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Track Transition Curve
A track transition curve, or spiral easement, is a mathematically-calculated curve on a section of highway, or railroad track, in which a straight section changes into a curve. It is designed to prevent sudden changes in lateral (or centripetal) acceleration. In plane (viewed from above), the start of the transition of the horizontal curve is at infinite radius, and at the end of the transition, it has the same radius as the curve itself and so forms a very broad spiral. At the same time, in the vertical plane, the outside of the curve is gradually raised until the correct degree of bank is reached. If such an easement were not applied, the lateral acceleration of a rail vehicle would change abruptly at one point (the tangent point where the straight track meets the curve), with undesirable results
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Osculating Circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p. Its center lies on the inner normal line, and its curvature is the same as that of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named circulus osculans (Latin for "kissing circle") by Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point
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Coaling Tower
A coaling tower, coal stage or coaling station is a facility used to load coal as fuel into railway steam locomotives. Coaling towers were often sited at motive power depots or locomotive maintenance shops. Coaling towers were constructed of wood, steel-reinforced concrete, or steel. In almost all cases coaling stations used a gravity fed method, with one or more large storage bunkers for the coal elevated on columns above the railway tracks, from which the coal could be released to slide down a chute into the waiting locomotive's coal storage area. The method of lifting the bulk coal into the storage bin varied. The coal usually was dropped from a hopper car into a pit below tracks adjacent to the tower
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International Standard Book Number
The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency. An ISBN is assigned to each separate edition and variation (except reprintings) of a publication. For example, an e-book, a paperback and a hardcover edition of the same book will each have a different ISBN. The ISBN is ten digits long if assigned before 2007, and thirteen digits long if assigned on or after 1 January 2007. The method of assigning an ISBN is nation-specific and varies between countries, often depending on how large the publishing industry is within a country. The initial ISBN identification format was devised in 1967, based upon the 9-digit Standard Book Numbering (SBN) created in 1966
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Cartesian Coordinates
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines)
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Circular Arc
In Euclidean geometry, an arc (symbol: ) is a closed segment of a differentiable curve. A common example in the plane (a two-dimensional manifold), is a segment of a circle called a circular arc. In space, if the arc is part of a great circle (or great ellipse), it is called a great arc. Every pair of distinct points on a circle determines two arcs
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Quadratic Equation
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. Because the quadratic equation involves only one unknown, it is called "univariate"
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Three-dimensional Space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol 3--->. This serves as a three-parameter model of the physical universe (that is, the spatial part, without considering time) in which all known matter exists. However, this space is only one example of a large variety of spaces in three dimensions called 3-manifolds
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Arthur N. Talbot
Arthur Newell Talbot (October 21, 1857 – April 3, 1942) was an American civil engineer. He made many contributions to several engineering fields including structures, sewage management, and education
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Leonhard Euler
Leonhard Euler (/ˈɔɪlər/ OY-lər; Swiss Standard German: [ˈɔɪlər] (About this sound listen); German Standard German: [ˈɔʏlɐ] (About this sound listen); 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory
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William John Macquorn Rankine
Prof William John Macquorn Rankine (/ˈræŋkɪn/) FRSE FRS LLD (5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularly focusing on the first of the three thermodynamic laws. He developed the Rankine scale, an equivalent to the Kelvin scale of temperature, but in degrees fahrenheit rather than centigrade. Rankine developed a complete theory of the steam engine and indeed of all heat engines. His manuals of engineering science and practice were used for many decades after their publication in the 1850s and 1860s
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Sine Wave
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields
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History Of Rail Transport
The history of rail transport began in 6th century BC in Ancient Greece
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