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Arithmetical Operations ARITHMETIC (from the Greek ἀριθμός arithmos, "number ") is a branch of mathematics that consists of the study of numbers , especially the properties of the traditional operations on them—addition , subtraction , multiplication and division . Arithmetic Arithmetic is an elementary part of number theory , and number theory is considered to be one of the toplevel divisions of modern mathematics , along with algebra , geometry , and analysis . The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory [...More...]  "Arithmetical Operations" on: Wikipedia Yahoo 

Nicomachus NICOMACHUS OF GERASA (Greek : Νικόμαχος; c. 60 – c. 120 CE) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek . He was born in Gerasa Gerasa , in the Roman province of Syria (now Jerash Jerash , Jordan ), and was strongly influenced by Aristotle Aristotle . He was a Neopythagorean , who wrote about the mystical properties of numbers. CONTENTS * 1 Life * 2 Works * 2.1 Introduction to Arithmetic * 2.2 Manual of Harmonics * 2.3 Lost works * 3 See also * 4 Notes * 5 References * 6 External links LIFELittle is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa Gerasa . Historians consider him a Neopythagorean based on his tendency to view the numbers having mystical properties. The age in which he lived (c [...More...]  "Nicomachus" on: Wikipedia Yahoo 

Greek Mathematics GREEK MATHEMATICS, as the term is used in this article, is the mathematics written in Greek , developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean . Greek mathematicians lived in cities spread over the entire Eastern Mediterranean Mediterranean from Italy to North Africa but were united by culture and language . Greek mathematics Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. The word "mathematics" itself derives from the ancient Greek μάθημα (mathema), meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is the key difference between Greek mathematics Greek mathematics and those of preceding civilizations [...More...]  "Greek Mathematics" on: Wikipedia Yahoo 

Pythagoreanism PYTHAGOREANISM originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism . Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism or Neoplatonism . Pythagorean ideas exercised a marked influence on Aristotle Aristotle , and Plato Plato , and through them, all of Western philosophy Western philosophy . Historians from the Stanford Encyclopedia of Philosophy Philosophy pointed out Aristotle Aristotle makes clear that there are several groups of people included under the heading "socalled Pythagoreans," by explicitly distinguishing those Pythagoreans who posited the table of opposites from the main Pythagorean system [...More...]  "Pythagoreanism" on: Wikipedia Yahoo 

Introduction To Arithmetic The book INTRODUCTION TO ARITHMETIC (Greek : Ἀριθμητικὴ εἰσαγωγή, Arithmetike eisagoge) is the only extant work on mathematics by Nicomachus (60–120 AD). CONTENTS * 1 Summary * 2 Editions * 3 See also * 4 References * 5 External links SUMMARYThe work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to Plato Plato quite often, and writes that philosophy can only be possible if one knows enough about mathematics . Nicomachus also describes how natural numbers and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twentythree and twentynine chapters, respectively [...More...]  "Introduction To Arithmetic" on: Wikipedia Yahoo 

Greek Numerals GREEK NUMERALS, also known as IONIC, IONIAN, MILESIAN, or ALEXANDRIAN NUMERALS, are a system of writing numbers using the letters of the Greek alphabet . In modern Greece Greece , they are still used for ordinal numbers and in contexts similar to those in which Roman numerals Roman numerals are still used elsewhere in the West. For ordinary cardinal numbers , however, Greece Greece uses Arabic numerals Arabic numerals . CONTENTS * 1 History * 2 Description * 3 Table * 4 Higher numbers * 5 Zero * 6 See also * 7 References * 8 External links HISTORYThe Minoan and Mycenaean civilizations ' Linear A and Linear B alphabets used a different system, called Aegean numerals Aegean numerals , which included specialized symbols for numbers: 𐄇 = 1, 𐄐 = 10, 𐄙 = 100, 𐄢 = 1000, and 𐄫 = 10000 [...More...]  "Greek Numerals" on: Wikipedia Yahoo 

Euclid EUCLID (/ˈjuːklᵻd/ ; Greek : Εὐκλείδης, Eukleidēs Ancient Greek: ; fl. 300 BCE), sometimes called EUCLID OF ALEXANDRIA to distinguish him from Euclides of Megara , was a Greek mathematician , often referred to as the "father of geometry". He was active in Alexandria Alexandria during the reign of Ptolemy I (323–283 BCE). His Elements is one of the most influential works in the history of mathematics , serving as the main textbook for teaching mathematics (especially geometry ) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms . Euclid Euclid also wrote works on perspective , conic sections , spherical geometry , number theory , and rigor [...More...]  "Euclid" on: Wikipedia Yahoo 

Hellenistic Civilization The HELLENISTIC PERIOD covers the period of ancient Greek (Hellenic) history and Mediterranean history between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire Roman Empire as signified by the Battle of Actium Battle of Actium in 31 BC and the subsequent conquest of Ptolemaic Egypt Egypt the following year. At this time, Greek cultural influence and power was at its peak in Europe Europe , Africa Africa and Asia Asia , experiencing prosperity and progress in the arts , exploration , literature , theatre , architecture , music , mathematics , philosophy , and science . It is often considered a period of transition, sometimes even of decadence or degeneration , compared to the enlightenment of the Greek Classical era [...More...]  "Hellenistic Civilization" on: Wikipedia Yahoo 

Sexagesimal SEXAGESIMAL (BASE 60) is a numeral system with sixty as its base . It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians , and is still used—in a modified form—for measuring time , angles , and geographic coordinates . The number 60, a superior highly composite number , has twelve factors , namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers . With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted [...More...]  "Sexagesimal" on: Wikipedia Yahoo 

Babylonian Numerals BABYLONIAN NUMERALS were written in cuneiform , using a wedgetipped 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 Babylonians , who were famous for their astronomical observations and calculations (aided by their invention of the abacus ), used a sexagesimal (base60) positional numeral system inherited from either the Sumerian or the Eblaite civilizations. Neither of the predecessors was a positional system (having a convention for which ‘end’ of the numeral represented the units). CONTENTS * 1 Origin * 2 Characters * 3 Zero * 4 See also * 5 Notes * 6 Bibliography * 7 External links ORIGINThis system first appeared around 2000 BC; its structure reflects the decimal lexical numerals of Semitic languages Semitic languages rather than Sumerian lexical numbers [...More...]  "Babylonian Numerals" on: Wikipedia Yahoo 

Vigesimal 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 ). CONTENTS* 1 Places * 1.1 Converting table * 2 Fractions * 3 Cyclic numbers * 4 Real numbers * 5 Use * 5.1 Africa * 5.2 Americas * 5.3 Asia * 5.4 In Europe Europe * 5.4.1 Origins * 5.4.2 Examples * 5.5 Related observations * 6 Examples in Mesoamerican languages * 6.1 Powers of twenty in Yucatec Maya and Nahuatl * 6.2 Counting in units of twenty * 7 Further reading * 8 Notes PLACESIn a vigesimal place system, twenty individual numerals (or digit symbols) are used, ten more than in the usual decimal system [...More...]  "Vigesimal" on: Wikipedia Yahoo 

Maya Numerals The MAYA NUMERAL SYSTEM is a vigesimal (base20) positional notation used in the Maya civilization to represent numbers. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar). For example, thirteen is written as three dots in a horizontal row above two horizontal lines stacked above each other. 400s 20s 1s 33 429 5125 Numbers after 19 were written vertically in powers of twenty. For example, thirtythree would be written as one dot above three dots, which are in turn atop two lines. The first dot represents "one twenty" or "1×20", which is added to three dots and two bars, or thirteen. Therefore, (1×20) + 13 = 33. Upon reaching 202 or 400, another row is started (203 or 8000, then 204 or 160,000, and so on). The number 429 would be written as one dot above one dot above four dots and a bar, or (1×202) + (1×201) + 9 = 429 [...More...]  "Maya Numerals" on: Wikipedia Yahoo 

Archimedes ARCHIMEDES OF SYRACUSE (/ˌɑːkɪˈmiːdiːz/ ; Greek : Ἀρχιμήδης; c. 287 – c. 212 BC) was a Greek mathematician , physicist , engineer , inventor , and astronomer . Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity . Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems , including the area of a circle , the surface area and volume of a sphere , and the area under a parabola . Other mathematical achievements include deriving an accurate approximation of pi , defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers [...More...]  "Archimedes" on: Wikipedia Yahoo 

Diophantus DIOPHANTUS OF ALEXANDRIA ( Ancient Greek Ancient Greek : Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299), sometimes called "the father of algebra ", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica Arithmetica , many of which are now lost. These texts deal with solving algebraic equations . While reading Claude Gaspard Bachet de Méziriac 's edition of Diophantus' Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat\'s Last Theorem [...More...]  "Diophantus" on: Wikipedia Yahoo 

Brahmagupta BRAHMAGUPTA ( listen (help ·info )) (born c. 598, died after 665) was an Indian mathematician and astronomer . He is the author of two early works on mathematics and astronomy : the Brāhmasphuṭasiddhānta (BSS, "correctly established doctrine of Brahma Brahma ", dated 628), a theoretical treatise, and the Khaṇḍakhādyaka ("edible bite", dated 665), a more practical text. Brahmagupta was the first to give rules to compute with zero . The texts composed by Brahmagupta were composed in elliptic verse in Sanskrit Sanskrit , as was common practice in Indian mathematics . As no proofs are given, it is not known how Brahmagupta's results were derived [...More...]  "Brahmagupta" on: Wikipedia Yahoo 

Aryabhata ARYABHATA ( IAST IAST : Āryabhaṭa) or ARYABHATA I (476–550 CE ) was the first of the major mathematician astronomers from the classical age of Indian mathematics and Indian astronomy Indian astronomy . His works include the Āryabhaṭīya (499 CE, when he was 23 years old) and the Aryasiddhanta [...More...]  "Aryabhata" on: Wikipedia Yahoo 