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Related Concept Videos

Theorem of Pappus01:24

Theorem of Pappus

The Theorem of Pappus, also known as the Pappus–Guldinus Theorem, provides a geometric method for determining the volume and surface area of solids generated by the revolution of a plane region or a plane curve about an external axis. The theorem consists of two related statements. The first addresses the volume of solids formed by rotating plane areas, while the second addresses the surface area generated by rotating plane curves. Both results depend on the location of the centroid, which...
Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
Alternative Sets of Equilibrium Equations01:31

Alternative Sets of Equilibrium Equations

When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
One example of such a situation can be observed in a...
Basic Equation for Pressure Field01:13

Basic Equation for Pressure Field

The basic equation for a pressure field in fluid mechanics captures the balance of forces within any segment of fluid, providing a foundational understanding of how pressure changes within fluids under various forces. Generally, two main types of forces act on any part of a fluid: surface forces and body forces. Surface forces arise from pressure differences across points within the fluid, which result in net forces that can vary depending on the local pressure gradient. Body forces, on the...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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SOME A PRIORI PATHOMETRIC EQUATIONS

R Ross

    British Medical Journal
    |August 27, 2010
    PubMed
    Summary

    No abstract available in PubMed .

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