The Alexandrov-Fenchel inequality is a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes. It is one of the central results in convex geometry, and has deep connections with other areas of mathematics. The characterization of its extremal bodie
From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability
Spectrahedral lifts of convex sets – Rekha Thomas – ICM2018
Control Theory and Optimization Invited Lecture 16.6 Spectrahedral lifts of convex sets Rekha Thomas Abstract: Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expr
From playlist Control Theory and Optimization
Seminar 1: Larry Abbott - Mind in the Fly Brain
MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 View the complete course: https://ocw.mit.edu/RES-9-003SU15 Instructor: Larry Abbott Modeling neural processes in the mushroom bodies of the insect brain to understand how flies learn to recognize scents. Training flies w
From playlist MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015
NOTACON 7: Newbie Neurohacking
Speaker: Ne0nRa1n & Tottenkoph Have a keen interest in the many flavours of neurohacking, but don't know where to get started? Discover the direction that is right for you and let our understanding and passionate advisers with a proven success record help guide you through the basics on y
From playlist Notacon 7
How We Think with Bodies and Things
(May 7, 2010) David Kirsh, Professor of Cognitive Science at University of California-San Diego, discusses the concept of enactive thought and provides data from extensive ethnographic studies and a few simple experiments to prove that it exists. Stanford University: http://www.stanford.e
From playlist Lecture Collection | Human-Computer Interaction Seminar (2009-2010)
Jean-Louis Colliot-Thélène : H3 non ramifié et cycles de codimension 2
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 Algebraic and Complex Geometry
Lec 13 | MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008
Lecture 13: Laser schemes for rotational assignment first lines for Ω', Ω" assignments Instructor: Robert Field http://ocw.mit.edu/5-80F08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008
Geometric Algebra, First Course, Episode 13: Position and Attitude
In this video we begin to construct a 2D Physics simulation framework with visualization. Our first step will be to define a rigid body with position and attitude so that we can translate and rotate it in the plane, and render it as a Square (paying homage to Flatland).
From playlist Geometric Algebra, First Course, in STEMCstudio
Most Insane Immersive Movie Experience EVER, Part 1
Check out this guy's room totally change into the movie he is watching! No SFX, no post production, no cuts, everything you see here is 100% for real. We were funded by the Video Store of PlayStation® Store (http://www.greatfilmsfillrooms.com) to make a series of movie related videos us
From playlist Projection Mapping inspirations