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

Hypothesis: Accept or Fail to Reject?01:17

Hypothesis: Accept or Fail to Reject?

29.6K
The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P-values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?
There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null...
29.6K
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

8.1K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
8.1K
Hydraulic Jump: Problem Solving01:16

Hydraulic Jump: Problem Solving

577
To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:Calculate Effective Upstream Velocity:When the downstream gate closes, a hydraulic jump forms, traveling upstream at 2 meters per second. This wave speed combines with the initial channel flow velocity, creating an effective upstream velocity.Identify Flow Velocities Before and After the Hydraulic Jump:Upstream of the hydraulic jump, the effective flow velocity includes both the...
577
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

2.6K
Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
2.6K
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

66
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
66

You might also read

Related Articles

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

Sort by
Same author

New signatures of the spin gap in quantum point contacts.

Nature communications·2021
Same author

Toy Models of Top Down Causation.

Entropy (Basel, Switzerland)·2020
Same author

Summoning, No-Signalling and Relativistic Bit Commitments.

Entropy (Basel, Switzerland)·2020
Same author

Globe-hopping.

Proceedings. Mathematical, physical, and engineering sciences·2020
Same author

S-money: virtual tokens for a relativistic economy.

Proceedings. Mathematical, physical, and engineering sciences·2019
Same author

Testing causal quantum theory.

Proceedings. Mathematical, physical, and engineering sciences·2019
Same journal

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta.

Proceedings. Mathematical, physical, and engineering sciences·2025
Same journal

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

Proceedings. Mathematical, physical, and engineering sciences·2023
Same journal

The Elbert range of magnetostrophic convection. I. Linear theory.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Soft wetting with (a)symmetric Shuttleworth effect.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

The quantum theory of time: a calculus for q-numbers.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Integrable nonlinear evolution equations in three spatial dimensions.

Proceedings. Mathematical, physical, and engineering sciences·2022
See all related articles

Related Experiment Video

Updated: Feb 17, 2026

Linking Predation Risk, Herbivore Physiological Stress and Microbial Decomposition of Plant Litter
10:20

Linking Predation Risk, Herbivore Physiological Stress and Microbial Decomposition of Plant Litter

Published on: March 12, 2013

14.0K

The grasshopper problem.

Olga Goulko1, Adrian Kent2,3

  • 1Department of Physics, University of Massachusetts, Amherst, MA 01003, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|December 12, 2017
PubMed
Summary
This summary is machine-generated.

Maximizing grasshopper survival on a planar lawn involves finding the optimal shape. Surprisingly, a disc is not best; cogwheel shapes are often superior for this geometric probability problem.

Keywords:
Bell inequalitiesgeometric combinatoricsspin modelsstatistical physics

More Related Videos

Maintaining Laboratory Cultures of Gryllus bimaculatus, a Versatile Orthopteran Model for Insect Agriculture and Invertebrate Physiology
08:30

Maintaining Laboratory Cultures of Gryllus bimaculatus, a Versatile Orthopteran Model for Insect Agriculture and Invertebrate Physiology

Published on: June 8, 2022

3.9K
Extracellular Wire Tetrode Recording in Brain of Freely Walking Insects
15:28

Extracellular Wire Tetrode Recording in Brain of Freely Walking Insects

Published on: April 1, 2014

17.2K

Related Experiment Videos

Last Updated: Feb 17, 2026

Linking Predation Risk, Herbivore Physiological Stress and Microbial Decomposition of Plant Litter
10:20

Linking Predation Risk, Herbivore Physiological Stress and Microbial Decomposition of Plant Litter

Published on: March 12, 2013

14.0K
Maintaining Laboratory Cultures of Gryllus bimaculatus, a Versatile Orthopteran Model for Insect Agriculture and Invertebrate Physiology
08:30

Maintaining Laboratory Cultures of Gryllus bimaculatus, a Versatile Orthopteran Model for Insect Agriculture and Invertebrate Physiology

Published on: June 8, 2022

3.9K
Extracellular Wire Tetrode Recording in Brain of Freely Walking Insects
15:28

Extracellular Wire Tetrode Recording in Brain of Freely Walking Insects

Published on: April 1, 2014

17.2K

Area of Science:

  • Geometric combinatorics
  • Geometric probability
  • Mathematical physics

Background:

  • Inspired by Bell inequalities, this study addresses a geometric optimization problem.
  • The problem involves a 'grasshopper' jumping a fixed distance on a unit area planar lawn.

Purpose of the Study:

  • To determine the optimal shape of a planar lawn that maximizes the probability of a grasshopper remaining on the lawn after a fixed-distance jump.
  • To investigate the non-optimality of a disc shape for this problem.

Main Methods:

  • Introduced a discrete version of the grasshopper problem using a spin model.
  • Employed simulated annealing and parallel tempering for computational searches.
  • Analyzed geometric properties of potential optimal lawn shapes.

Main Results:

  • Demonstrated that a disc-shaped lawn is not optimal for any jump distance d > 0.
  • For jump distances d < π^(-1/2), the optimal lawn shape approximates a cogwheel with n cogs, where n is near a specific value.
  • Observed transitions to different optimal shapes for larger jump distances.

Conclusions:

  • The optimal lawn shape for maximizing grasshopper retention is non-trivial and deviates from a simple disc.
  • Cogwheel-like shapes emerge as optimal for certain parameter ranges, suggesting complex geometric solutions.
  • The study provides insights into geometric optimization problems with applications in probability and physics.