Wolfram Research Mathworld, Repository hosted at UIUC
(13.662 recursos)
Wolfram Research's MathWorld is a comprehensive and interactive mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers. It has been assembled by internet encyclopedist Eric W.ÊWeisstein with assistance from the mathematics and internet communities. Like the discipline of mathematics, this site is continuously updated to include new material and incorporate new discoveries. This is a free service for the mathematical community provided by Wolfram Research, makers of Mathematica, with additional support from the National Science Foundation.
Mostrando recursos 1 - 20 de 30
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Differential Equation -- from MathWorld - Weisstein, Eric W.
An equation which involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called a partial differential equation; if only ordinary derivatives are present, the equation is called an ordinary differential equation. Differential equations play an extremely important and useful role in applied math, engineering, and physics, and much mathematical and numerical machinery has been developed for the solution of differential equations....
2.
Abacus -- from MathWorld - Weisstein, Eric W.
A mechanical counting device consisting of a frame holding a series of parallel rods on each of which beads are strung. Each bead represents a counting unit, and each rod a place value. The primary purpose of the abacus is not to perform actual computations, but to provide a quick means of storing numbers during a calculation. Abaci were used by the Japanese and Chinese, as well as the Romans. See also: Roman Numerals, Slide Rule
3.
Anaglyph -- from MathWorld - Weisstein, Eric W.
A stereogram made of two pictures, one red and one blue, taken from offset positions. When the pictures are viewed through glasses with one lens of each color, the picture appears to be three-dimensional. See also: Stereogram
4.
Baguenaudier -- from MathWorld - Weisstein, Eric W.
A puzzle involving disentangling a set of rings from a looped double rod, originally used by French peasants to lock chests (Steinhaus 1999). The word "baguenaudier" means "time-waster" in French, and the puzzle is also called the Chinese rings or Devil's needle puzzle. ("Bague" also means "ring," but this appears to be an etymological coincidence. Interestingly, the bladder-senna tree is also known as "baguenaudier" in French.) Culin (1965)...
5.
Compass -- from MathWorld - Weisstein, Eric W.
A tool with two arms joined at their ends which can be used to draw circles. In geometric constructions, the classical Greek rules stipulate that the compass cannot be used to mark off distances, so it must "collapse" whenever one of its arms is removed from the page. This results in significant complication in the complexity of geometric constructions. See also: Constructible Polygon, Euclidean Tools, Geometric Construction, Geometrography, Mascheroni Construction, Plane Geometry,...
6.
Finite Element Method -- from MathWorld - Weisstein, Eric W.
A method for solving an equation by approximating continuous quantities as a set of quantities at discrete points, often regularly spaced into a so-called grid or mesh. Because finite element methods can be adapted to problems of great complexity and unusual geometry, they are an extremely powerful tool in the solution of important problems in heat transfer, fluid mechanics, and mechanical systems. Furthermore, the availability of fast and inexpensive computers allows problems which are...
7.
Finite Volume Method -- from MathWorld - Weisstein, Eric W.
The finite volume method is a numerical method for solving partial differential equations that calculates the values of the conserved variables averaged across the volume. One advantage of the finite volume method over finite difference methods is that it does not require a structured mesh (although a structured mesh can also be used). Furthermore, the finite volume method is preferable to other methods as a result of the fact that boundary conditions can be applied noninvasively. This is true...
8.
French Curve -- from MathWorld - Weisstein, Eric W.
French curves are plastic (or wooden) templates having an edge composed of several different curves. French curves are used in drafting (or were before computer-aided design) to draw smooth curves of almost any desired curvature in mechanical drawings. Several typical French curves are illustrated above. While an undergraduate at MIT, Feynman (1997, p. 23) used a French curve to illustrate the fallacy of learning without understanding. When he pointed out to his colleagues in a mechanical...
9.
Galton Board -- from MathWorld - Weisstein, Eric W.
Also known as quincunx, Galton's board is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of Pascals triangle, where the binomial coefficients are replaced by pegs. These form a lattice of walks for balls falling from the top to the bottom row. Each time a ball hits one of the pegs, it can choose to turn right or left with probability p and q=1-p respectively. If the rows are numbered from 0 to N-1, the path of each falling ball is a Bernoulli...
10.
Genaille Rods -- from MathWorld - Weisstein, Eric W.
Numbered rods which can be used to perform multiplication. See also: Napier's Bones
11.
Guilloché Pattern -- from MathWorld - Weisstein, Eric W.
Guilloche patterns are spirograph-like curves that frame a curve within an inner and outer envelope curve. They are used on banknotes, securities, and passports worldwide for added security against counterfeiting. For currency, the precise techniques used by the governments of Russia, the United States, Brazil, the European Union, Madagascar, Egypt, and all other countries are likely quite different. The figures above show the same guilloche pattern plotted in polar and Cartesian coordinates...
12.
Harmonograph -- from MathWorld - Weisstein, Eric W.
A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, complicated curves which eventually terminate in a point as the motion of the pendula is damped by friction. In the absence of friction (and for small displacements so that the general pendulum equations of motion become simple harmonic motion), the figures produced by a harmonograph would be Lissajous curves. See also: Lissajous...
13.
Hart's Inversor -- from MathWorld - Weisstein, Eric W.
A linkage which draws the inverse of a given curve. It can also convert circular to linear motion. The rods satisfy AB = CD and BC = DA, and O, P, and P' remain collinear. Coxeter (1969, p. 428) shows that if AO=\mu AB, then OP\times OP' = \mu(1-\mu)(AD^2-AB^2). See also: Linkage, Peaucellier Inversor
14.
Kempe Linkage -- from MathWorld - Weisstein, Eric W.
A double rhomboid linkage which gives rectilinear motion from circular without an inversion. See also: Peaucellier Inversor
15.
Linkage -- from MathWorld - Weisstein, Eric W.
Linkages are linked (or constrained) mechanical structures such as those used in robots, excavators, engines, etc. They are also extensively used for character animation in modeling systems. Sylvester, Kempe and Cayley developed the geometry associated with the theory of linkages in the 1870s. Kempe proved that every finite segment of an algebraic curve can be generated by a linkage in the manner of Watt's curve. See also: Hart's Inversor, Kempe Linkage, Pantograph, Peaucellier Inversor,...
16.
Longimeter -- from MathWorld - Weisstein, Eric W.
A longimeter is a transparent sheet of plastic with a regular grid of lines inclined at an angle of 30° to the sides of the sheet. By counting the number of squares occupied by a linear feature on a map (such as a river) for six different rotations of the sheet, the length of the feature can be determined. See also: Coastline Paradox
17.
Moiré Pattern -- from MathWorld - Weisstein, Eric W.
An interference pattern produced by overlaying similar but slightly offset templates. A simple example is obtained by taking two identical ruled transparent sheets of plastic, superposing them, and rotating one about its center as the other is held fixed. Moiré patterns can also be created by plotting series of curves on a computer screen. Here, the interference is provided by the discretization of the finite-sized pixels. For example, the illustrations above show a number of...
18.
Napier's Bones -- from MathWorld - Weisstein, Eric W.
Napier's bones, also called Napier's rods, are numbered rods which can be used to perform multiplication of any number by a number 2-9. By placing "bones" corresponding to the multiplier on the left side and the bones corresponding to the digits of the multiplicand next to it to the right, and product can be read off simply by adding pairs of numbers (with appropriate carries as needed) in the row determined by the multiplier. This process was published by Napier in 1617 an a book...
19.
Nomogram -- from MathWorld - Weisstein, Eric W.
A graphical plot which can be used for solving certain types of equations. According to Steinhaus (1983, p. 301), the Nomogram was invented by the French mathematicians Massau and M. P. Ocagne in 1889.
20.
Pantograph -- from MathWorld - Weisstein, Eric W.
A linkage invented in 1630 by Christoph Scheiner for making a scaled copy of a given figure. The linkage is pivoted at O; hinges are denoted \odot. By placing a pencil at P (or P'), a dilated image is obtained at P' (or P). See also: Homothetic, Linkage
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