Determining the length of an irregular arc segment is also called rectification of a curve. Historically, many methods were used for specific curves. The advent of infinitesimal calculus led to a general formula that provides closed-form solutions in some cases.
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Elastic energy
Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume or shape. Elasticity theory primarily develops an analytical understanding of the mechanics of solid bodies and materials. The essence of elasticity is reversibility. Forces applied to an elastic material transfer energy into the material which, upon yielding that energy to its surroundings, can recover its original shape.
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Plane curve
In mathematics, a plane curve is a curve in a Euclidean plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a real Euclidean plane R and is a one-dimensional smooth manifold. Equivalently, a smooth plane curve can be given locally by an equation {{{1}}} where ƒ : R → R is a smooth function, and the partial derivatives ∂ƒ/∂x and ∂ƒ/∂y are never both 0.
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Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems. Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length. The total energy contained in an object is identified with its mass, and energy (like mass), cannot be created or destroyed.
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Solution
In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. The solvent does the dissolving. The solution more or less takes on the characteristics of the solvent including its phase, and the solvent is commonly the major fraction of the mixture. The concentration of a solute in a solution is a measure of how much of that solute is dissolved in the solvent.
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Short film
A short film is any film not long enough to be considered a feature film. No consensus exists as to where that boundary is drawn: the Academy of Motion Picture Arts and Sciences defines a short film as "an original motion picture that has a running time of 40 minutes or less, including all credits". The term featurette originally applied to a film longer than a short subject, but shorter than a standard feature film. The increasingly rare term short subject means approximately the same thing.
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