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Dot Planimeter
A dot planimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots. To estimate the area of a shape, the sheet is overlaid on the shape and the dots within the shape are counted. The estimate of area is the number of dots counted multiplied by the area of a single grid square. In some variations, dots that land on or near the boundary of the shape are counted as half of a unit. The dots may also be grouped into larger square groups by lines drawn onto the transparency, allowing groups that are entirely within the shape to be added to the count rather than requiring their dots to be counted one by one. The estimation of area by means of a dot grid has also been called the dot grid method or (particularly when the alignment of the grid with the shape is random) systematic sampling. Perhaps because of its simplicity, it has been repeatedly reinvented. Application In forestry, cartography, and geogr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grid Points In Radius-5 Circle
Grid, The Grid, or GRID may refer to: Common usage * Cattle grid or stock grid, a type of obstacle is used to prevent livestock from crossing the road * Grid reference, used to define a location on a map Arts, entertainment, and media * News grid, used in communications/public relations Fictional entities * Grid (comics), a fictional character in the DC Comics Universe * Grid (Jotun), Gríðr, a giantess in Norse mythology * The grid, the virtual environment of the game ''Second Life ''Second Life'' is an online multimedia platform that allows people to create an avatar for themselves and then interact with other users and user created content within a multi player online virtual world. Developed and owned by the San Fra ...'' * ''The Grid'', the computerized virtual world in which the Tron (franchise), Tron franchise exists Games and gaming * Nvidia GRID, a cloud gaming platform for Nvidia Tegra products * ''Power Grid'', the English-language edition of the multiplayer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two together, may be called a polygon. The segments of a polygonal circuit are called its '' edges'' or ''sides''. The points where two edges meet are the polygon's '' vertices'' (singular: vertex) or ''corners''. The interior of a solid polygon is sometimes called its ''body''. An ''n''-gon is a polygon with ''n'' sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. Mathematicians are often concerned only with the bounding polygonal chains of simple polygons and they often define a polygon accordingly. A polygonal boundary may be allowed to cross over itself, creating star polygons and other self-intersecting polygons. A polygon is a 2-dimensional example of the more general polytope in any number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Points
In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point. Closure under addition and subtraction means that a lattice must be a subgroup of the additive group of the points in the space, and the requirements of minimum and maximum distance can be summarized by saying that a lattice is a Delone set. More abstractly, a lattice can be described as a free abelian group of dimension n which spans the vector space \mathbb^n. For any basis of \mathbb^n, the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can be formed from a basis in this way. A lattice may be viewed as a regular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Instruments
A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Established standard objects and events are used as units, and the process of measurement gives a number relating the item under study and the referenced unit of measurement. Measuring instruments, and formal test methods which define the instrument's use, are the means by which these relations of numbers are obtained. All measuring instruments are subject to varying degrees of instrument error and measurement uncertainty. These instruments may range from simple objects such as rulers and stopwatches to electron microscopes and particle accelerators. Virtual instrumentation is widely used in the development of modern measuring instruments. Time In the past, a common time measuring instrument was the sundial. Today, the usual measuring instrument ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A pl ... or planar lamina, while ''surface area'' refers to the area of an open surface or the boundary (mathematics), boundary of a solid geometry, three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a plane curve, curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. See also * ''Bulletin of the American Mathematical Society'' * '' Journal of the American Mathematical Society'' * ''Memoirs of the American Mathematical Society'' * ''Notices of the American Mathematical Society'' * ''Proceedings of the American Mathematical Society'' External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ... American Mathematical Society academic journals Mathematics journals Publications established in 1900 {{math-journal-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steinhaus Longimeter
The Steinhaus longimeter, patented by the professor Hugo Steinhaus, is an instrument used to measure the lengths of curves on maps. Description It is a transparent sheet of three grids, turned against each other by 30 degrees, each consisting of parallel lines spaced at equal distances 3.82 mm. The measurement is done by counting crossings of the curve with grid lines. The number of crossings is the approximate length of the curve in millimetres. The design of the Steinhaus longimeter can be seen as an application of the Crofton formula, according to which the length of a curve equals the expected number of times it is crossed by a random line. See also * Opisometer, a mechanical device for measuring curve length by rolling a small wheel along the curve * Dot planimeter, a similar transparency-based device for estimating area, based on Pick's theorem References Bibliography * Hugo Steinhaus: Zur Praxis der Rectification und zum Längenbegriff, ''Berichte der Sächsisc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape. Construction There are several kinds of planimeters, but all operate in a similar way. The precise way in which they are constructed varies, with the main types of mechanical planimeter being polar, linear and Prytz or "hatchet" planimeters. The Swiss mathematician Jakob Amsler-Laffon built the first modern planimeter in 1854, the concept having been pioneered by Johann Martin Hermann in 1814. Many developments followed Amsler's famous planimeter, including electronic versions. The Amsler (polar) type consists of a two-bar linkage. At the end of one link is a pointer, used to trace around the boundary of the shape to be measured. The other end of the linkage pivots freely on a weight that keeps it from moving. Near the junction of the two links is a measuring wheel of calibrated diameter, with a scale to show fine rotation, and worm gearing for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss Circle Problem
In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius r. This number is approximated by the area of the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area. The first progress on a solution was made by Carl Friedrich Gauss, hence its name. The problem Consider a circle in \mathbb^2 with center at the origin and radius r\ge 0. Gauss's circle problem asks how many points there are inside this circle of the form (m,n) where m and n are both integers. Since the equation of this circle is given in Cartesian coordinates by x^2+y^2= r^2, the question is equivalently asking how many pairs of integers ''m'' and ''n'' there are such that :m^2+n^2\leq r^2. If the answer for a given r is denoted by N(r) then the following list shows the first few values of N(r) for ''r'' an integer between 0 and 12 followed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Frederick Blichfeldt
Hans Frederick Blichfeldt (1873–1945) was a Danish-American mathematician at Stanford University, known for his contributions to group theory, the representation theory of finite groups, the geometry of numbers, sphere packing, and quadratic forms. He is the namesake of Blichfeldt's theorem. Life Blichfeldt was one of five children of a Danish farming couple, Erhard Christoffer Laurentius Blichfeldt and Nielsine Maria Schlaper; many of his father's ancestors were ministers. He was born on January 9, 1873 in Iller, a village in the Sønderborg Municipality of Denmark. In 1881, the family moved to Copenhagen. In 1888, he passed with high honors the entrance examinations for the University of Copenhagen, but his family was unable to afford sending him to the university. Instead, later the same year, they moved again to the US. He worked for several years as a lumberman, a railway worker, a traveling surveyor, and then as a government draftsman in Bellingham, Washington. In 189 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
