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Triangle Area
In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is T=bh/2, where ''b'' is the length of the ''base'' of the triangle, and ''h'' is the ''height'' or ''altitude'' of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular from the vertex opposite the base onto the line containing the base. Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book ''Elements'' in 300 BCE. In 499 CE Aryabhata, used this illustrated method in the ''Aryabhatiya'' (section 2.6). Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but relatively difficult to construct a 'height'. Various methods may be used in practice, de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Heron Of Alexandria
Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentalist of antiquity and a representative of the Hellenistic scientific tradition. Hero published a well-recognized description of a steam-powered device called an ''aeolipile'', also known as "Hero's engine". Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. In his work ''Mechanics'', he described pantographs. Some of his ideas were derived from the works of Ctesibius. In mathematics, he wrote a commentary on Euclid's ''Elements'' and a work on applied geometry known as the ''Metrica''. He is mostly remembered for Heron's formula; a way to calculate the area of a triangle using only the lengths of its sides. Much of Hero's original writings and designs have been lost, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Wedge Product
A wedge is a triangular shaped tool, a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular ( normal) to its inclined surfaces. The mechanical advantage of a wedge is given by the ratio of the length of its slope to its width..''McGraw-Hill Concise Encyclopedia of Science & Technology'', Third Ed., Sybil P. Parker, ed., McGraw-Hill, Inc., 1992, p. 2041. Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle. The force is applied on a flat, broad surface. This energy is transported to the pointy, sharp end of the wedge, hence the force is transported. The wedge simply transports energy in the form of friction and collects it to the pointy end, consequently breaking the item. History Wedges have existed fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Displacement Vector
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another. For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity). Formulation A displacement may be formulated as a '' relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Vector (geometric)
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A '' vector quantity'' is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a '' directed line segment''. A vector is frequently depicted graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \stackrel \longrightarrow. A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word means 'carrier'. It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Parallelogram
In Euclidean geometry, a parallelogram is a simple polygon, simple (non-list of self-intersecting polygons, self-intersecting) quadrilateral with two pairs of Parallel (geometry), parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence (geometry), congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with at least one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. The word "parallelogram" comes from the Greek παραλληλό-γραμμον, ''parallēló-grammon'', which means "a shape of parallel lines". Special cases *Rectangle – A par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Circumcircle
In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertex (geometry), vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius. The circumcenter is the point of intersection (geometry), intersection between the three perpendicular bisectors of the triangle's sides, and is a triangle center. More generally, an -sided polygon with all its vertices on the same circle, also called the circumscribed circle, is called a cyclic polygon, or in the special case , a cyclic quadrilateral. All rectangles, isosceles trapezoids, right kites, and regular polygons are cyclic, but not every polygon is. Straightedge and compass construction The circumcenter of a triangle can be Compass-and-straightedge construction, constructed by drawing any two of the three Bisection#Perpendicular bisectors, perpendicular bisectors. For three non-collinear points, these two lines cannot be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Semiperimeter
In geometry, the semiperimeter of a polygon is half its perimeter. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently enough in formulas for triangles and other figures that it is given a separate name. When the semiperimeter occurs as part of a formula, it is typically denoted by the letter . Motivation: triangles The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side lengths :s = \frac. Properties In any triangle, any vertex and the point where the opposite excircle touches the triangle partition the triangle's perimeter into two equal lengths, thus creating two paths each of which has a length equal to the semiperimeter. If are as shown in the figure, then the segments connecting a vertex with the opposite excircle tangency (, shown in red in the diagram) are known as splitters, and :\begin s &= , AB, +, A'B, =, AB, +, AB', =, AC, +, A'C, \\ &= , AC, +, AC', =, BC, +, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Qin Jiushao
Qin Jiushao (, ca. 1202–1261), courtesy name Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering Horner's method as well as inventing Tianchi basins, a type of rain gauge instrument used to gather meteorological data. Biography Although Qin Jiushao was born in Ziyang, Sichuan, his family came from Shandong province. He is regarded as one of the greatest mathematicians in Chinese history. This is especially remarkable because Qin did not devote his life to mathematics. He was accomplished in many other fields and held a series of bureaucratic positions in several Chinese provinces. Qin wrote ''Shùshū Jiǔzhāng'' (" Mathematical Treatise in Nine Sections") in 1247 CE. This treatise covered a variety of topics including indeterminate equations and the numerical solution of certain polynomial equations up to 10th order, as well as discussions on military matters and surveying. In the treatise Qin inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Mathematical Treatise In Nine Sections
The ''Mathematical Treatise in Nine Sections'' () is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247. The mathematical text has a wide range of topics and is taken from all aspects of the society of that time, including agriculture, astronomy, water conservancy, urban layout, construction engineering, surveying, taxation, armament, military and so on. This book contains nine chapters: #Da Yan type (Indeterminate equations); #Heaven phenomena #Area of land and field #Surveying #Taxation #Storage of grains #Building construction #Military matters #Price and interest. Each chapter contains nine problems, a total of 81 problems. Apart from describing Chinese Remainder Theorem for the first time and providing a constructive proof for it, the text investigated: *Indeterminate equations *"Linglong method" (, roughly "method of harmoniously alternating evolution") for numerical solution of algebraic equations, 570 years before Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Indian Astronomy
Astronomy has a long history in the Indian subcontinent, stretching from History of India, pre-historic to History of India (1947–present), modern times. Some of the earliest roots of Indian astronomy can be dated to the period of Indus Valley civilisation or earlier. Astronomy later developed as a discipline of Vedanga, or one of the "auxiliary disciplines" associated with the study of the Vedas dating 1500 BCE or older. The oldest known text is the ''Vedanga Jyotisha'', dated to 1400–1200 BCE (with the extant form possibly from 700 to 600 BCE). Indian astronomy was influenced by Greek astronomy beginning in the 4th century BCEHighlights of Astronomy, Volume 11B: As presented at the XXIIIrd General Assembly of the IAU, 1997. Johannes Andersen Springer, 31 January 1999 – Science – 616 pages. p. 72/ref>Babylon to Voyager and Beyond: A History of Planetary Astronomy. David Leverington. Cambridge University Press, 29 May 2010 – Science – 568 pages. p. 4/ref>Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Indian Mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava of Sangamagrama, Madhava. The Decimal, decimal number system in use today: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own." was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of 0 (number), ze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |