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

Circles01:18

Circles

269
A circle in the coordinate plane is defined as the set of all points that lie at a constant distance, known as the radius, from a fixed point called the center. This relationship is captured using the distance formula. For a point (x, y) on the circle and a center (h, k), the distance between them equals the radius r. By squaring both sides of the distance formula, the equation of the circle is written in standard form:Constructing the Equation from Geometric InformationIf the center and the...
269
Mohr's Circle for Moments of Inertia: Problem Solving01:14

Mohr's Circle for Moments of Inertia: Problem Solving

3.3K
Mohr's circle is a graphical method for determining an area's principal moments by plotting the moments and product of inertia on a rectangular coordinate system. This circle can also be used to calculate the orientation of the principal axes.
Consider a rectangular beam. The moments of inertia of the beam about the x and y axis are 2.5(107) mm4 and 7.5(107) mm4, respectively. The product of inertia is 1.5(107) mm4. Determine the principal moments of inertia and the orientation of the major and...
3.3K
Defining Psychology01:24

Defining Psychology

8.0K
Psychology is the scientific discipline dedicated to understanding both observable behavior and the internal mental processes underlying such behavior. It aims to comprehend human nature and apply this understanding to solve practical problems, enhance well-being, and improve societal outcomes. An example of psychology's application is the study of prosocial behavior, such as why and under what conditions individuals might help strangers in need. This process involves describing observed...
8.0K
Mohr's Circle for Moments of Inertia01:10

Mohr's Circle for Moments of Inertia

1.3K
Mohr's circle is a graphical method to determine an area's principal moments of inertia by plotting the moments and product of inertia on a rectangular coordinate system.
1.3K
Mohr's Circle for Plane Stress01:23

Mohr's Circle for Plane Stress

1.4K
Mohr's circle is a graphical method for identifying the state of stress at a point in a material, making it easier to analyze stress transformations under plane stress conditions. This two-dimensional technique visualizes both normal and shearing stresses on an element.
Consider a set of Cartesian coordinates. The horizontal and vertical axes correspond to normal stress (σ) and shearing stress (τ), respectively. Two points, points A and B, are defined by the normal and shear...
1.4K
Mohr's Circle for Plane Strain01:18

Mohr's Circle for Plane Strain

1.3K
Mohr's circle is a crucial graphical method used to analyze plane strain by plotting strain on a set of cartesian coordinates, where the abscissa is normal strain ∈ and the ordinate is shear strain γ. Similarly to Mohr’s circle for plane stress, two points X and Y are plotted. Their coordinates are (∈x, -γXY) and (∈Y, γXY), respectively.
Mohr's circle visually represents the strain states under various conditions, which is essential for...
1.3K

You might also read

Related Articles

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

Sort by
Same author

DeepStrataAge: an interpretable deep-learning clock that reveals stage- and sex-divergent DNA methylation aging dynamics.

npj aging·2026
Same author

OMICmAge quantifies biological age by integrating multi-omics with electronic medical records.

Nature aging·2026
Same author

Neoadjuvant Pembrolizumab and Accelerated Methotrexate, Vinblastine, Doxorubicin, and Cisplatin in Nonurothelial Histologic Subtypes of Muscle-invasive Bladder Cancer: A Phase 2 Trial.

European urology·2025
Same author

Results from a Phase 2 Study of Induction Docetaxel and Carboplatin Followed by Maintenance Rucaparib in the Treatment of Patients with Metastatic Castration-resistant Prostate Cancer with DNA Homologous Recombination Repair Deficiency.

European urology oncology·2025
Same author

Unveiling the epigenetic impact of vegan vs. omnivorous diets on aging: insights from the Twins Nutrition Study (TwiNS).

BMC medicine·2024
Same author

Subjective brain fog: a four-dimensional characterization in 25,796 participants.

Frontiers in human neuroscience·2024

Related Experiment Video

Updated: Feb 16, 2026

Protocol for Isolating the Mouse Circle of Willis
06:30

Protocol for Isolating the Mouse Circle of Willis

Published on: October 22, 2016

13.6K

On Sets Defining Few Ordinary Circles.

Aaron Lin1, Mehdi Makhul2, Hossein Nassajian Mojarrad3

  • 1Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE United Kingdom.

Discrete & Computational Geometry
|December 30, 2017
PubMed
Summary
This summary is machine-generated.

This study reveals that point sets not on a line or circle define a minimum number of ordinary circles. It also establishes an upper bound for circles passing through four points, linking point distribution to algebraic curves.

Keywords:
Circular curvesGreen–TaoInversionOrdinary circlesSylvester–Gallai

More Related Videos

Simultaneous Quantification of T-Cell Receptor Excision Circles TRECs and K-Deleting Recombination Excision Circles KRECs by Real-time PCR
14:14

Simultaneous Quantification of T-Cell Receptor Excision Circles TRECs and K-Deleting Recombination Excision Circles KRECs by Real-time PCR

Published on: December 6, 2014

17.4K
CIRCLE-Seq for Interrogation of Off-Target Gene Editing
08:23

CIRCLE-Seq for Interrogation of Off-Target Gene Editing

Published on: November 1, 2024

1.6K

Related Experiment Videos

Last Updated: Feb 16, 2026

Protocol for Isolating the Mouse Circle of Willis
06:30

Protocol for Isolating the Mouse Circle of Willis

Published on: October 22, 2016

13.6K
Simultaneous Quantification of T-Cell Receptor Excision Circles TRECs and K-Deleting Recombination Excision Circles KRECs by Real-time PCR
14:14

Simultaneous Quantification of T-Cell Receptor Excision Circles TRECs and K-Deleting Recombination Excision Circles KRECs by Real-time PCR

Published on: December 6, 2014

17.4K
CIRCLE-Seq for Interrogation of Off-Target Gene Editing
08:23

CIRCLE-Seq for Interrogation of Off-Target Gene Editing

Published on: November 1, 2024

1.6K

Area of Science:

  • Discrete Geometry
  • Computational Geometry
  • Combinatorial Geometry

Background:

  • The study of ordinary circles (circles through exactly 3 points) and their relationship to point set configurations is a key area in discrete geometry.
  • The orchard problem investigates the maximum number of circles determined by a set of points.

Purpose of the Study:

  • To determine the minimum number of ordinary circles spanned by a set of n points in the plane, provided they are not collinear or concyclic.
  • To establish the maximum number of circles passing through exactly four points of a given point set.
  • To uncover the underlying structure of point sets that yield a small number of ordinary circles.

Main Methods:

  • Utilizing a recent result by Green and Tao on ordinary lines.
  • Applying circular inversion techniques.
  • Leveraging classical results concerning algebraic curves.
  • Analyzing extremal configurations for point sets.

Main Results:

  • For point sets not contained in a line or circle, the minimum number of ordinary circles is at least Ω(n^2).
  • The exact minimum number of ordinary circles is determined for sufficiently large n.
  • An upper bound of O(n^2) is established for the number of circles passing through exactly four points.
  • The extremal configurations for both ordinary circles and four-point circles are described.
  • A structure theorem states that point sets spanning few ordinary circles must have most points on a low-degree algebraic curve.

Conclusions:

  • The distribution of points in a plane significantly influences the number of ordinary circles and four-point circles they determine.
  • The study provides tight bounds and characterizes extremal configurations, advancing our understanding of geometric combinatorial problems.
  • The connection between point sets, ordinary circles, and algebraic curves is elucidated, offering new perspectives in discrete geometry.