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Number Theory NUMBER THEORY or, in older usage, ARITHMETIC is a branch of pure mathematics devoted primarily to the study of the integers . It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers ) or defined as generalizations of the integers (e.g., algebraic integers ). Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry ). Questions in number theory are often best understood through the study of analytical objects (e.g., the Riemann zeta function Riemann zeta function ) that encode properties of the integers, primes or other numbertheoretic objects in some fashion (analytic number theory ) [...More...]  "Number Theory" on: Wikipedia Yahoo 

Irrational Number In mathematics , the IRRATIONAL NUMBERS are all the real numbers which are not rational numbers , the latter being the numbers constructed from ratios (or fractions ) of integers . When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable , meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e , the golden ratio φ , and the square root of two ; in fact all square roots of natural numbers , other than of perfect squares , are irrational. It can be shown that irrational numbers, when expressed in a positional numeral system (e.g [...More...]  "Irrational Number" on: Wikipedia Yahoo 

Theodorus Of Cyrene THEODORUS OF CYRENE (Greek : Θεόδωρος ὁ Κυρηναῖος) was an ancient Libyan Greek and lived during the 5th century BC. The only firsthand accounts of him that survive are in three of Plato Plato 's dialogues: the Theaetetus , the Sophist , and the Statesman . In the former dialogue, he posits a mathematical theorem now known as the Spiral of Theodorus Spiral of Theodorus . CONTENTS * 1 Life * 2 Work in mathematics * 3 See also * 4 References LIFELittle is known of Theodorus' biography beyond what can be inferred from Plato's dialogues. He was born in the northern African colony of Cyrene, and apparently taught both there and in Athens. He complains of old age in the Theaetetus, whose dramatic date of 399 BC suggests his period of flourishing to have occurred in the mid5th century [...More...]  "Theodorus Of Cyrene" on: Wikipedia Yahoo 

Hippasus Of Metapontum HIPPASUS OF METAPONTUM (/ˈhɪpəsəs/ ; Greek : Ἵππασος ὁ Μεταποντῖνος, Híppasos; fl. 5th century BC), was a Pythagorean philosopher . Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers . The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this. However, the few ancient sources which describe this story either do not mention Hippasus Hippasus by name (e.g. Pappus) or alternatively tell that Hippasus Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere . The discovery of irrationality is not specifically ascribed to Hippasus Hippasus by any ancient writer [...More...]  "Hippasus Of Metapontum" on: Wikipedia Yahoo 

Polygonal Number In mathematics , a POLYGONAL NUMBER is a number represented as dots or pebbles arranged in the shape of a regular polygon . The dots are thought of as alphas (units). These are one type of 2dimensional figurate numbers . CONTENTS* 1 Definition and examples * 1.1 Triangular numbers * 1.2 Square numbers * 1.3 Pentagonal numbers * 1.4 Hexagonal numbers * 2 Formula * 2.1 Every hexagonal number is also a triangular number * 3 Table of values * 4 Combinations * 5 See also * 6 Notes * 7 References * 8 External links DEFINITION AND EXAMPLESThe number 10 for example, can be arranged as a triangle (see triangular number ): But 10 cannot be arranged as a square . The number 9, on the other hand, can be (see square number ): Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number ): By convention, 1 is the first polygonal number for any number of sides [...More...]  "Polygonal Number" on: Wikipedia Yahoo 

Square Root Of 2 The SQUARE ROOT OF 2, or the (1/2)th power of 2 , written in mathematics as √2 or 2 1⁄2, is the positive algebraic number that, when multiplied by itself, gives the number 2 . Technically, it is called the PRINCIPAL SQUARE ROOT OF 2, to distinguish it from the negative number with the same property. Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length ; this follows from the Pythagorean theorem Pythagorean theorem . It was probably the first number known to be irrational [...More...]  "Square Root Of 2" on: Wikipedia Yahoo 

Egypt Coordinates : 26°N 30°E / 26°N 30°E / 26; 30 Arab Republic Republic of Egypt جمهورية مصر العربية * ARABIC : Jumhūrīyat Miṣr alʿArabīyah EGYPTIAN : Gomhoreyet Maṣr El ʿArabeyah Flag Coat of arms ANTHEM: " Bilady, Bilady, Bilady " "بلادي، بلادي، بلادي" "My country, my country, my country" Capital and largest [...More...]  "Egypt" on: Wikipedia Yahoo 

Babylonian Astronomy According to Asger Aaboe , the origins of Western astronomy can be found in Mesopotamia , and all Western efforts in the exact sciences are descendants in direct line from the work of the late Babylonian astronomers. Modern knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BC. The fact that many star names appear in Sumerian suggests a continuity reaching into the Early Bronze Age Bronze Age . The history of astronomy in Mesopotamia, and the world, begins with the Sumerians who developed the earliest writing system —known as cuneiform —around 3500–3200 BC. The Sumerians developed a form of astronomy that had an important influence on the sophisticated astronomy of the Babylonians. Astrolatry , which gave planetary gods an important role in Mesopotamian mythology and religion , began with the Sumerians [...More...]  "Babylonian Astronomy" on: Wikipedia Yahoo 

Numerology NUMEROLOGY is any belief in the divine, mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value of the letters in words, names and ideas. It is often associated with the paranormal , alongside astrology and similar divinatory arts. Despite the long history of numerological ideas, the word "numerology" is not recorded in English before c.1907. The term NUMEROLOGIST can be used for those who place faith in numerical patterns and draw pseudoscientific inferences from them, even if those people do not practice traditional numerology. For example, in his 1997 book Numerology: Or What Pythagoras Pythagoras Wrought, mathematician Underwood Dudley uses the term to discuss practitioners of the Elliott wave principle of stock market analysis [...More...]  "Numerology" on: Wikipedia Yahoo 

Pythagoras PYTHAGORAS OF SAMOS (US : /pᵻˈθæɡərəs/ ; UK : /paɪˈθæɡərəs/ ; Greek : Πυθαγόρας ὁ Σάμιος Pythagóras ho Sámios " Pythagoras Pythagoras the Samian ", or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek ; c. 570–495 BC) was an Ionian Greek philosopher , mathematician , and putative founder of the Pythagoreanism Pythagoreanism movement. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name. Legend and obfuscation cloud his work, so it is uncertain whether he truly contributed much to mathematics or natural philosophy . Many of the accomplishments credited to Pythagoras Pythagoras may actually have been accomplishments of his colleagues or successors [...More...]  "Pythagoras" on: Wikipedia Yahoo 

Thales THALES OF MILETUS (/ˈθeɪliːz/ ; Greek : Θαλῆς (ὁ Μῑλήσιος), Thalēs; c. 624 – c. 546 BC) was a preSocratic Greek philosopher , mathematician and astronomer from Miletus Miletus in Asia Minor (presentday Milet Milet in Turkey Turkey ). He was one of the Seven Sages of Greece . Many, most notably Aristotle Aristotle , regard him as the first philosopher in the Greek tradition , and he is otherwise historically recognized as the first individual in Western civilization known to have entertained and engaged in scientific philosophy . Thales Thales is recognized for breaking from the use of mythology to explain the world and the universe, and instead explaining natural objects and phenomena by theories and hypotheses , i.e [...More...]  "Thales" on: Wikipedia Yahoo 

Figurate Numbers The term FIGURATE NUMBER is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean * polygonal number * a number represented as a discrete rdimensional regular geometric pattern of rdimensional balls such as a polygonal number (for r = 2) or a POLYHEDRAL NUMBER (for r = 3). * a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions. CONTENTS * 1 Terminology * 2 History * 3 Triangular numbers * 4 Gnomon * 5 Notes * 6 References TERMINOLOGYSome kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics Greek mathematics the preferred term used to be figured number [...More...]  "Figurate Numbers" on: Wikipedia Yahoo 

Egyptian Mathematics ANCIENT EGYPTIAN MATHEMATICS is the mathematics that was developed and used in Ancient Egypt Ancient Egypt c. 3000 to c. 300 BC, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt . The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions . Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyri . From these texts it is known that ancient Egyptians understood concepts of geometry , such as determining the surface area and volume of threedimensional shapes useful for architectural engineering , and algebra , such as the false position method and quadratic equations [...More...]  "Egyptian Mathematics" on: Wikipedia Yahoo 

Theaetetus (dialogue) The THEAETETUS (/ˌθiːɪˈtiːtəs/ ; Greek : Θεαίτητος) is one of Plato Plato 's dialogues concerning the nature of knowledge , written circa 369 BC. In this dialogue, Socrates Socrates and Theaetetus discuss three definitions of knowledge : knowledge as nothing but perception , knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions is shown to be unsatisfactory. Socrates Socrates declares Theaetetus will have benefited from discovering what he does not know, and that he may be better able to approach the topic in the future. The conversation ends with Socrates' announcement that he has to go to court to face a criminal indictment [...More...]  "Theaetetus (dialogue)" on: Wikipedia Yahoo 

Theaetetus Of Athens THEAETETUS OF ATHENS (/ˌθiːɪˈtiːtəs/ ; Greek : Θεαίτητος; c. 417 – 368 BC ), possibly the son of Euphronius of the Athenian Athenian deme Sunium Sunium , was a Greek mathematician. His principal contributions were on irrational lengths, which was included in Book X of Euclid Euclid 's Elements , and proving that there are precisely five regular convex polyhedra . A friend of Socrates Socrates and Plato Plato , he is the central character in Plato's eponymous Socratic dialogue . Theaetetus, like Plato Plato , was a student of the Greek mathematician Theodorus of Cyrene . Cyrene was a prosperous Greek colony on the coast of North Africa, in what is now Libya, on the eastern end of the Gulf of Sidra Gulf of Sidra [...More...]  "Theaetetus Of Athens" on: Wikipedia Yahoo 

Commensurability (mathematics) In mathematics , two nonzero real numbers a and b are said to be COMMENSURABLE if a/b is a rational number . CONTENTS * 1 History of the concept * 2 Commensurability in group theory * 3 In topology * 4 In physics * 5 See also * 6 References HISTORY OF THE CONCEPTThe Pythagoreans are credited with the proof of the existence of irrational numbers . When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable. A separate, more general and circuitous ancient Greek doctrine of proportionality for geometric magnitude was developed in Book V of Euclid's Elements Euclid's Elements in order to allow proofs involving incommensurable lengths, thus avoiding arguments which applied only to a historically restricted definition of number [...More...]  "Commensurability (mathematics)" on: Wikipedia Yahoo 