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How Round Is Your Circle
''How Round Is Your Circle? Where Engineering and Mathematics Meet'' is a book on the mathematics of physical objects, for a popular audience. It was written by chemical engineer John Bryant and mathematics educator Chris Sangwin, and published by the Princeton University Press in 2008. Topics The book has 13 chapters, whose topics include: *Lines, the thickness of physically drawn or cut lines, and the problem of testing straightness of physical objects *The construction of physical measuring and calculating devices including rulers, protractors, pantographs, planimeters, integrators, and slide rules *Mechanical linkages, pantographs, four-bar linkages, and the problem of converting rotary to linear motion, solved by the Peaucellier–Lipkin linkage and by Hart's inversor *Geometric dissections, straightedge and compass constructions, angle trisection, and mathematical origami *The catenary and the tractrix, curves formed from physical forces, and their use in bridges and bearin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tractrix
In geometry, a tractrix (; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the ''tractor'') that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed. It is therefore a curve of pursuit. It was first introduced by Claude Perrault in 1670, and later studied by Isaac Newton (1676) and Christiaan Huygens (1693). Mathematical derivation Suppose the object is placed at (or in the example shown at right), and the puller at the origin (mathematics), origin, so is the length of the pulling thread (4 in the example at right). Then the puller starts to move along the axis in the positive direction. At every moment, the thread will be tangent to the curve described by the object, so that it becomes completely determined by the movement of the puller. Mathematically, if the coordinates of the object are , the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gömböc
The Gömböc ( ) is the first known physical example of a class of convex three-dimensional homogeneous bodies, called mono-monostatic, which, when resting on a flat surface have just one stable and one unstable point of equilibrium. The existence of this class was conjectured by the Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by the Hungarian scientists Gábor Domokos and Péter Várkonyi by constructing at first a mathematical example and subsequently a physical example. Mono-monostatic shapes exist in countless varieties, most of which are close to a sphere, with a stringent shape tolerance (about one part in a thousand). Gömböc is the first mono-monostatic shape which has been constructed physically. It has a sharpened top, as shown in the photo. Its shape helped to explain the body structure of some tortoises in relation to their ability to return to an equilibrium position after being placed upside down. Copies of the Gömböc have been donate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superegg
In geometry, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of superellipsoid. Unlike an elongated ellipsoid, an elongated superegg can stand upright on a flat surface, or on top of another superegg. This is due to its curvature being zero at the tips. The shape was popularized by Danish poet and scientist Piet Hein (1905–1996). Supereggs of various materials, including brass, were sold as novelties or "executive toys" in the 1960s. Mathematical description The superegg is a superellipsoid whose horizontal cross-sections are circles. It is defined by the inequality :\left, \frac\^p + \left, \frac\^p \leq 1 where ''R'' is the horizontal radius at the "equator" (the widest part), and ''h'' is one half of the height. The exponent ''p'' determines the degree of flattening at the tips and equator. Hein's choice was ''p'' = 2.5 (the same one he used for the Ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block-stacking Problem
In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire , also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table. Statement The block-stacking problem is the following puzzle: Place N identical rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang. provide a long list of references on this problem going back to mechanics texts from the middle of the 19th century. Variants Single-wide The single-wide problem involves having only one block at any given level. In the ideal case of perfectly rectangular blocks, the solution to the single-wide problem is that the maximum overhang is given by \sum_^\frac times the width of a block. This sum is one half of the corresponding partial sum of the harmonic series. Because the harmonic series diverges, the maximal overhang tends to infinity as N increases, meaning that it is poss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Equilibrium
In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity, the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity, that particle is in static equilibrium. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reuleaux Triangle
A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circular disks, each having its center on the boundary of the other two. Constant width means that the separation of every two parallel supporting lines is the same, independent of their orientation. Because its width is constant, the Reuleaux triangle is one answer to the question "Other than a circle, what shape can a manhole cover be made so that it cannot fall down through the hole?" Reuleaux triangles have also been called spherical triangles, but that term more properly refers to triangles on the curved surface of a sphere. They are named after Franz Reuleaux,. a 19th-century German engineer who pioneered the study of machines for translating one type of motion into another, and who used Reuleaux triangles in his designs. However, these shapes were known before his time, for instance by the des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve Of Constant Width
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. Standard examples are the circle and the Reuleaux triangle. These curves can also be constructed using circular arcs centered at crossings of an arrangement of lines, as the involutes of certain curves, or by intersecting circles centered on a partial curve. Every body of constant width is a convex set, its boundary crossed at most twice by any line, and if the line crosses perpendicularly it does so at both crossings, separated by the width. By Barbier's theorem, the body's perimeter is exactly times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roundness (object)
Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle. Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing. In geometric dimensioning and tolerancing, control of a cylinder can also include its fidelity to the longitudinal axis, yielding cylindricity. The analogue of roundness in three dimensions (that is, for spheres) is sphericity. Roundness is dominated by the shape's gross features rather than the definition of its edges and corners, or the surface roughness of a manufactured object. A smooth ellipse can have low roundness, if its eccentricity is large. Regular polygons increase their roundness with increasing numbers of sides, even though they are still sharp-edged. In geology and the study of sediments (where three-dimensional particles are most important), roundness is considered to be the measurement of surfa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calendar
A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a physical record (often paper) of such a system. A calendar can also mean a list of planned events, such as a court calendar or a partly or fully chronological list of documents, such as a calendar of wills. Periods in a calendar (such as years and months) are usually, though not necessarily, synchronized with the cycle of the sun or the moon. The most common type of pre-modern calendar was the lunisolar calendar, a lunar calendar that occasionally adds one intercalary month to remain synchronized with the solar year over the long term. Etymology The term ''calendar'' is taken from , the term for the first day of the month in the Roman calendar, related to the verb 'to call out', referring to the "calling" of the new moon when it was first se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pixelization
Pixelization (British English, pixelisation) or mosaic processing is any technique used in editing images or video, whereby an image is blurred by displaying part or all of it at a markedly lower Image resolution, resolution. It is primarily used for censorship. The effect is a standard graphics filter, available in all but the most basic Raster graphics editor, bitmap graphics editors. As censorship A familiar example of pixelization can be found in majority of television news and documentary productions, in which vehicle license plates and faces of suspects at crime scenes are routinely obscured to maintain the presumption of innocence, such as how it appears in the television series ''Cops (TV series), COPS''. This is especially used in Hungary and Slovakia by RTL Klub. Bystanders and others who do not sign release forms are also customarily pixelized. Footage of nudity (including human male reproductive system, male and human female reproductive system, female genitals, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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