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In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
This was the beginning of the coastline problem, which is a mathematical uncertainty inherent in the measurement of boundaries that are irregular. [6] The prevailing method of estimating the length of a border (or coastline) was to lay out n equal straight-line segments of length l with dividers on a map or aerial photograph. Each end of the ...
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...
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Then the curved scale used for the expected value is selected based on the range. For example, an observed value of 9 would use the tick mark above the 9 in range A, and curved scale A would be used for the expected value. An observed value of 81 would use the tick mark above 81 in range E, and curved scale E would be used for the expected value.
The atomic length scale is ℓ a ~ 10 −10 m and is given by the size of hydrogen atom (i.e., the Bohr radius, approximately 53 pm).; The length scale for the strong interactions (or the one derived from QCD through dimensional transmutation) is around ℓ s ~ 10 −15 m, and the "radii" of strongly interacting particles (such as the proton) are roughly comparable.