Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Radius of Gyration of an Area01:12

Radius of Gyration of an Area

1.6K
The second moment of area, also known as the moment of inertia of area, is a crucial factor in understanding an object's resistance against bending deformation, or stiffness. To accurately estimate the second moment of area along any axis, one needs to concentrate all areas associated with that object into a thin strip, which should be placed parallel to that particular axis.
1.6K
Degree of Curvature and Radius of Curvature01:19

Degree of Curvature and Radius of Curvature

57
The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of...
57
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

7.5K
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
7.5K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.6K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.6K
Gravitational Potential Energy for Extended Objects01:07

Gravitational Potential Energy for Extended Objects

1.4K
Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:
1.4K
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

170
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
170

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Correction: "Distinguishing Phylogenetic Level-2 Networks with Quartets and Inter-Taxon Quartet Distances".

Bulletin of mathematical biology·2026
Same author

Characterizing semi-directed phylogenetic networks and their multi-rootable variants.

Theory in biosciences = Theorie in den Biowissenschaften·2025
Same author

Distinguishing Phylogenetic Level-2 Networks with Quartets and Inter-Taxon Quartet Distances.

Bulletin of mathematical biology·2025
Same author

Algebraic Invariants for Inferring 4-Leaf Semi-Directed Phylogenetic Networks.

Systematic biology·2025
Same author

Spaces of ranked tree-child networks.

Journal of mathematical biology·2025
Same author

When are Quarnets Sufficient to Reconstruct Semi-directed Phylogenetic Networks?

Bulletin of mathematical biology·2025
Same journal

Some Fast Algorithms for Curves in Surfaces.

Discrete & computational geometry·2026
Same journal

A Full Halin Grid Theorem.

Discrete & computational geometry·2026
Same journal

Stability and Inference of the Euler Characteristic Transform.

Discrete & computational geometry·2026
Same journal

Error Resilient Space Partitioning.

Discrete & computational geometry·2026
Same journal

A Faithful Discretization of Verbose Directional Transforms.

Discrete & computational geometry·2026
Same journal

Maximum Betti Numbers of Čech Complexes.

Discrete & computational geometry·2026
See all related articles

Related Experiment Video

Updated: Jul 9, 2025

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.5K

Diversities and the Generalized Circumradius.

David Bryant1, Katharina T Huber2, Vincent Moulton2

  • 1Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand.

Discrete & Computational Geometry
|November 29, 2023
PubMed
Summary
This summary is machine-generated.

The generalized circumradius, a concept in geometry, is explored for its function properties. Researchers characterized which geometric functions can arise from this concept, using a novel framework called diversities.

Keywords:
Convex geometryDiversityGeneralized Minkowski spacesGeneralized circumradiusMetric geometry

More Related Videos

Integrating Augmented Reality Tools in Breast Cancer Related Lymphedema Prognostication and Diagnosis
06:03

Integrating Augmented Reality Tools in Breast Cancer Related Lymphedema Prognostication and Diagnosis

Published on: February 6, 2020

6.7K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.5K

Related Experiment Videos

Last Updated: Jul 9, 2025

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.5K
Integrating Augmented Reality Tools in Breast Cancer Related Lymphedema Prognostication and Diagnosis
06:03

Integrating Augmented Reality Tools in Breast Cancer Related Lymphedema Prognostication and Diagnosis

Published on: February 6, 2020

6.7K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.5K

Area of Science:

  • Convex Geometry
  • Geometric Analysis
  • Metric Theory

Background:

  • The generalized circumradius of a point set A with respect to a convex body K is defined as the smallest scaling factor such that a translated copy of K contains A.
  • Different choices of K yield distinct functions on bounded sets, prompting an investigation into the nature of these functions.

Purpose of the Study:

  • To characterize the set of functions that can be generated by the generalized circumradius for various convex bodies K.
  • To explore the properties of these functions, particularly when restricted to finite subsets of points.

Main Methods:

  • Leveraging the theory of diversities, a recent generalization of metrics applicable to finite subsets.
  • Analyzing the functional properties arising from the generalized circumradius definition.

Main Results:

  • A comprehensive characterization of functions generatable by the generalized circumradius is established.
  • Elegant characterizations are derived for specific cases where K is a simplex or a parallelotope.

Conclusions:

  • The study provides a theoretical framework for understanding functions derived from generalized geometric concepts.
  • The findings offer new insights into the relationship between convex bodies, point sets, and generalized metric spaces.