21. Greek Mathematics - History For Kids! greek mathematics for Kids what math did the Greeks invent? what math did the Greeks History of greek mathematics From Aristarchus to Diophantus, http://www.historyforkids.org/learn/greeks/science/math/

Greek Mathematics for Kids - what math did the Greeks invent? what math did the Greeks learn from other people? why is it important? Europe, Asia, and Africa before 1500 AD Teachers Parents Sitemap This site The Web By region China India West Asia Greece ... About History for Kids Updated Wednesday, Aug 31, 2005 Tired of seeing these ads? For only 99 cents (US) through PayPal you can get a NO ADS VERSION NO WAITING See no ads on this site - just click here to get a password in seconds! Advertisement Check out this timeline from History for Kids or go to a topic area: Egypt or West Asia Ancient China or Africa Ancient Greece or India Ancient Rome Ancient Germany The Islamic Empires ... Medieval Europe Need more info? Send us a message , and we'll try to answer your question. 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

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

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Ancient / Classical History Ancient Greece ... Mathematics Greek Mathematics Homework Help Ancient History Essentials Ancient World Maps ... Help zau(256,140,140,'el','http://z.about.com/0/ip/417/C.htm','');w(xb+xb+' ');zau(256,140,140,'von','http://z.about.com/0/ip/496/7.htm','');w(xb+xb); FREE Newsletter Sign Up Now for the Ancient / Classical History newsletter! See Online Courses Search Ancient / Classical History Greece - Greek Math Resources on ancient Greek mathematics, calculations, geometry, and on Zeno, Archimedes, and Roman numerals. Alphabetical Recent Up a category 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? Euclid An Alexandrian mathematician and teacher, Euclid is most famous for his geometry with its logical deductions, axioms and postulates. Euclid An Alexandrian mathematician and teacher, Euclid is most famous for his geometry with its logical deductions, axioms and postulates. The Number 60 in Distance and Time Sixty may be an arbitrary number but it approximates the numbers of days in the year and is easier to work with because it has so many factors than a decimal system.

23. Greek Mathematics Instead of using the numerals 1, 2, 3, etc., the Greeks used the letters of the alphabet, so they represented one with their first letter, alpha; http://ancienthistory.about.com/b/a/026618.htm

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Ancient / Classical History Homework Help ... Help zau(256,140,140,'el','http://z.about.com/0/ip/417/C.htm','');w(xb+xb+' ');zau(256,140,140,'von','http://z.about.com/0/ip/496/7.htm','');w(xb+xb); FREE Newsletter Sign Up Now for the Ancient / Classical History newsletter! See Online Courses Search Ancient / Classical History Greek Mathematics Ancient/Classical History Blog Main September 16, 2003 Greek Mathematics Instead of using the numerals 1, 2, 3, etc., the Greeks used the letters of the alphabet, so they represented one with their first letter, alpha; 2 with their second letter, beta, etc. BBC News reports that the Greek alphabetic numeral system may not have been invented by the Greeks. Instead, the Greeks may have borrowed it from the Egyptians. Greeks 'borrowed Egyptian numbers' MORE: Greek Mathematics Elsewhere: Greek Language Instruction and Pronunciation Email a Friend Display Latest Headlines Read Archives Advertisement Most Popular Ancient Atlas Attila the Hun Etymology - Greek and Latin Roots - Prefixes and Affixes The Trojan War ... Fall of Rome What's Hot Euripides - Greek Tragedy Writer Euripides - Life and Contri...

24. Basic Ideas In Greek Mathematics Basic Ideas in greek mathematics. Michael Fowler UVa Physics Department. Index of Lectures and Overview of the Course Link to Previous Lecture http://galileoandeinstein.physics.virginia.edu/lectures/greek_math.htm

Michael Fowler UVa Physics Department Index of Lectures and Overview of the Course Link to Previous Lecture Closing in on the Square Root of 2 In our earlier discussion of the irrationality of the square root of 2, we presented a list of squares of the first 17 integers, and remarked that there were several "near misses" to solutions of the equation m n . Specifically, 3 + 1. These results were also noted by the Greeks, and set down in tabular form as follows: After staring at this pattern of numbers for a while, the pattern emerges: 3 + 2 = 5 and 7 + 5 = 12, so the number in the right-hand column, after the first row, is the sum of the two numbers in the row above. Furthermore, 2 + 5 = 7 and 5 + 12 = 17, so the number in the left-hand column is the sum of the number to its right and the number immediately above that one. The question is: does this pattern continue? To find out, we use it to find the next pair. The right hand number should be 17 + 12 = 29, the left-hand 29 + 12 = 41. Now 41 = 1681, and 29

25. Math Lair - Ancient Greek Mathematics History Ancient greek mathematics History. View a note on these timelines. 600 BC Thales introduces deductive geometry. It was developed over the years by http://www.stormloader.com/ajy/greek.html

Ancient Greek Mathematics History View a note on these timelines 600 B.C. Thales introduces deductive geometry. It was developed over the years by Pythagoras and the Pythagoreans, Plato, Aristotle, Euclid, and others. 540 B.C. Pythagoras does geometrical work. 450 B.C. Zeno of Elea (489 B.C. - 430? B.C.) formulates Zeno's paradox 380 B.C. Plato, whose ideas were influenced by the Pythagoreans, is writing philosophy. 340 B.C. Aristotle is writing philosophy. 300 B.C. Euclid compiles, organizes and systematizes geometric ideas which had been discovered and proven into thirteen books, called The Elements 240 B.C. Eratosthenes determines that the Earth is spherical and computes its diameter. 225 B.C. Archimedes (287 B.C. - 212 B.C.) does work on circles, spheres, areas, infinite series, and other things. 225 B.C. Appolonius works on conic sections If you're using , you can view a graphical timeline of famous mathematicians . If you're not, a text version may be more to your liking. After this point, see Greco-Roman mathematical history The main number system used by the Greeks during this period was the Attic system.

26. The Stoa Consortium » Blog Archive » Greek Mathematics greek mathematics. Filed by Ross Scaife @ 433 pm. Anne Mahoney has an interesting new review up of Reviel Netz, The Transformation of Mathematics in the http://www.stoa.org/index.php?p=39

27. The Stoa Consortium » Blog Archive » Greek Mathematics greek mathematics. Anne Mahoney has an interesting new review up of Reviel Netz, The Transformation of Mathematics in the Early Mediterranean World From http://www.stoa.org/?p=39

28.     Greek Mathematics Geminus ~ Theory of Mathematics, Proclus ~ Student at Plato s Academy They are (typically) considered as Greek rather than Middle Eastern. http://www.mathisradical.com/Greece.htm

CDs 800+ Posters on one CD for $25.00 Price Includes Shipping Price Includes Shipping See Details of this CD Customize Your CD Greece ~ 2 Sets Below Posters are 11" x 8-1/2" Greece Set 1 The BC Years Please click the thumbnails with an * in front of the title to view a larger image. Thales ~ Geometry to Babylonia * Pythagoras ~ Teaches Geometry Hippasus ~ Introduces Deodecahedron 1st use of Written Numerals Zeno ~ Presents Paradoxes Hippocrates ~ Writes Elements of Geometry Hippiaus ~ Creates Quadratirix * Plato ~ Opens his Academy Aristaeus ~ Conic Sections Aristarchus ~ Distance to Moon * Theano, wife of Pythagoras Posters are 11" x 8-1/2" Greece Set 2 Please click the thumbnails with an * in front of the title to view a larger image. * Nicomedes ~ Concoid Curve Diocles ~ Burning Mirrors Geminus ~ Theory of Mathematics Proclus ~ Student at Plato's Academy Metrodorus ~ 46 Math Problems The following posters are of men from the Middle East, when Greece ruled the land. They are (typically) considered as Greek rather than Middle Eastern.

29. Classical Greek Mathematics A few words about mathematics in ancient Greece. known as the classical period of greek mathematics, mathematics was transformed from an ecclectic 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.

30. Real Numbers - Some History The first is the period of classical greek mathematics in which mathematics Though greek mathematics understood as numbers only what we call the natural http://www.rbjones.com/rbjpub/maths/math008.htm

Real Numbers - some history Greek beginnings building on sand back to basics There are two major periods in the historical development of the real number system which we consider here. The first is the period of classical Greek mathematics in which mathematics first emerged as a deductive science. The second is that of the rigourisation of analysis and the formalisation of mathematics which took place mostly in the 19th century. Between these periods mathematics expanded very much in areas which depended on real numbers despite weakness in the understanding of real numbers. Greek Beginnings Number in Classical Greek Mathematics The social division in classical Greece, between slaves and citizens, supported a division of practical computation and mathematical theory. Though Greek mathematics understood as numbers only what we call the natural numbers, they dealt also with whole number ratios, and with geometric magnitudes, corresponding to what we now call rationals and reals. None of these systems were treated as we would treat them today, but even geometric magnitudes were treated in Greece with greater rigour than at any subsequent period until the real number system was placed on a firm foundation in the 19th century. The Method of Exhaustion Before any of the number systems had been established to modern standards Eudoxus developed the Method of Exhaustion. This was used extensively in Book XII of

31. Mathematics (Rome Reborn: The Vatican Library & Renaissance Culture) where faith and science were not yet seen as two, irreconcilable cultures. greek mathematics and its Modern Heirs; Ptolemy s Geography; Greek Astronomy http://www.loc.gov/exhibits/vatican/math.html

The Library of Congress Exhibitions HOME Exhibition Sections: Introduction The Vatican Library Archaeology Humanism ... Credits MATHEMATICS Greek Mathematics and its Modern Heirs Ptolemy's Geography Greek Astronomy Greek Mathematics and its Modern Heirs Euclid, Elements In Greek Parchment Ninth century Euclid's Elements, written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Archimedes, Works In Latin Translated by Jacobus Cremonensis ca. 1458 In the early 1450s, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' On Conoids and Spheroids with highly ornate, and rather curious, illumination.

32. Ancient Greek Mathematics Ancient greek mathematics. LINKS. The Science of Magnitudes. Classical greek mathematics, survey of the achievements from a logical point of view http://www.mlahanas.de/Greeks/MathLinks.htm

Ancient Greek Mathematics LINKS The Science of Magnitudes. The Beginnings: The Greeks, Scientists and Artists See some beautiful Proofs of Ancient Greek Mathematicians http://www.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/VignettesAncientMath.html Read Euclid Elements and learn ancient Greek to read the original text http://www.du.edu/~etuttle/classics/nugreek/contents.htm Euclid Elements, a well known Website http://aleph0.clarku.edu/~djoyce/java/elements/toc.html Ancient Mathematicians (French Language with links) http://perso.wanadoo.fr/jean-paul.davalan/hist/ Geometric Problems of Antiquity Eric W. Weisstein. "Geometric Problems of Antiquity." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/GeometricProblemsofAntiquity.html University of St. Andrews (Includes an extensive list with biographies of Greek mathematicians and from all other countries ) The classic Greek mathematic Problems Squaring the circle Doubling the cube Trisecting an angle The teaching of mathematics in Ancient Greece ... Enquiries about the genesis of formal thinking and about syntactic knowledge representation Individual Biographies from the University of St Andrews of the mathematical work of: Anaxagoras Anthemius Antiphon Apollonius ... Zenodorus Various mathematical problems The Ten Means of Ancient Greece When is a Triangle Not a Triangle?

33. Ancient Greek Mathematics The influence of greek mathematics continues through the ages. Arithmetic, music, geometry, and astronomy – pure number, applied number, http://www.mlahanas.de/Greeks/GreekMathematics.html

Ancient Greek Mathematics Griechische Mathematik The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell. Saint Augustine Poetry is the only place where the power of numbers proves to be nothing Odysseas Elytis, Nobel Prize Literature 1979 Republic Ancient Greece Mathematics Timeline Mathematicians and other Scientists: Graphical Timeline from 800 BC - 700 AD Thales of Miletus, the first Greek scientist Boyer in A History of Mathematics a) Pythagoras of Samos, strange and mysterious b) The Life of Pythagoras by Diogenes Laertios Pythagoras most important achievement is his idea that everything in the Universe can be expressed by numbers. Plato was fascinated by this idea and he used the Platonic solids as the building blocks of the Universe, the first primitive mathematical cosmological model. Today mathematical physicists try to fulfill the dream of Pythagoras. The only mistake of Pythagoras is that mathematics can describe everything except that what is really personally important. Pythagoras: Everything is a number: The revival of his idea The irrational behavior of Pythagoras discovering the irrational numbers The irrationality in the Pentagon and the most irrational number The Ten Means of Ancient Greece ... The Prime numbers, infinite, perfect and amicable their erotic effects and the number of the fish

34. Aristotle And First Principles In Greek Mathematics: A Supplement To Aristotle A Elsewhere in greek mathematics, and even in the Elements, we find other treatments first principles, some of which are closer in other ways to Aristotle s http://plato.stanford.edu/entries/aristotle-mathematics/supplement1.html

Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information Aristotle and First Principles in Greek Mathematics It has long been a tradition to read Aristotle's treatment of first principles as reflected in the first principles of Euclid's Elements I. There are similarities and differences. Euclid divides his principles into Definitions horoi Postulates ), and Common Notions koinai ennoiai Elements i is tenuous at best. Elsewhere in Greek mathematics, and even in the Elements , we find other treatments first principles, some of which are closer in other ways to Aristotle's conceptions. For example, Archimedes' On the Sphere and Cylinder opens with existence hypotheses (that certain lines exist) and stipulations (that they should be called such-and-such). A more fundamental distinction between Aristotle's treatment of first principles and those found in Greek mathematics is that Aristotle seems to think that each first principle has both a logical and an explanatory role in a treatise. Yet it is typical, especially in treatises which are introductory to a topic, to have principles which serve a logical and explanatory role, but also to have principles whose only explicit role is pedagogical. For they serve no obvious role in the demonstrations. Such might be the definitions of point and line in Elements i. Hence, if there is a relation between Aristotle's conception of first principles and those of the mathematicians, Aristotle provides an ideal framework based on contemporary mathematical practice and which may or may not have been noticed by authors such as Euclid.

35. Aristotle And Greek Mathematics: A Supplement To Aristotle And Mathematics The problem must be as old as greek mathematics, given that the problem marks a transition from Egyptian to Greek style mathematics. http://plato.stanford.edu/entries/aristotle-mathematics/supplement4.html

Stanford Encyclopedia of Philosophy Supplement to Aristotle and Mathematics Citation Information Aristotle and Greek Mathematics This supplement provides some general indications of Aristotle's awareness and participation in mathematical activities of his time. Greek mathematics in Aristotle's Works Here are twenty-five of his favorite propositions (the list is not exhaustive). Where a proposition occurs in Euclid's Elements , the number is given, * indicates that we can reconstruct from what Aristotle says a proof different from that found in Euclid). Where the attribution is in doubt, I cite the scholar who endorses it. In many cases, the theorem is inferred from the context. In a given circle equal chords form equal angles with the circumference of the circle ( Prior Analytics i.24; not at all Euclidean in conception) The angles at the base of an isosceles triangle are equal ( Prior Analytics i.24; Eucl. i.5*). The angles about a point are two right angles ( Metaphysics ix 9; Eucl. follows from i def. 10). If two straight-lines are parallel and a straight-line intersects them, the interior angle is equal to the exterior angle (

36. ¥±. The Greek Mathematics : Demonstrative Geometry Characteristic of greek mathematics. ? Pythagorean Mathematics. ? The Three Famous Problems. ? Euclid s Elements . ? greek mathematics After Euclid http://seoul-gchs.seoul.kr/~contest/tq/mathematics/temh2200.htm

HOME Back Graphic Version ¥±. The Greek Mathematics : Demonstrative Geometry ¢º Characteristic of Greek Mathematics ¢º Pythagorean Mathematics ¢º The Three Famous Problems ¢º Greek Mathematics After Euclid ¡ßCharacteristic of Greek Mathematics In the 600 B.C. Mathematics was focused as a study and a science in the ancient Greek as a matter of course in China, India and Babylonia and to learn Geometry in Egypt. Thales, Pythagoras and Plato in Greek studied in Egypt and joined with Egypt culture Greek produced achivements at mathematics formed a term of now civilization accepting the Egypt culture. That is "Elements" of Euclid, "The Theory of conic sections " of Apollonius, "Arithmetica" of Diophantus and many reserch achivements of Archimedes. Many scholar represented as Aristotle. Plato focused only philosophy and mathematics. The story, Plato wrote "NO one knows Geometry, No admission" at the enterance to a hall, is famous. Euclid is known affected by Aristotle and plato. His "Elements" is the first arranged and systematized book logically and had been used as a textbook toward the end of the 1800's in Europe.

37. Greek Mathematics - Wikipedia, The Free Encyclopedia greek mathematics, as that term is used in this article, is the mathematics greek mathematics also contributed importantly to ideas on number theory, http://en.wikipedia.org/wiki/Greek_mathematics

Greek mathematics From Wikipedia, the free encyclopedia. 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 centres 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 edit Origins 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.

38. The Shaping Of Deduction In Greek Mathematics - Cambridge University Press Introduction a specimen of greek mathematics; 1. The lettered diagram; 2. The pragmatics of letters; 3. The mathematical lexicon; 4. Formulae; 5. http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521541204

39. Proofs And Pythagoras - Greek Mathematics Sample Proofs and Pythagoras greek mathematics Worksheet Reading Comprehension Worksheets edHelper.com Subscribers Build a printable worksheet with the http://www.edhelper.com/ReadingComprehension_35_195.html

Sample Proofs and Pythagoras - Greek Mathematics Worksheet Reading Comprehension Worksheets edHelper.com Subscribers: Build a printable worksheet with the complete story and puzzles Build a proofreading activity With just one subscription, you will have access to the math, spelling, vocabulary, and critical thinking worksheets! Sign up now for the subscriber materials! Proofs and Pythagoras - Greek Mathematics By Colleen Messina In the high mountains of Greece in the northeastern part of the Mediterranean, a civilization was born that influenced the world for centuries. Ancient Greece made great strides in the areas of art, philosophy, and politics, and its civilization lasted from approximately 2000 BC to 300 BC. Greece also produced some of the finest mathematical minds that ever pondered numbers. The Greeks were the first people of the ancient world who systematically studied geometry, which is the study of the size and shape of an object. While the first surveyors of Egypt understood practical elements of geometry, the Greeks asked why these applications worked. The Greeks wrote down rules for geometry that verified the observations of other ancient mathematicians. The Greek language formed the basis of some of the mathematical words we use today. The word geometry comes from a Greek word for "earth measuring." Another modern word that comes from Greek is arithmetic, which comes from

40. History For Kids! wwwadm.pdx.edu/user/sinq/greekciv2/science/mathem greek mathematics (from mathematics, history of) Encyclopædia greek mathematics (from mathematics, history of) Critical editions of Greek mathematical texts include e The Thirteen Books of Euclid s Elements /e , http://www-adm.pdx.edu/user/sinq/greekciv/science/mathematics/IT.html

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