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Running Angle
In mathematics, the running angle is the angle of consecutive vectors (Xt,Yt) with respect to the base line, i.e. : \phi(t) = \arctan\left(\frac \right) . Usually, it is more informative to compute it using a four-quadrant version of the arctan function in a mathematical software library. See also * Differential geometry * Polar distribution In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range A circular distribution is often a continuous probability di ... Penmanship {{term-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baseline (typography)
In European and West Asian typography and penmanship, the baseline is the line upon which most letters ''sit'' and below which descenders extend. In the example to the right, the letter 'p' has a descender; the other letters sit on the (red) baseline. Most, though not all, typefaces are similar in the following ways as regards the baseline: * capital letters sit on the baseline. The most common exceptions are the J and Q. *Lining figures (see Arabic numerals) sit on the baseline. *The following text figures have descenders: 3 4 5 7 9. *The following lowercase letters have descenders: g j p q y. * Glyphs with rounded lower and upper extents (0 3 6 8 c C G J o O Q) dip very slightly below the baseline ("overshoot") to create the optical illusion that they sit on the baseline, and rise above the x-height or capital height to create the illusion that they have the same height as flat glyphs (such as those for H x X 1 5 7). Peter Karow's ''Digital Typefaces'' suggests that typi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arctan
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry. Notation Several notations for the inverse trigonometric functions exist. The most common convention is to name inverse trigonometric functions using an arc- prefix: , , , etc. (This convention is used throughout this article.) This notation arises from the following geometric relationships: when measuring in radians, an angle of ''θ'' radians will correspond to an arc whose length is ''rθ'', where ''r'' is the radius of the circle. Thus in the u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Distribution
In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range A circular distribution is often a continuous probability distribution, and hence has a probability density, but such distributions can also be discrete, in which case they are called circular lattice distributions. Circular distributions can be used even when the variables concerned are not explicitly angles: the main consideration is that there is not usually any real distinction between events occurring at the lower or upper end of the range, and the division of the range could notionally be made at any point. Graphical representation If a circular distribution has a density :p(\phi) \qquad \qquad (0\le\phi<2\pi),\, it can be graphically represented as a closed : |
