|
Hacoversine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'', Section I) trigonometric tables. The versine of an angle is 1 minus its . There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the haversine formula of navigation. Overview The versine[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometric Function
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent functions. Their multiplicative inverse, reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions has a corresponding Inverse trigonometric functions, inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bow (weapon)
The bow and arrow is a ranged weapon system consisting of an elastic launching device (bow) and long-shafted projectiles (arrows). Humans used bows and arrows for hunting and aggression long before recorded history, and the practice was common to many prehistoric cultures. They were important weapons of war from ancient history until the early modern period, when they were rendered increasingly obsolete by the development of the more powerful and accurate firearms. Today, bows and arrows are mostly used for hunting and sports. Archery is the art, practice, or skill of using bows to shoot arrows.Paterson ''Encyclopaedia of Archery'' p. 17 A person who shoots arrows with a bow is called a bowman or an archer. Someone who makes bows is known as a bowyer,Paterson ''Encyclopaedia of Archery'' p. 31 someone who makes arrows is a fletcher,Paterson ''Encyclopaedia of Archery'' p. 56 and someone who manufactures metal arrowheads is an arrowsmith.Paterson ''Encyclopaedia of Archery'' p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equatorial Bulge
An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere. On Earth The planet Earth has a rather slight equatorial bulge; its equatorial diameter is about greater than its polar diameter, with a difference of about of the equatorial diameter. If Earth were scaled down to a globe with an equatorial diameter of , that difference would be only . While too small to notice visually, that difference is still more than twice the largest deviations of the actual surface from the ellipsoid, including the tallest mountains and deepest oceanic trenches. Earth's rotation also affects the sea level, the imaginary surface used as a reference frame from which to measure altitudes. This surface coincides with the mean water surface level in oceans, and is extrapolated over land by taking into account the loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface (mathematics), surface obtained by Surface of revolution, rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a ''prolate spheroid'', elongated like a rugby ball. The ball (gridiron football), American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an ''oblate spheroid'', flattened like a lentil or a plain M&M's, M&M. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation of the Earth, rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattening, flattened in the direction of its axis of rotation. For that reason, in cartography and geode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy
Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzantine, Islamic science, Islamic, and Science in the Renaissance, Western European science. The first was his astronomical treatise now known as the ''Almagest'', originally entitled ' (, ', ). The second is the ''Geography (Ptolemy), Geography'', which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian physics, Aristotelian natural philosophy of his day. This is sometimes known as the ' (, 'On the Effects') but more commonly known as the ' (from the Koine Greek meaning 'four books'; ). The Catholic Church promoted his work, which included the only mathematically sound geocentric model of the Sola ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-angle Formula
In trigonometry, trigonometric identities are Equality (mathematics), equalities that involve trigonometric functions and are true for every value of the occurring Variable (mathematics), variables for which both sides of the equality are defined. Geometrically, these are identity (mathematics), identities involving certain functions of one or more angles. They are distinct from Trigonometry#Triangle identities, triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integral, integration of non-trigonometric functions: a common technique involves first using the Trigonometric substitution, substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity. Pythagorean identities The basic relationship betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surya Siddhanta
The ''Surya Siddhanta'' (; ) is a Sanskrit treatise in Indian astronomy dated to 4th to 5th century,Menso Folkerts, Craig G. Fraser, Jeremy John Gray, John L. Berggren, Wilbur R. Knorr (2017)Mathematics Encyclopaedia Britannica, Quote: "(...) its Hindu inventors as discoverers of things more ingenious than those of the Greeks. Earlier, in the late 4th or early 5th century, the anonymous Hindu author of an astronomical handbook, the ''Surya Siddhanta'', had tabulated the sine function (...)" in fourteen chapters.Plofkerpp. 71–72 The ''Surya Siddhanta'' describes rules to calculate the motions of various planets and the moon relative to various constellations, diameters of various planets, and calculates the orbits of various astronomical bodies. The text is known from a palm-leaf manuscript, and several newer manuscripts. It was composed or revised probably c. 800 CE from an earlier text also called the ''Surya Siddhanta''. The ''Surya Siddhanta'' text is composed of verses mad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy's Table Of Chords
The table of chords, created by the Greece, Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's ''Almagest'', a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function. It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of ). Since the 8th and 9th centuries, the sine and other trigonometric functions have been used in Islamic mathematics and astronomy, reforming the production of sine tables. Muhammad ibn Musa al-Khwarizmi, Khwarizmi and Habash al-Hasib al-Marwazi, Habash al-Hasib later produced a set of trigonometric tables. The chord function and the table A chord (geometry), chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithmic Table
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks, and specialized tables were published for numerous applications. History and use The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. The table produced by the Indian mathematician Āryabhaṭa (476–550 CE) is considered the first sine table ever constructed. Ārya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , then is the logarithm of to base , written , so . As a single-variable function, the logarithm to base is the inverse of exponentiation with base . The logarithm base is called the ''decimal'' or ''common'' logarithm and is commonly used in science and engineering. The ''natural'' logarithm has the number as its base; its use is widespread in mathematics and physics because of its very simple derivative. The ''binary'' logarithm uses base and is widely used in computer science, information theory, music theory, and photography. When the base is unambiguous from the context or irrelevant it is often omitted, and the logarithm is written . Logarithms were introduced by John Napier in 1614 as a means of simplifying calculation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Round-off Error
In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error. When using approximation equations or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits), one of the goals of numerical analysis is to estimate computation errors. Computation errors, also called numerical errors, include both truncation errors and roundoff errors. When a sequence of calculations with an input involving any roundoff error are made, errors may accumulate, sometimes dominating the calculation. In ill-conditioned problems, significant error may accumulate. In short, there are two major facets ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
