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History Of Mathematical Notation
The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness. Mathematical notation comprises the symbols used to write mathematical equations and formulas. Notation generally implies a set of well-defined representations of quantities and symbols operators. The history includes Hindu–Arabic numerals, letters from the Roman, Greek, Hebrew, and German alphabets, and a host of symbols invented by mathematicians over the past several centuries. The development of mathematical notation can be divided in stages. The "''rhetorical''" stage is where calculations are performed by words and no symbols are used. The "''syncopated''" stage is where frequently used operations and quantities are represented by symbolic syntactical abbreviations. From ancient times through the post-classical age,Or the Middle Ages. bursts o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Florian Cajori
Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics. Biography Florian Cajori was born in Zillis, Switzerland, as the son of Georg Cajori and Catherine Camenisch. He attended schools first in Zillis and later in Chur. In 1875, Florian Cajori emigrated to the United States at the age of sixteen, and attended the State Normal school in Whitewater, Wisconsin. After graduating in 1878, he taught in a country school, and then later began studying mathematics at University of Wisconsin–Madison. In 1883, Cajori received both his bachelor's and master's degrees from the University of Wisconsin–Madison, briefly attended Johns Hopkins University for 8 months in between degrees. He taught for a few years at Tulane University, before being appointed as professor of applied mathematics there in 1887. He was then driven north by tuberculosis. He founded the Colorado College Scientific Society and taught at Colorado College where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syncopated
In music, syncopation is a variety of rhythms played together to make a piece of music, making part or all of a tune or piece of music off-beat. More simply, syncopation is "a disturbance or interruption of the regular flow of rhythm": a "placement of rhythmic stresses or accents where they wouldn't normally occur". It is the correlation of at least two sets of time intervals. Syncopation is used in many musical styles, especially dance music. According to music producer Rick Snoman, "All dance music makes use of syncopation, and it's often a vital element that helps tie the whole track together". Syncopation can also occur when a strong harmony is simultaneous with a weak beat, for instance, when a 7th-chord is played on the second beat of measure or a dominant chord is played at the fourth beat of a measure. The latter occurs frequently in tonal cadences for 18th- and early-19th-century music and is the usual conclusion of any section. A hemiola (the equivalent Latin term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Structure
An abstract structure is an abstraction that might be of the Euclidean space, geometric spaces or a set structure, or a hypostatic abstraction that is defined by a set of mathematical theorems and laws, properties and relationships in a way that is logically if not always historically independent However historical dependencies are partially considered in event theory as part of the combinatorics theory in Kolmogorov complexity and Wiener–Khinchin theorem, Kolmogorov-Khinchin equations of the structure of contingent experiences, for example, those involving physical objects. Abstract structures are studied not only in logic and mathematics but in the fields that apply them, as computer science and computer graphics, and in the studies that reflect on them, such as philosophy (especially the philosophy of mathematics). Indeed, modern mathematics has been defined in a very general sense as the study of abstract structures (by the Nicolas Bourbaki, Bourbaki group: see discussion there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Civilization
A civilization (or civilisation) is any complex society characterized by the development of a state, social stratification, urbanization, and symbolic systems of communication beyond natural spoken language (namely, a writing system). Civilizations are intimately associated with additional characteristics such as centralization, the domestication of plant and animal species (including humans), specialization of labour, culturally-ingrained ideologies of progress, monumental architecture, taxation, societal dependence upon farming, and expansionism. Historically, a civilization has often been understood as a larger and "more advanced" culture, in implied contrast to smaller, supposedly less advanced cultures. In this broad sense, a civilization contrasts with non-centralized tribal societies, including the cultures of nomadic pastoralists, Neolithic societies or hunter-gatherers; however, sometimes it also contrasts with the cultures found within civilizations themselv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phoenicia
Phoenicia () was an ancient thalassocratic civilization originating in the Levant region of the eastern Mediterranean, primarily located in modern Lebanon. The territory of the Phoenician city-states extended and shrank throughout their history, and they possessed several enclaves such as Arwad and Tell Sukas (modern Syria). The core region in which the Phoenician culture developed and thrived stretched from Tripoli and Byblos in northern Lebanon to Mount Carmel in modern Israel. At their height, the Phoenician possessions in the Eastern Mediterranean stretched from the Orontes River mouth to Ashkelon. Beyond its homeland, the Phoenician civilization extended to the Mediterranean from Cyprus to the Iberian Peninsula. The Phoenicians were a Semitic-speaking people of somewhat unknown origin who emerged in the Levant around 3000 BC. The term ''Phoenicia'' is an ancient Greek exonym that most likely described one of their most famous exports, a dye also known as Tyrian purpl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic period (), and the Classical period (). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical periods of the language. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regarded as a separate historical stage, although its earliest form closely resembles Attic Greek and its latest form approaches Medieval Greek. There were several regional dialects of Ancient Greek, of which Attic Greek developed into Koine. Dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acrophonic And Milesian Numeration
Acrophony (; Greek: ἄκρος ''akros'' uppermost + φωνή ''phone'' sound) is the naming of letters of an alphabetic writing system so that a letter's name begins with the letter itself. For example, Greek letter names are acrophonic: the names of the letters α, β, γ, δ, are spelled with the respective letters: (''alpha''), (''beta''), (''gamma''), (''delta''). The paradigm for acrophonic alphabets is the Proto-Sinaitic script and the succeeding Phoenician alphabet, in which the letter A, representing the sound , is thought to have derived from an Egyptian hieroglyph representing an ox, and is called "ox", ''ʾalp'', which starts with the glottal stop sound the letter represents. The Latin alphabet is descended from the Phoenician, and the stylized head of an ox can still be seen if the letter A is turned upside-down: ∀. The second letter of the Phoenician alphabet is ''bet'' (which means "house" and looks a bit like a shelter) representing the sound and from '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars. The earliest mathematical texts available are from Mesopotamia and Egypt – '' Plimpton 322'' ( Babylonian c. 2000 – 1900 BC), the ''Rhind Mathematical Papyrus'' ( Egyptian c. 1800 BC) and the '' Moscow Mathematical Papyrus'' (Egyptian c. 1890 BC). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most anci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contemporary Era
Contemporary history, in English-language historiography, is a subset of modern history that describes the historical period from approximately 1945 to the present. Contemporary history is either a subset of the late modern period, or it is one of the three major subsets of modern history, alongside the early modern period and the late modern period. In the social sciences, contemporary history is also continuous with, and related to, the rise of postmodernity. Contemporary history is politically dominated by the Cold War (1947–1991) between the Western Bloc, led by the United States, and the Eastern Bloc, led by the Soviet Union. The confrontation spurred fears of a nuclear war. An all-out "hot" war was avoided, but both sides intervened in the internal politics of smaller nations in their bid for global influence and via proxy wars. The Cold War ultimately ended with the Revolutions of 1989 and the dissolution of the Soviet Union in 1991. The latter stages and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
