268 relations: Absolute zero, Absorbing element, Abstract algebra, Additive identity, Al-Mansur, Alain Prost, Algebra, Algebraic number, ALGOL 58, Algorism, Almagest, Amir Aczel, Ancient Greece, Andalé Mono, Andes, Anemoi, Anno Domini, Application programming interface, Arabic, Arabic numerals, Array data type, Aryabhatiya, Association football, Astrolabe, Astronomical year numbering, Astronomy, Atom, Atomic nucleus, Atomic number, Śūnyatā, Babylonian mathematics, Babylonian numerals, Bakhshali manuscript, Bede, Bengali language, Binary number, Birch, Brahmagupta, Brāhmasphuṭasiddhānta, Business telephone system, Byzantine Empire, C (programming language), Calendar era, Cambodia, Cardinality, Category (mathematics), Category theory, Central Kurdish, Charles Seife, Chaturbhuj Temple (Orchha), ..., Chemical element, Chiapas, Chinese characters of Empress Wu, Chinese numerals, COBOL, Compile time, Complex number, Composite number, Computability theory, Computable function, Computer monitor, Computer science, Computus, Constant function, Cosmology, Counting rods, Cricket, Damon Hill, Decibel, Decimal, Definition, Determinant, Dionysius Exiguus, Division by zero, Divisor, DVD region code, Eastern Arabic numerals, Edsger W. Dijkstra, Egyptian numerals, Empty product, Empty set, Empty sum, Epoch (reference date), Even and odd functions, Exit status, Factorial, FE-Schrift, Fibonacci, Fibonacci Quarterly, Floating-point arithmetic, Formula One, Fortran, Free variables and bound variables, Glyph, Grammatical number, Greatest and least elements, Greece, Greek numerals, Gupta Empire, Gwalior, Gwalior Fort, Han dynasty, Hieroglyph, Hindu–Arabic numeral system, Hinduism, Hipparchus, History of mathematics, Holomorphic function, Iberian Peninsula, IBM 3270, IBM Floating Point Architecture, Identity element, IEEE 754, Inca Empire, Indeterminate form, Indian numerals, Indian subcontinent, Infinity, Initial and terminal objects, Integer, Interstate Highway System, Isaac Asimov, Italian language, Jainism, Japanese numerals, Java (programming language), Java Database Connectivity, Johannes de Sacrobosco, John D. Barrow, John Wiley & Sons, Kelvin, Khmer numerals, Kish (Sumer), Kratié Province, L'Hôpital's rule, Latin, Lattice (order), Leading zero, Lemma (mathematics), Limit of a function, Lisp (programming language), List of Formula One World Drivers' Champions, List of international call prefixes, Lokavibhaga, MacOS, Mathematical Association of America, Mathematical Treatise in Nine Sections, Mathematics, Matrix (mathematics), Matter, Maya numerals, Mekong, Melting point, Mesoamerican Long Count calendar, Middle Ages, Moors, Morse code, Muhammad ibn Ahmad al-Khwarizmi, Muhammad ibn Musa al-Khwarizmi, Multiplicative inverse, Muslim, Names for the number 0 in English, Natural number, Negative temperature, Neutron, Neutronium, Nicolas Bourbaki, Nigel Mansell, Null (SQL), Null pointer, Number, Number line, Number theory, Numeral system, Numerical digit, O, Old World, Olmecs, Omicron, Ones' complement, Operating system, Operator assistance, Ordinal number, Oxford University Press, Palm OS, Parity (mathematics), Parity of zero, PDF, Peano axioms, Periodic table, Persian people, Phon, Physical system, Physics, Pingala, Pope Sylvester II, Positional notation, Prakrit, Prime number, Princeton University Press, Propositional calculus, Proton, Ptolemy, Ptolemy's table of chords, Qin Jiushao, Quantum mechanics, Quatrefoil, Quipu, Radiocarbon dating, Rational number, Real number, Return code, Roman numerals, Roulette, Sanskrit, Sanskrit prosody, Scientific American, Set theory, Sexagesimal, Shaka era, Sign (mathematics), Signed number representations, Signed zero, Slashed zero, Springer Nature, Stationary state, Sunzi Suanjing, Tennis, Tetraneutron, Thai numerals, The Guardian, The Nine Chapters on the Mathematical Art, Theoretical astronomy, Thermodynamic temperature, Three-valued logic, Tortoise, Trunk prefix, Truth value, Turing degree, Turtle shell, Two's complement, Typewriter, Undefined (mathematics), Unix time, Vacuum, Vehicle registration plates of Germany, Vigesimal, Von Neumann cardinal assignment, W. W. Norton & Company, Walter Eugene Clark, Well-order, Wu Zetian, Year zero, Zeno of Elea, Zeno's paradoxes, Zero element, Zero morphism, Zero of a function, Zero to the power of zero, Zero-based numbering, Zero-point energy, Zero: The Biography of a Dangerous Idea, Zeros and poles, 0, 0th, 1, 2, 690. Expand index (218 more) » « Shrink index
Absolute zero is the lower limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0.
In mathematics, an absorbing element is a special type of element of a set with respect to a binary operation on that set.
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.
Al-Mansur or Abu Ja'far Abdallah ibn Muhammad al-Mansur (95 AH – 158 AH (714 AD– 6 October 775 AD); أبو جعفر عبدالله بن محمد المنصور) was the second Abbasid Caliph reigning from 136 AH to 158 AH (754 AD – 775 AD)Axworthy, Michael (2008); A History of Iran; Basic, USA;.
Alain Marie Pascal Prost (born 24 February 1955) is a retired French racing driver.
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).
ALGOL 58, originally known as IAL, is one of the family of ALGOL computer programming languages.
Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits.
The Almagest is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts of all time, its geocentric model was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus.
Amir Dan Aczel (November 6, 1950 – November 26, 2015) was an Israeli-born American lecturer in mathematics and the history of mathematics and science, and an author of popular books on mathematics and science.
Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).
Andalé Mono (for technical reasons also Andale Mono) is a monospaced sans-serif typeface designed by Steve Matteson for terminal emulation and software development environments, originally for the Taligent project by Apple Inc. and IBM.
The Andes or Andean Mountains (Cordillera de los Andes) are the longest continental mountain range in the world.
In ancient Greek religion and myth, the Anemoi (Greek: Ἄνεμοι, "Winds") were wind gods who were each ascribed a cardinal direction from which their respective winds came (see Classical compass winds), and were each associated with various seasons and weather conditions.
The terms anno Domini (AD) and before Christ (BC) are used to label or number years in the Julian and Gregorian calendars.
In computer programming, an application programming interface (API) is a set of subroutine definitions, protocols, and tools for building software.
Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.
Arabic numerals, also called Hindu–Arabic numerals, are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system, the most common system for the symbolic representation of numbers in the world today.
Language support for array types may include certain built-in array data types, some syntactic constructions (array type constructors) that the programmer may use to define such types and declare array variables, and special notation for indexing array elements.
Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.
Association football, more commonly known as football or soccer, is a team sport played between two teams of eleven players with a spherical ball.
An astrolabe (ἀστρολάβος astrolabos; ٱلأَسْطُرلاب al-Asturlāb; اَختِرِیاب Akhteriab) is an elaborate inclinometer, historically used by astronomers and navigators to measure the inclined position in the sky of a celestial body, day or night.
Astronomical year numbering is based on AD/CE year numbering, but follows normal decimal integer numbering more strictly.
Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.
An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.
The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of an atom.
Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.
The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.
Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.
Christmas traditions vary from country to country.
New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.
New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.
In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.
Śūnyatā (Sanskrit; Pali: suññatā), pronounced ‘shoonyataa’, translated into English most often as emptiness and sometimes voidness, is a Buddhist concept which has multiple meanings depending on its doctrinal context.
Babylonian mathematics (also known as Assyro-Babylonian mathematics) was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC.
Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.
The Bakhshali manuscript is a mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan).
Bede (italic; 672/3 – 26 May 735), also known as Saint Bede, Venerable Bede, and Bede the Venerable (Bēda Venerābilis), was an English Benedictine monk at the monastery of St.
Bengali, also known by its endonym Bangla (বাংলা), is an Indo-Aryan language spoken in South Asia.
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).
A birch is a thin-leaved deciduous hardwood tree of the genus Betula, in the family Betulaceae, which also includes alders, hazels, and hornbeams.
Brahmagupta (born, died) was an Indian mathematician and astronomer.
The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628.
A business telephone system is a multiline telephone system typically used in business environments, encompassing systems ranging from small key telephone systems to large-scale private branch exchanges.
The Byzantine Empire, also referred to as the Eastern Roman Empire and Byzantium, was the continuation of the Roman Empire in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, which had been founded as Byzantium).
C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.
A calendar era is the year numbering system used by a calendar.
Cambodia (កម្ពុជា, or Kampuchea:, Cambodge), officially known as the Kingdom of Cambodia (ព្រះរាជាណាចក្រកម្ពុជា, prĕəh riəciənaacak kampuciə,; Royaume du Cambodge), is a sovereign state located in the southern portion of the Indochina peninsula in Southeast Asia.
In mathematics, the cardinality of a set is a measure of the "number of elements of the set".
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
Central Kurdish (کوردیی ناوەندی, Kurdîy nawendî), also called Sorani (سۆرانی, Soranî) is a Kurdish language spoken in Iraq, mainly in Iraqi Kurdistan, as well as the Kurdistan Province and West Azerbaijan Province of western Iran.
Charles Seife is an American author and journalist, a professor at New York University.
Chaturbhuj Temple (Devanagri: चतुर्भुज मंदिर), dedicated to Vishnu, is situated at Orchha in Madhya Pradesh, India.
A chemical element is a species of atoms having the same number of protons in their atomic nuclei (that is, the same atomic number, or Z).
Chiapas, officially the Free and Sovereign State of Chiapas (Estado Libre y Soberano de Chiapas), is one of the 31 states that with Mexico City make up the 32 federal entities of Mexico.
Chinese characters of Empress Wu, or the Zetian characters, are Chinese characters introduced by Empress Wu Zetian, the only reigning female in the history of China, to demonstrate her power.
Chinese numerals are words and characters used to denote numbers in Chinese.
COBOL (an acronym for "common business-oriented language") is a compiled English-like computer programming language designed for business use.
In computer science, compile time refers to either the operations performed by a compiler (the "compile-time operations"), programming language requirements that must be met by source code for it to be successfully compiled (the "compile-time requirements"), or properties of the program that can be reasoned about during compilation.
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.
Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
Computable functions are the basic objects of study in computability theory.
A computer monitor is an output device which displays information in pictorial form.
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
Computus (Latin for "computation") is a calculation that determines the calendar date of Easter.
In mathematics, a constant function is a function whose (output) value is the same for every input value.
Cosmology (from the Greek κόσμος, kosmos "world" and -λογία, -logia "study of") is the study of the origin, evolution, and eventual fate of the universe.
Counting rods are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia.
Cricket is a bat-and-ball game played between two teams of eleven players each on a cricket field, at the centre of which is a rectangular pitch with a target at each end called the wicket (a set of three wooden stumps upon which two bails sit).
Damon Graham Devereux Hill, (born 17 September 1960) is a British former racing driver.
The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a physical property to another on a logarithmic scale.
The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
Dionysius Exiguus (Latin for "Dionysius the Humble"; –) was a 6th-century monk born in Scythia Minor (probably modern Dobruja, in Romania and Bulgaria).
In mathematics, division by zero is division where the divisor (denominator) is zero.
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.
DVD (digital versatile disc) region codes are a digital rights management technique designed to allow rights holders to control the international distribution of a DVD release, including its content, release date, and price, all according to the appropriate region.
The Eastern Arabic numerals (also called Arabic–Hindu numerals, Arabic Eastern numerals and Indo–Persian numerals) are the symbols used to represent the Hindu–Arabic numeral system, in conjunction with the Arabic alphabet in the countries of the Mashriq (the east of the Arab world), the Arabian Peninsula, and its variant in other countries that use the Perso-Arabic script in the Iranian plateau and Asia.
Edsger Wybe Dijkstra (11 May 1930 – 6 August 2002) was a Dutch systems scientist, programmer, software engineer, science essayist, and early pioneer in computing science.
The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BC until the early first millennium AD.
In mathematics, an empty product, or nullary product, is the result of multiplying no factors.
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero.
In the fields of chronology and periodization, an epoch is an instant in time chosen as the origin of a particular era.
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
The exit status of a process in computer programming is a small number passed from a child process (or callee) to a parent process (or caller) when it has finished executing a specific procedure or delegated task.
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
The FE-Schrift or Fälschungserschwerende Schrift (forgery-impeding typeface) is a typeface introduced for use on license plates.
Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".
The Fibonacci Quarterly is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year.
In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.
Formula One (also Formula 1 or F1) is the highest class of single-seater auto racing sanctioned by the Fédération Internationale de l'Automobile (FIA) and owned by the Formula One Group.
Fortran (formerly FORTRAN, derived from Formula Translation) is a general-purpose, compiled imperative programming language that is especially suited to numeric computation and scientific computing.
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.
In typography, a glyph is an elemental symbol within an agreed set of symbols, intended to represent a readable character for the purposes of writing.
In linguistics, grammatical number is a grammatical category of nouns, pronouns, and adjective and verb agreement that expresses count distinctions (such as "one", "two", or "three or more").
In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S that is greater than every other element of S. The term least element is defined dually, that is, it is an element of S that is smaller than every other element of S. Formally, given a partially ordered set (P, ≤), an element g of a subset S of P is the greatest element of S if Hence, the greatest element of S is an upper bound of S that is contained within this subset.
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet.
The Gupta Empire was an ancient Indian empire, existing from approximately 240 to 590 CE.
Gwalior is a major and the northern-most city in the Indian state of Madhya Pradesh and one of the Counter-magnet cities.
Gwalior Fort (ग्वालियर क़िला Gwalior Qila) is a hill fort near Gwalior, Madhya Pradesh, central India.
The Han dynasty was the second imperial dynasty of China (206 BC–220 AD), preceded by the Qin dynasty (221–206 BC) and succeeded by the Three Kingdoms period (220–280 AD). Spanning over four centuries, the Han period is considered a golden age in Chinese history. To this day, China's majority ethnic group refers to themselves as the "Han Chinese" and the Chinese script is referred to as "Han characters". It was founded by the rebel leader Liu Bang, known posthumously as Emperor Gaozu of Han, and briefly interrupted by the Xin dynasty (9–23 AD) of the former regent Wang Mang. This interregnum separates the Han dynasty into two periods: the Western Han or Former Han (206 BC–9 AD) and the Eastern Han or Later Han (25–220 AD). The emperor was at the pinnacle of Han society. He presided over the Han government but shared power with both the nobility and appointed ministers who came largely from the scholarly gentry class. The Han Empire was divided into areas directly controlled by the central government using an innovation inherited from the Qin known as commanderies, and a number of semi-autonomous kingdoms. These kingdoms gradually lost all vestiges of their independence, particularly following the Rebellion of the Seven States. From the reign of Emperor Wu (r. 141–87 BC) onward, the Chinese court officially sponsored Confucianism in education and court politics, synthesized with the cosmology of later scholars such as Dong Zhongshu. This policy endured until the fall of the Qing dynasty in 1911 AD. The Han dynasty saw an age of economic prosperity and witnessed a significant growth of the money economy first established during the Zhou dynasty (c. 1050–256 BC). The coinage issued by the central government mint in 119 BC remained the standard coinage of China until the Tang dynasty (618–907 AD). The period saw a number of limited institutional innovations. To finance its military campaigns and the settlement of newly conquered frontier territories, the Han government nationalized the private salt and iron industries in 117 BC, but these government monopolies were repealed during the Eastern Han dynasty. Science and technology during the Han period saw significant advances, including the process of papermaking, the nautical steering ship rudder, the use of negative numbers in mathematics, the raised-relief map, the hydraulic-powered armillary sphere for astronomy, and a seismometer for measuring earthquakes employing an inverted pendulum. The Xiongnu, a nomadic steppe confederation, defeated the Han in 200 BC and forced the Han to submit as a de facto inferior partner, but continued their raids on the Han borders. Emperor Wu launched several military campaigns against them. The ultimate Han victory in these wars eventually forced the Xiongnu to accept vassal status as Han tributaries. These campaigns expanded Han sovereignty into the Tarim Basin of Central Asia, divided the Xiongnu into two separate confederations, and helped establish the vast trade network known as the Silk Road, which reached as far as the Mediterranean world. The territories north of Han's borders were quickly overrun by the nomadic Xianbei confederation. Emperor Wu also launched successful military expeditions in the south, annexing Nanyue in 111 BC and Dian in 109 BC, and in the Korean Peninsula where the Xuantu and Lelang Commanderies were established in 108 BC. After 92 AD, the palace eunuchs increasingly involved themselves in court politics, engaging in violent power struggles between the various consort clans of the empresses and empresses dowager, causing the Han's ultimate downfall. Imperial authority was also seriously challenged by large Daoist religious societies which instigated the Yellow Turban Rebellion and the Five Pecks of Rice Rebellion. Following the death of Emperor Ling (r. 168–189 AD), the palace eunuchs suffered wholesale massacre by military officers, allowing members of the aristocracy and military governors to become warlords and divide the empire. When Cao Pi, King of Wei, usurped the throne from Emperor Xian, the Han dynasty would eventually collapse and ceased to exist.
A hieroglyph (Greek for "sacred writing") was a character of the ancient Egyptian writing system.
The Hindu–Arabic numeral systemDavid Eugene Smith and Louis Charles Karpinski,, 1911 (also called the Arabic numeral system or Hindu numeral system) is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world.
Hinduism is an Indian religion and dharma, or a way of life, widely practised in the Indian subcontinent.
Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
The Iberian Peninsula, also known as Iberia, is located in the southwest corner of Europe.
The IBM 3270 is a class of block oriented computer terminal (sometimes called display devices) introduced by IBM in 1971 normally used to communicate with IBM mainframes.
IBM System/360 computers, and subsequent machines based on that architecture (mainframes), support a hexadecimal floating-point format.
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
The Inca Empire (Quechua: Tawantinsuyu, "The Four Regions"), also known as the Incan Empire and the Inka Empire, was the largest empire in pre-Columbian America, and possibly the largest empire in the world in the early 16th century.
In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is said to take on an indeterminate form.
Indian numerals are the symbols representing numbers in India.
The Indian subcontinent is a southern region and peninsula of Asia, mostly situated on the Indian Plate and projecting southwards into the Indian Ocean from the Himalayas.
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
The Dwight D. Eisenhower National System of Interstate and Defense Highways, commonly known as the Interstate Highway System, is a network of controlled-access highways that forms part of the National Highway System in the United States.
Isaac Asimov (January 2, 1920 – April 6, 1992) was an American writer and professor of biochemistry at Boston University.
Italian (or lingua italiana) is a Romance language.
Jainism, traditionally known as Jain Dharma, is an ancient Indian religion.
The system of Japanese numerals is the system of number names used in the Japanese language.
Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.
Java Database Connectivity (JDBC) is an application programming interface (API) for the programming language Java, which defines how a client may access a database.
Johannes de Sacrobosco, also written Ioannis de Sacro Bosco (1195 – 1256), was a scholar, monk and astronomer who was a teacher at the University of Paris.
John David Barrow (born 29 November 1952) is an English cosmologist, theoretical physicist, and mathematician.
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics.
Khmer numerals are the numerals used in the Khmer language.
Kish (Sumerian: Kiš; transliteration: Kiški; cuneiform:; Akkadian: kiššatu) was an ancient tell (hill city) of Sumer in Mesopotamia, considered to have been located near the modern Tell al-Uhaymir in the Babil Governorate of Iraq, east of Babylon and 80 km south of Baghdad.
Kratié or Kraches (ក្រចេះ, "Powder Cosmetic") is a province (khaet) of Cambodia located in the northeast.
In mathematics, and more specifically in calculus, L'Hôpital's rule or L'Hospital's rule uses derivatives to help evaluate limits involving indeterminate forms.
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.
A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation.
In mathematics, a "helping theorem" or lemma (plural lemmas or lemmata) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.
Lisp (historically, LISP) is a family of computer programming languages with a long history and a distinctive, fully parenthesized prefix notation.
The Formula One World Drivers' Championship (WDC) is awarded by the Fédération Internationale de l'Automobile (FIA) to the most successful Formula One racing car driver over a season, as determined by a points system based on individual Grand Prix results.
An international call prefix or dial out code is a trunk prefix used to select an international telephone circuit for placing an international call.
The Lokavibhāga is a Jain cosmological text originally composed in Prakrit by a Digambara monk, Sarvanandin, surviving in a later Sanskrit translation by one Siṃhasūri.
macOS (previously and later) is a series of graphical operating systems developed and marketed by Apple Inc. since 2001.
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level.
The Mathematical Treatise in Nine Sections is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
In the classical physics observed in everyday life, matter is any substance that has mass and takes up space by having volume.
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization.
The Mekong is a trans-boundary river in Southeast Asia.
The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid at atmospheric pressure.
The Mesoamerican Long Count calendar is a non-repeating, vigesimal (base-20) and base-18 calendar used by several pre-Columbian Mesoamerican cultures, most notably the Maya.
In the history of Europe, the Middle Ages (or Medieval Period) lasted from the 5th to the 15th century.
The term "Moors" refers primarily to the Muslim inhabitants of the Maghreb, the Iberian Peninsula, Sicily, Sardinia, Corsica, and Malta during the Middle Ages.
Morse code is a method of transmitting text information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment.
Abū ʿAbdallāh Muḥammad ibn Aḥmad ibn Yūsuf al-Kātib al-Khwārizmī, also referred to as al-Balkhī, was a 10th-century Persian encyclopedist and the author of the early encyclopedia Mafātīḥ al-ʿulūm (“Key to the Sciences”) in the Arabic language.
There is some confusion in the literature on whether al-Khwārizmī's full name is ابو عبد الله محمد بن موسى الخوارزمي or ابو جعفر محمد بن موسی الخوارزمی.
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
A Muslim (مُسلِم) is someone who follows or practices Islam, a monotheistic Abrahamic religion.
There are names for the number 0 in English and related concepts, and there are concomitant names for the decades whose tens column contains the number 0.
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
In physics, certain systems can achieve negative temperature; that is, their thermodynamic temperature can be expressed as a negative quantity on the Kelvin or Rankine scales.
Neutronium (sometimes shortened to neutrium, also referred to as neutrite) is a hypothetical substance composed purely of neutrons.
Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.
Nigel Ernest James Mansell, (born 8 August 1953) is a British former racing driver who won both the Formula One World Championship (1992) and the CART Indy Car World Series (1993).
Null (or NULL) is a special marker used in Structured Query Language to indicate that a data value does not exist in the database.
In computing, a null pointer has a value reserved for indicating that the pointer does not refer to a valid object.
A number is a mathematical object used to count, measure and also label.
In basic mathematics, a number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by \mathbb.
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems.
O (named o, plural oes) is the 15th letter and the fourth vowel in the modern English alphabet and the ISO basic Latin alphabet.
The term "Old World" is used in the West to refer to Africa, Asia and Europe (Afro-Eurasia or the World Island), regarded collectively as the part of the world known to its population before contact with the Americas and Oceania (the "New World").
The Olmecs were the earliest known major civilization in Mexico following a progressive development in Soconusco.
Omicron (uppercase Ο, lowercase ο, literally "small o": όμικρον back rounded vowel. Letters that arose from omicron include Roman O and Cyrillic O. The upper-case letter of omicron (O) was originally used in mathematics as a symbol for Big O notation (representing a function's asymptotic growth rate), but has fallen out of favor because omicron is indistinguishable from the Latin letter O and easily confused with the digit zero (0). Omicron is used to designate the fifteenth star in a constellation group, its ordinal placement a function of both magnitude and position. Such stars include Omicron Andromedae, Omicron Ceti, and Omicron Persei.
The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).
An operating system (OS) is system software that manages computer hardware and software resources and provides common services for computer programs.
Operator assistance refers to a telephone call in which the calling party requires an operator to provide some form of assistance in completing the call.
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
Palm OS (also known as Garnet OS) is a discontinued mobile operating system initially developed by Palm, Inc., for personal digital assistants (PDAs) in 1996.
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
Zero is an even number.
The Portable Document Format (PDF) is a file format developed in the 1990s to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties, whose structure shows periodic trends.
The Persians--> are an Iranian ethnic group that make up over half the population of Iran.
The phon is a unit of loudness level for pure tones.
In physics, a physical system is a portion of the physical universe chosen for analysis.
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
Pingala (Devanagari: पिङ्गल) (c. 3rd/2nd century BC) was an ancient Indian mathematician who authored the (also called Pingala-sutras), the earliest known treatise on Sanskrit prosody.
Pope Sylvester II or Silvester II (– 12 May 1003) was Pope from 2 April 999 to his death in 1003.
Positional notation or place-value notation is a method of representing or encoding numbers.
The Prakrits (प्राकृत; pāuda; pāua) are any of several Middle Indo-Aryan languages formerly spoken in India.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
Princeton University Press is an independent publisher with close connections to Princeton University.
Propositional calculus is a branch of logic.
Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.
The table of chords, created by the 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.
Qin Jiushao (ca. 1202–1261), courtesy name Daogu (道古), was a Chinese mathematician, inventor, politician and author.
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
A quatrefoil (anciently caterfoil) is a decorative element consisting of a symmetrical shape which forms the overall outline of four partially overlapping circles of the same diameter.
Quipu (also spelled khipu) or talking knots, were recording devices fashioned from strings historically used by a number of cultures, particularly in the region of Andean South America.
Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In computer programming, a return code or an error code is an enumerated message that corresponds to the status of a specific software application.
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.
Roulette is a casino game named after the French word meaning little wheel.
Sanskrit is the primary liturgical language of Hinduism; a philosophical language of Hinduism, Sikhism, Buddhism and Jainism; and a former literary language and lingua franca for the educated of ancient and medieval India.
Sanskrit prosody or Chandas refers to one of the six Vedangas, or limbs of Vedic studies.
Scientific American (informally abbreviated SciAm) is an American popular science magazine.
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
Sexagesimal (base 60) is a numeral system with sixty as its base.
The Shaka era (IAST: Śaka era) is a historical calendar era, corresponding to Julian year 78.
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
In computing, signed number representations are required to encode negative numbers in binary number systems.
Signed zero is zero with an associated sign.
The slashed zero is a representation of the number '0' (zero), with a slash through it.
Springer Nature is an academic publishing company created by the May 2015 merger of Springer Science+Business Media and Holtzbrinck Publishing Group's Nature Publishing Group, Palgrave Macmillan, and Macmillan Education.
A stationary state is a quantum state with all observables independent of time.
Sunzi Suanjing was a mathematical treatise written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the Tang dynasty.
Tennis is a racket sport that can be played individually against a single opponent (singles) or between two teams of two players each (doubles).
A tetraneutron is a hypothetical stable cluster of four neutrons.
Thai numerals (เลขไทย, IPA) are a set of numerals traditionally used in Thailand, although the Arabic numerals are more common due to pervasive westernization of Thailand in the modern Rattanakosin Era.
The Guardian is a British daily newspaper.
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE.
Theoretical astronomy is the use of the analytical models of physics and chemistry to describe astronomical objects and astronomical phenomena.
Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.
Tortoises are a family, Testudinidae. Testudinidae is a Family under the order Testudines and suborder Cryptodira.
A trunk prefix is a digit sequence to be dialed before a telephone number to initiate a telephone call for the purpose of selecting an appropriate telecommunications circuit by which the call is to be routed.
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.
The turtle shell is a highly complicated shield for the ventral and dorsal parts of turtles, tortoises and terrapins (all classified as "turtles" by zoologists), completely enclosing all the vital organs of the turtle and in some cases even the head.
Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.
A typewriter is a mechanical or electromechanical machine for writing characters similar to those produced by printer's movable type.
In mathematics, undefined has several different meanings, depending on the context.
Unix time (also known as POSIX time or UNIX Epoch time) is a system for describing a point in time, defined as the number of seconds that have elapsed since 00:00:00 Coordinated Universal Time (UTC), Thursday, 1 January 1970,.
Vacuum is space devoid of matter.
German vehicle registration plates (Kraftfahrzeug-Kennzeichen or, more colloquially, Nummernschilder) indicate the place where the vehicle bearing them was once registered.
The vigesimal or base 20 numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten).
The von Neumann cardinal assignment is a cardinal assignment which uses ordinal numbers.
Walter Eugene Clark (September 8, 1881 – September 30, 1960), was an American philologist.
In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering.
Wu Zetian (624 December16, 705),Paludan, 100 alternatively named Wu Zhao, Wu Hou, and during the later Tang dynasty as Tian Hou, also referred to in English as Empress Consort Wu or by the deprecated term "Empress Wu", was a Chinese sovereign who ruled unofficially as empress consort and empress dowager and later, officially as empress regnant (皇帝) during the brief Zhou dynasty (周, 684–705), which interrupted the Tang dynasty (618–690 & 705–907).
Year zero does not exist in the Anno Domini system usually used to number years in the Gregorian calendar and in its predecessor, the Julian calendar.
Zeno of Elea (Ζήνων ὁ Ἐλεάτης) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides.
Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.
In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures.
In category theory, a branch of mathematics, a zero morphism is a special kind of morphism exhibiting properties like the morphisms to and from a zero object.
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
Zero to the power of zero, denoted by 00, is a mathematical expression with no obvious value.
Zero-based numbering or index origin.
Zero-point energy (ZPE) or ground state energy is the lowest possible energy that a quantum mechanical system may have.
Zero: The Biography of a Dangerous Idea is a book by American author and journalist Charles Seife.
In mathematics, a zero of a function is a value such that.
0 (zero) is both a number and the numerical digit used to represent that number in numerals.
0th or zeroth is an ordinal for the number zero sometimes used under zero-based numbering, and may refer to.
1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.
2 (two) is a number, numeral, and glyph.
Year 690 (DCXC) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.
2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.
2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.
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