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Angle
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle. Angles formed by two rays are also known as ''plane angles'' as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called '' dihedral angles''. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. The magnitude of an angle is called an angular measure or simply "angle". ''Angle of rotation'' is a measure conventionally defined as the ratio of a circular arc length to its radius, and may be a negative number. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. History and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. ''Angle'' is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. History and etymology The word ''angle'' comes from the Latin word ''angulus'', meaning "corner"; cognate words are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cognate
In historical linguistics, cognates or lexical cognates are sets of words in different languages that have been inherited in direct descent from an etymological ancestor in a common parent language. Because language change can have radical effects on both the sound and the meaning of a word, cognates may not be obvious, and often it takes rigorous study of historical sources and the application of the comparative method to establish whether lexemes are cognate or not. Cognates are distinguished from loanwords, where a word has been borrowed from another language. The term ''cognate'' derives from the Latin noun '' cognatus blood relative'. Characteristics Cognates need not have the same meaning, which may have changed as the languages developed independently. For example English '' starve'' and Dutch '' sterven'' 'to die' or German '' sterben'' 'to die' all descend from the same Proto-Germanic verb, '' *sterbaną'' 'to die'. Cognates also do not need to look or sound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi (letter)
Pi (uppercase Π, lowercase π and ϖ; el, πι ) is the sixteenth letter of the Greek alphabet, representing the voiceless bilabial plosive . In the system of Greek numerals it has a value of 80. It was derived from the Phoenician letter Pe (). Letters that arose from pi include Latin P, Cyrillic Pe (П, п), Coptic pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀). Uppercase Pi The uppercase letter Π is used as a symbol for: * In textual criticism, '' Codex Petropolitanus'', a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia. * In legal shorthand, it represents a plaintiff. In science and engineering: * The product operator in mathematics, indicated with capital pi notation (in analogy to the use of the capital Sigma as summation symbol). * The osmotic pressure in chemistry. * The viscous stress tensor in continuum mechanics and fluid dynamics. Lowercase Pi The lowercase letter π is used as a symbol for: * The mathematical re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (mathematics)
In mathematics, a variable (from Latin '' variabilis'', "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set. Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. In mathematical logic, a ''variable'' is either a symbol representing an unspecified term of the theory (a meta-variable), or a basic object of the theory that is manipulated without referring to its possible intuitive interpretation. History In ancient works such as Euclid's ''Elements'', single letters refer to geometric points and shapes. In the 7th century, Brahmagupta used different colours to represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Letter
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin during the modern era. Sound values and conventional transcriptions for some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax. Many authors distinguish an expression from a ''formula'', the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. For example, 8x-5 is an expression, while 8x-5 \geq 5x-8 is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to ''true'' or ''false'', depending on the values that are given to the variables occurring in the expressions. For example 8x-5 \geq 5x-8 takes the value ''false'' if is given a value less than –1, and the value ''true'' otherwise. Examples The use of expr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carpus Of Antioch
Carpus of Antioch ( el, Κάρπος) was an ancient Greek mathematician. It is not certain when he lived; he may have lived any time between the 2nd century BC and the 2nd century AD. He wrote on mechanics, astronomy, and geometry. Proclus quotes from an ''Astronomical Treatise'' by Carpus concerning whether problems should come before theorems, in which Carpus may (or may not) have been criticising Geminus. Proclus also quotes the view of Carpus that "an angle In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles ... is a quantity, namely a distance between the lines of surfaces containing it." According to Pappus, Carpus made use of mathematics for practical applications. According to Iamblichus, Carpus also constructed a curve for the purpose of squaring the circle, which he calls a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Straight Line
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment in everyday life, which has two points to denote its ends. Lines can be referred by two points that lay on it (e.g., \overleftrightarrow) or by a single letter (e.g., \ell). Euclid described a line as "breadthless length" which "lies evenly with respect to the points on itself"; he introduced several postulates as basic unprovable properties from which he constructed all of geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of the 19th century (such as non-Euclidean, projective and affine geometry). In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eudemus Of Rhodes
Eudemus of Rhodes ( grc-gre, Εὔδημος) was an ancient Greek philosopher, considered the first historian of science, who lived from c. 370 BCE until c. 300 BCE. He was one of Aristotle's most important pupils, editing his teacher's work and making it more easily accessible. Eudemus' nephew, Pasicles, was also credited with editing Aristotle's works. Life Eudemus was born on the isle of Rhodes, but spent a large part of his life in Athens, where he studied philosophy at Aristotle's Peripatetic School. Eudemus's collaboration with Aristotle was long-lasting and close, and he was generally considered to be one of Aristotle's most brilliant pupils: he and Theophrastus of Lesbos were regularly called not Aristotle's "disciples", but his "companions" (ἑταῖροι). It seems that Theophrastus was the greater genius of the two, continuing Aristotle's studies in a wide range of areas. Although Eudemus too conducted original research, his ''forte'' lay in systematizing Arist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proclus
Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, Early Islamic philosophy, and Scholastic philosophy. Biography The primary source for the life of Proclus is the eulogy ''Proclus, or On Happiness'' that was written for him upon his death by his successor, Marinus, Marinus' biography set out to prove that Proclus reached the peak of virtue and attained eudaimonia. There are also a few details about the time in which he lived in the similarly structured ''Life of Isidore'' written by the philosopher Damascius in the following century. According to Marinus, Proclus was born in 412 AD in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid
Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Elements'' treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. Until the early Renaissance he was often mistaken for the earlier philosopher Euclid of Megara, causing his biograph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proto-Indo-European Language
Proto-Indo-European (PIE) is the reconstructed common ancestor of the Indo-European language family. Its proposed features have been derived by linguistic reconstruction from documented Indo-European languages. No direct record of Proto-Indo-European exists. Far more work has gone into reconstructing PIE than any other proto-language, and it is the best understood of all proto-languages of its age. The majority of linguistic work during the 19th century was devoted to the reconstruction of PIE or its daughter languages, and many of the modern techniques of linguistic reconstruction (such as the comparative method) were developed as a result. PIE is hypothesized to have been spoken as a single language from 4500 BC to 2500 BC during the Late Neolithic to Early Bronze Age, though estimates vary by more than a thousand years. According to the prevailing Kurgan hypothesis, the original homeland of the Proto-Indo-Europeans may have been in the Pontic–Caspian st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
