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Related Concept Videos

Coordination Number and Geometry02:57

Coordination Number and Geometry

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For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Geometric Mean01:15

Geometric Mean

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The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
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Perpendicular-Axis Theorem01:16

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The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
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Degree of Curvature and Radius of Curvature01:19

Degree of Curvature and Radius of Curvature

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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...
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Coplanar Forces01:25

Coplanar Forces

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Consider an object upon which multiple forces are acting. If the lines of action of each force lie within the same plane, the system can be considered coplanar. The Cartesian vector form can be used to resolve each force into its respective components. For a coplanar system, the system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. If the sum of the forces is not equal to zero, then the object will not be in equilibrium...
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Related Experiment Video

Updated: Jul 1, 2025

Multimodal Optical Microscopy Methods Reveal Polyp Tissue Morphology and Structure in Caribbean Reef Building Corals
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Coral geometry and why it matters.

Samuel E Kahng1,2,3, Eric Odle4, Kevin C Wakeman2,4

  • 1Oceanography, University of Hawaii, Honolulu, HI, United States of America.

Peerj
|March 4, 2024
PubMed
Summary

Coral colony shape influences growth, impacting physiological and ecological strategies. Geometry dictates how size affects biomass and calcification, revealing size-dependent and independent growth patterns in reef-building corals.

Keywords:
CalcificationCoral ecologyGeometryGrowthMorphologyProductivity

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Measuring the Structure, Composition, and Change of Underwater Environments with Large-area Imaging
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Area of Science:

  • Marine Biology
  • Ecology
  • Biophysics

Background:

  • Reef-building corals display diverse colony morphologies with significant physiological and ecological consequences.
  • Colony geometry influences the interplay between volume, surface area, and growth parameters in clonal organisms.
  • Calcifying organisms like corals exhibit dual growth components: biomass production and calcification.

Purpose of the Study:

  • To model mathematical relationships between coral growth parameters and colony geometry.
  • To determine how colony geometry influences size-dependent versus size-independent growth.
  • To investigate the ecological implications of geometric constraints on coral growth strategies.

Main Methods:

  • Utilized basic geometric shapes to model coral growth.
  • Analyzed the relationship between surface area, volume, and growth rates.
  • Examined how biomass production and calcification interact based on colony geometry.

Main Results:

  • Coral linear extension rates can be size-dependent due to geometry, contrary to traditional assumptions.
  • The ratio of mass to surface area, influenced by geometry, determines growth rate variations.
  • Specific geometries, like branching corals, prioritize surface area for resource acquisition, while hemispheroidal corals face calcification constraints at larger sizes.

Conclusions:

  • Colony geometry fundamentally shapes coral life history strategies and ecological interactions.
  • Geometric constraints on surface area to volume ratios explain size-dependent growth in certain coral morphologies.
  • Understanding these ontogenetic geometric relationships supports coral restoration techniques like microfragmentation.