21. Ancient Greek Mathematics - History For Kids! Ancient Greek Mathematics for Kids. Ancient Greek Mathematics for Kids what math did the Greeks invent? what math did the Greeks learn from other people? why is it important? http://www.historyforkids.org/learn/greeks/science/math/

Ancient Greek Mathematics for Kids - what math did the Greeks invent? what math did the Greeks learn from other people? why is it important? Ancient Greek Mathematics Because the Greeks had only very clumsy ways of writing down numbers , they didn't like algebra. They found it very hard to write down equations or number problems. Instead, Greek mathematicians were more focused on geometry, and used geometric methods to solve problems that you might use algebra for. Greek mathematicians were also very interested in proving that certain mathematical ideas were true. So they spent a lot of time using geometry to prove that things were always true, even though people like the Egyptians and Babylonians already knew that they were true most of the time anyway. The Greeks in general were very interested in rationality , in things making sense and hanging together. They wanted to tie up the loose ends. They liked music , because music followed strict rules to produce beauty. So did architecture , and so did mathematics.

22. Mathematics Greek Mathematics. Ptolemy's Geography. Greek Astronomy. Also, someone left a note on the wall. When you have seen everything, walk back to the Main Hall. http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Mathematics.ht

Mathematics Ancient Science and Its Modern Fates Until recently, historians of the Scientific Revolution of the 16th and 17th centuries treated it as a kind of rebellion against the authority of ancient books and humanist scholarship. In fact, however, it began with the revival of several tremendously important and formidably difficult works of Greek science. Scholarship supported science in this world where faith and science were not yet seen as two, irreconcilable cultures. The three ancient doors to the next rooms all have signs written on them in Greek and Latin. Luckily for you we created modern metal plates with the translations, next to the doors. So you can pick any of: Greek Mathematics Ptolemy's Geography Greek Astronomy Also, someone left a note on the wall. When you have seen everything, walk back to the Main Hall

23. Greek Mathematics Greek mathematicsPeriodization Classical Greek mathematics refers to the mathematics studied before the Hellenistic period, when Greek mathematics was limited to Greece. http://www.docstoc.com/docs/15285800/Greek-mathematics

24. 2. Greek Mathematics And Pythagoras. Next 3. Geometric algebra. Up BEING AND SIGN Previous 1. Mesopotamian and . 2. Greek mathematics and Pythagoras. 'Mathema' means ''study subject'' and in the PythagoreanPlatonic http://www.dm.uniba.it/~psiche/bas2/node3.html

Next: 3. Geometric algebra. Up: BEING AND SIGN Previous: 1. Mesopotamian and 2. Greek mathematics and Pythagoras. 'Mathema' means ''study subject'' and in the Pythagorean-Platonic tradition the term ''mathematics'' comprehended geometry, arithmetic, music and astronomy, the so called ''quadrivium'', that in the Platonic Academia was not an introductory discipline, but a sort of 'final training' for the aristocratic Guardians described in the Platonic Respublica. They appear organised as two pairs: geometry/astronomy and arithmetic/music, each pair including both the abstract and the concrete aspects, and describing respectively the being and signs worlds. In the Greek mathematics it is noteworthy the distinction between arithmetic and logistics. The former is a ''number theory'' and concerns with the numbers 'in themselves', by distinguishing even and odd, linear, plane and solid numbers, with a likely evident genetic reference to their ancient representation as pebbles on a surface, according to the ancient Pythagorean tradition. Following definitions are those of prime, square, cubic, oblong numbers. Proofs are geometric too, representing the numbers as figures, squares, rectangles, triangles, gnomons, and so on, according to the so called ''dot-algebra'' ((KNORR 1975)), and are the bases of that ''geometric algebra'' which we are going to analyse in the following sections. The latter copes with the practical aspects in measurement and trade, and deals with ''specific numbers of perceived and counted things'', using also special number-names depending on the numbered things: as, for example, 'phialites' ''number of bowls'', from 'phiale', ''bowl''. From this point of view, it is worthwhile to remind the adjectival nature of the Greek numbers (in Greek 1, 2, 3, 4, hundreds, thousands, ten thousands are inflected for genders and cases). Logistics comprehends elementary arithmetic operations and simple equations solution too.

25. Ancient Greek Mathematics - Crystalinks Greek mathematics, as that term is used in this article, is the mathematics developed from the 6th century BC to the 5th century AD around the shores of the Mediterranean. http://www.crystalinks.com/greekmath.html

Greek mathematics, as that term is used in this article, is the mathematics developed from the 6th century BC to the 5th century AD around the shores of the Mediterranean. It constitutes a major period of the history of mathematics, fundamental in respect of geometry and the idea of formal proof. Greek mathematics also contributed importantly to ideas on number theory, mathematical analysis, applied mathematics, and, at times, approached close to integral calculus. Mathematical developments took place in Greek-speaking centers as far apart as Sicily and Egypt, and with a high estimation of the intellectual and cultural status of mathematics (for example in the school of Plato). Greek mathematics has origins that are presumed to go back to the 7th century BC, but are not easily documented. It is generally believed that it built on the computational methods of earlier Babylonian and Egyptian mathematics, and it may well have had Phoenician influences. Some of the most well-known figures in Greek mathematics are Pythagoras, a shadowy figure from the isle of Samos associated partly with number mysticism and numerology, but more commonly with his theorem, and Euclid, who is known for his Elements, a canon of geometry for centuries. The Sand Reckoner by Archimedes bespeaks a man who made major discoveries, and whose originality and accomplishments are commonly reckoned to be on par with those of Isaac Newton and C. F. Gauss.

26. Greece - Greek Math Resources on ancient Greek mathematics, calculations, geometry, and on Zeno, Archimedes, and Roman numerals. http://ancienthistory.about.com/od/greekmath/Greece_Greek_Math.htm

zWASL=1 zGL='0';zGR='ca-about-radlink'; zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') zDO=0 Home Education Ancient / Classical History Ancient / Classical History Search Ancient History Wars Filed In: Philosophy / Science Mathematics Resources on ancient Greek mathematics, calculations, geometry, and on Zeno, Archimedes, and Roman numerals. Hippocrates of Chios Hippocrates of Chios, who lived about the same time as the medical Hippocrates, wrote the first known work on geometry. Archimedes Archimedes probably studied mathematics in Alexandria with the successors of Euclid. The name Archimedes is connected to a pumping device now known as a Archimedes Screw, which he may have seen in operation in Egypt. zSB(3,3) Abacus - Base 10 and Greek Counting If the ancient Greeks used letters for their numbers, were they able to and did they use a counting system like an abacus that relies on a base like the decimal system? Finger Counting Counting on one's fingers seems a natural way to compute numbers, but the Greeks and Romans didn't just count "on" their fingers. They counted with their fingers, and not to be quick and accurate with the finger symbols could be embarrassing.

27. Perseus Digital Library Welcome to Perseus 4.0, also known as the Perseus Hopper. Read more on the Perseus version history. New to Perseus? Click here for a short tutorial. http://www.perseus.tufts.edu/hopper?redirect=true

28. Explore: Greece - Mathematics The two pioneers of Greek mathematics, Thales and Pythagoras, therefore have no surviving texts to their credit. Much of what we know from them is http://library.thinkquest.org/C0122667/greece/maths.html

Explore Gallery Interactive Forum ... Warfare A n c i e n t F a c t s Greece Mathematics Introduction Early Greek Mathematics (650-400 BCE) Thales Of Miletus (ca. 624-548 BCE) Thales was, by legend, a clever man, who was said to have learned much from the Egyptians and Babylonians. He is reputed to have demonstrated that the angle inscribed in a semicircle is a right angle (Theorem of Thales) and put down a series of rules regarding the angles of triangles. He was reported to have measured the height of the Pyramids by comparing the length of their shadows to that of a vertical stick. At the moment the length of the stick�s shadow was equal to its height, the length of the Pyramids� shadow would indicate their height. Though much of the knowledge attributed to Thales originated from Egypt and Babylon, he is credited with organising them in a rational manner. Thales also broke away from the rigidity of using geometry solely for measurement and tried to apply it in practical methods. This logical structure he provided to geometry set forth a great idea followed by later mathematicians such as Pythagoras and Plato. Pythagoras of Samos (ca. 580-500 BCE)

29. The Origins Of Greek Mathematics About this document . The Origins of Greek Mathematics. Though the Greeks certainly borrowed from other civilizations, they built a culture and civilization on their own which is http://www.math.tamu.edu/~don.allen/history/greekorg/greekorg.html

Next: About this document The Origins of Greek Mathematics Though the Greeks certainly borrowed from other civilizations, they built a culture and civilization on their own which is The most impressive of all civilizations, The most influential in Western culture, The most decisive in founding mathematics as we know it. Basic facts about the origin of Greek civilization and its mathematics. The best estimate is that the Greek civilization dates back to 2800 B.C. just about the time of the construction of the great pyramids in Egypt. The Greeks settled in Asia Minor, possibly their original home, in the area of modern Greece, and in southern Italy, Sicily, Crete, Rhodes, Delos, and North Africa. About 775 B.C. they changed from a hieroglyphic writing to the Phoenician alphabet. This allowed them to become more literate, or at least more facile in their ability to express conceptual thought. The ancient Greek civilization lasted until about 600 B.C. The Egyptian and Babylonian influence was greatest in Miletus, a city of Ionia in Asia Minor and the birthplace of Greek philosophy, mathematics and science. From the viewpoint of its mathematics, it is best to distinguish between the two periods: the

30. Mathematics :: Greek Mathematics -- Britannica Online Encyclopedia mathematics, Greek mathematics, Britannica Online Encyclopedia, The Greeks divided the field of mathematics into arithmetic (the study of “multitude,” or discrete quantity http://www.britannica.com/EBchecked/topic/369194/mathematics/65977/Greek-mathema

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. mathematics My Britannica CREATE MY mathematics NEW ARTICLE ... SAVE mathematics Table of Contents: mathematics Article Article Ancient mathematical sources Ancient mathematical sources Mathematics in ancient Mesopotamia Mathematics in ancient Mesopotamia - The numeral system and arithmetic ope... The numeral system and arithmetic operations - Geometric and algebraic problems Geometric and algebraic problems - Mathematical astronomy Mathematical astronomy Mathematics in ancient Egypt Mathematics in ancient Egypt - The numeral system and arithmetic ope... The numeral system and arithmetic operations - Geometry Geometry - Assessment of Egyptian mathematics Assessment of Egyptian mathematics Greek mathematics Greek mathematics - The development of pure mathematics The development of pure mathematics - - The pre-Euclidean period The pre-Euclidean period - - The Elements The Elements - - The three classical problems The three classical problems - Geometry in the 3rd century BC Geometry in the 3rd century BC - - Archimedes

31. GREEK MATHEMATICS GREEK MATHEMATICS . By Helena Velić. Vesna Lešić. Ana Stubičar. Martina Rohtek. Emina Lulić http://www.mathos.hr/~hvelic/seminar/GREEK.ppt

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32. History Of Mathematics: Greece A manual of Greek mathematics. Clarendon Press, Oxford, 1931. (An abbreviated version of Heath's History of Greek Mathematics.) Reviewed Isis 16 (1931), 450451. http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

33. Greek Mathematics Index JOC/EFR May 2010 The URL of this page is School_of_Mathematics_and_Statistics University_of_St_Andrews,_Scotland http//wwwhistory.mcs.st-andrews.ac.uk/Indexes/Greeks.html http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Greeks.html

History Topics: Index of Ancient Greek mathematics Articles about Greek mathematics. Squaring the circle Doubling the cube Trisecting an angle Greek Astronomy ... Geography Various lists of Greek mathematicians. Full list Mathematicans/Philosophers Mathematicians/Astronomers Mathematicians/Astronomers/Philosophers ... Later circle squarers Click on a name below to go to that biography. Full List of Greek Mathematicians in our archive Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Greek Mathematicans/Philosophers Anaxagoras Antiphon Archytas Aristotle ... Zeno of Elea Greek Mathematicians/Astronomers Apollonius Archimedes Aristarchus Aristotle ... Theon of Smyrna Greek Mathematicians/Astronomers/Philosophers Aristotle Cleomedes Democritus Eudoxus ... Thales Greek Circle squarers Anaxagoras Antiphon Apollonius Archimedes ... Bryson Carpus Dinostratus Hippias Hippocrates Nicomedes ... Sporus Later Circle squarers Al-Haytham Johann Bernoulli Cusa James Gregory ... Search Form JOC/EFR May 2010 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Greeks.html

34. Greek Mathematics Ancient Greek Mathematics. Ancient Greek mathematics achieve the full flower of intellectual development on an equal par with modern levels. The brought the full flower of http://www.math.tamu.edu/~dallen/masters/Greek/content4.htm

Ancient Greek Mathematics Ancient Greek mathematics achieve the full flower of intellectual development on an equal par with modern levels. The brought the full flower of geometry as an axiomatic system. They also seem to have created the basis of logical argument and the axiomatic method. Probably there is no other epoch of human civilization where evidence of such fundamental and sweeping changes in though have occurred. Many of the results from Greek mathematics are advanced mathematical topics still today. As well, most mathematicians haven't a glimmer of its depth. While everyone has heard of Euclid, few know that the famous Elements was a compendium of plane geometry, number theory, and solid geometry. From this work of thirteen book, just the first two are studied in high school. As you will see the theoretical content is remarkable, exceeded perhaps only by mathematical technique as achieved by Archimedes and Apollonius. Greek Mathematics Goals Readings Problems I n most cases the readings will be presented in the form of Acrobat (PDF) documents. To read and print them you will need the Adobe Acrobat Reader.

35. Greek Mathematics GREEK MATHEMATICIANS. The ancient Greeks were very interested in scientific thought. They were not satisfied with just knowing the facts; they wanted to know the why and how. http://atschool.eduweb.co.uk/sirrobhitch.suffolk/Portland State University Greek

GREEK MATHEMATICIANS The ancient Greeks were very interested in scientific thought. They were not satisfied with just knowing the facts; they wanted to know the why and how. It should be no surprise that the Greeks were extremely successful in the area of mathematics. The mathematics we use today, and its content, are for the most part Greek. The Greeks laid down the first principles, and invented methods for solving problems. Though most people don't realize it, mathematics is a Greek science - regardless of what modern day analysis might bring. When people look back on Greek genius, they may naturally call to mind masterpieces in Greek literature and art . But the Greeks, with their insatiable desire to know the true meaning of everything and give a rational explanation of it, were irresistibly drawn to the sciences, exact reasoning in general, and logic. There are many famous Greek names in mathematics. One of which is Aristotle , who said he could conceive of nothing more beautiful than the objects of mathematics. Plato , delighted in geometry and the wonders of numbers, inscribed, "let no one destitute of geometry enter my doors" over the entrance to his academy.

36. Greek Mathematics This article is a candidate for the History of Science Collaboration of the Month. Please visit that page to support or comment on the nomination. http://english.turkcebilgi.com/Greek mathematics

EnglishInfo Search Türkçe Home Information Translation ... Greek mathematics Information about Greek mathematics Greek mathematics Information about Greek mathematics Double click any English word, to find Turkish meaning This article is a candidate for the History of Science Collaboration of the Month . Please visit that page to support or comment on the nomination. Greek mathematics , as that term is used in this article, is the mathematics written in Greek , developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean Periods Classical Greek mathematics refers to the mathematics studied before the Hellenistic period , when Greek mathematics was mostly limited to the Greek city-states in ancient Greece Asia Minor Libya , and Sicily Greek mathematics studied from the time of the Hellenistic period onwards (from 323 BC ) refers to all mathematics of those who wrote in the Greek language , since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean . Greek mathematics from this point merged with Egyptian and Babylonian mathematics to give rise to the latter phase of Greek mathematics known as Hellenistic mathematics . The most important centre of learning during this period was Alexandria in Egypt , which attracted scholars from across the Hellenistic world, including mostly Greek and Egyptian scholars, as well as

37. Greek Mathematics - Wolfram Demonstrations Project Remember me Note Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific http://demonstrations.wolfram.com/topic.html?topic=Greek Mathematics&limit=2

38. Classical Greek Mathematics A few words about mathematics in ancient Greece. During the period from about 600 B.C. to 300 B.C., known as the classical period of Greek mathematics, mathematics was http://www.rbjones.com/rbjpub/maths/math005.htm

Classical Greek Mathematics During the period from about 600 B.C. to 300 B.C. , known as the classical period of Greek mathematics, mathematics was transformed from an ecclectic collection of practical techniques into a coherent structure of deductive knowledge. For many mathematicians, the discipline we call mathematics was founded in this period. Here we briefly survey the achievements from a logical point of view From Procedural to Declarative Knowledge The change of focus from practical problem solving methods to knowledge of general mathematical truths and the development of a body of theory transforms mathematics into a scientific discipline. Abstraction Pythagorean abstraction and Plato's "ideals" make the subject matter of mathematics out of this world Logic The cannons of deductive reasoning are systematised by Aristotle in his syllogistic logic Foundations The Greeks showed concern for the logical structure of mathematics. The Pythagorean's sought to found all of mathematics on number but were confounded by the discovery of incommensurable ratios in geometry. This prevented them from giving an account of geometric magnitudes in terms of their numbers (what we now call the natural numbers or positive integers). By the end of the Pythagorean period geometry has come to be regarded as fundamental. The problem of incommensurable ratios will remain unresolved for more than two millenia. Deduction From very early in the classical period deduction is perceived as the primary method of arriving at mathematical truths. This contrasts with (but does not entirely displace) non-deductive generalisation from particulars.

39. ANCIENT GREEK MATHEMATICS Space provided by Angelfire Communications. Best viewed at 640 X 480 (256 colors). If you are interested in learning more about Greek mathematics, you can browse this website http://www.angelfire.com/me/Huffamoose/

ANCIENT GREEK MATHEMATICS Space provided by Angelfire Communications. Best viewed at 640 X 480 (256 colors). If you are interested in learning more about Greek mathematics, you can browse this website or chat (below) with others about the influence of Greek mathematics on western civilization. For those who have little knowledge about this subject, ask yourself: "How will I ever use these postulates and theorems, and who has come up with all of these interesting ideas? Where did all of this come from?".... If you guessed Ancient Greece, you're right! While Alexander the Great was out on his conquests, mathematicians like Euclid and Aristotle were coming up with new ideas which would benefit western civilization 2300 years later. If you look at the Parthenon (bottom of page) from a distance away, it looks perfectly rectangular. But in fact, the floor, walls, and columns are actually bowed. The ancient Greek architects who calculated the measurements that would be used in the construction of the Parthenon, used mathematics to come up with their designs. Buildings, like the Parthenon, have influenced many modern buildings like the Philadelphia Art Museum. Greek mathematics has made an astonishing impact on our world. By scrolling down this page, you will be able to see the influence that Ancient Greek mathematics has had on Western Civilization.... Your journey begins here.

40. The Story Of Mathematics - Greek Mathematics As the Greek empire began to spread its sphere of influence into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the http://www.storyofmathematics.com/greek.html

The Story of Mathematics Prehistoric Mathematics Sumerian/Babylonian Mathematics Egyptian Mathematics ... Contact GREEK MATHEMATICS Ancient Greek Herodianic numerals As the Greek empire began to spread its sphere of influence into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they conquered. This was as true of their mathematics as anything else, and they adopted elements of mathematics from both the Babylonians and the Egyptians . But they soon started to make important contributions in their own right and, for the first time, we can acknowledge contributions by individuals. By the Hellenistic period , the Greeks had presided over one of the most dramatic and important revolutions in mathematical thought of all time. The ancient Greek numeral system, known as Attic or Herodianic numerals, was fully developed by about 450 BC, and in regular use possibly as early as the 7th Century BC. It was a base 10 system similar to the earlier Egyptian one (and even more similar to the later Roman system), with symbols for 1, 5, 10, 50, 100, 500 and 1,000 repeated as many times needed to represent the desired number. Addition was done by totalling separately the symbols (1s, 10s, 100s, etc) in the numbers to be added, and multiplication was a laborious process based on successive doublings (division was based on the inverse of this process).

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