Geometry.Net - Mathematicians: Greek Mathematicians

Chalk Board Math Resources For Students
Andrews, Scotland) The History of Mathematics (Trinity College, Dublin) Indexof greek mathematicians (St.Andrews.ac.uk) Greek Mathematics (Chris Weinkopf
http://www.hitmill.com/college/math.html
Greek.htm
greek mathematicians. Pythagoras (500 BC). He developed the first generalproof of the Pythagorean theorem. The square of the longest
http://www.ga.k12.pa.us/academics/us/math/geometry/stwk98/RYANMS/Greek.htm

Extractions: Greek Mathematicians He developed the first general proof of the Pythagorean theorem. The square of the longest side of the right triangle equals the sum of the squares of the other two sides. He discovered the existence of irrational numbers and created doctrines which inspired the systematic study of mathematics and the numeral aspects of musical harmony. One of the world's greatest philosophers, he expanded Greek learning throughout the world in astronomy, mathematics, and metaphysics. He developed the Academy and taught philosophy and different levels of mathematics as well as theoretical astronomy. Euclid made great Advancements in Geometry. He developed the revolutionary progress in the analysis of two and three- dimensional space. He created the geometry that endures to this day known as Euclidean Geometry. He determined the areas and volumes of numerous geometric figures and derived equations for them. He pioneered mathematical geography. He caculated the circumference of the earth with astonishing accuracy for his time.
Readings In Greek Mathematics
How do we know about greek mathematicians? The timeline of greek mathematicians;Translations of Euclid's Elements. Trisectrix animation; Epicycle animation.
http://www.math.tamu.edu/~dallen/masters/Greek/readings4.htm

Extractions: The Origins of Mathematics; the schools Thales , by Dmitri Panchenko Thales, his Philosophy and Mathmatics Pythagoras and the Pythagoreans Anaxagorus and the Heroic Age ... Greek Enumeration and Arithmetic Eudoxus Euclid Archimedes Apollonius and other geometers Ancient Algebra Diophantus ... Pappus How do we know about Greek mathematics? How do we know about Greek mathematicians? The timeline of Greek mathematicians Translations of Euclid's Elements. ... Epicycle animation. Some files are long and make take a few minutes to download. To read and print them you will need the Adobe Acrobat Reader. Each reading, in Acrobat (pdf) format, is a short paper on the aspect in question. Upon completing a reading, try to answer the questions that pertain to it.
Ancient Greece Resources For 6th Grade Social Studies
Collection of links geared toward middle school students.Category Kids and Teens School Time Ancient History Greece Mathematics. A Chronological List of Mathematicians tells you all thegreek mathematicians and their dates. Some of the mathematicians
http://www.dalton.org/groups/Greece/

Extractions: The Perseus Project mounted by Tufts University (near Boston) has organized a tremendous amount of Ancient Greek material. Part of their work brings together lots of pictures of Greek artifacts from many museums around the world. Two good things to look at are COINS and VASES The Perseus Project people let you search in a lot different categories, including animals, atheletics and historical people. Once you have chosen a category you just have to keep clicking until you get a picture ... with their stories and some pictures. They even let you search by vase shapes. Try clicking on "select another kind of search" if you want to search vases by period or region.Don't bother to click on "collection" because it just shows you who owns the vases today.
Term Papers (model), Term Papers (model) And More Term Papers (model) Mathematic
The Importance of Mathematics in Early Greek Culture A 12 page comprehensivestudy of early greek mathematicians and their cultural significance.
http://www.termpapers-on-file.com/mathmatics.htm

Extractions: MORE EXAMPLE TERM PAPERS ON MATHEMATICS A 15 page paper that provides an overview of the history and development of the abacus. The report essentially compares the Chinese, Roman, Greek, Russian and Indian counting methods utilizing similar instruments. Bibliography lists 6 sources. Abacus.doc Benefits Of Computer-Taught Math Over Standard Textbook Practices A 10 page study that provides support for the hypothesis that computer taught math provides significant beneficial outcomes for learners in terms of test scores. Bibliography lists 10 sources. Mtcomp.wps Differential Equations An 18 page research paper on every available aspect of differential equations including Laplace Transforms and much more. A number of graphical illustrations are provided and the bibliography lists more than 8 sources. Diffequa.wps Linear Algebra A 15 page research paper on various concepts in linear algebra. The writer details multivariables, vectors, determinants, gaussian elimination, and other elements of linear algebra. Bibliography lists 6 sources. Linalgeb.wps
Mathematicians
following mathematicians Archimedes, Johann Bernoulli, Georg Cantro,Augustus De Morgan, Euclid, and Zeno. greek mathematicians.
http://www.ramona.k12.ca.us/rhs/rhslmc/math/mathematicians.htm

Extractions: Mathematicians General Reference Biographical Index includes biographies about: Apollonius, Archimedes, Charles Babbage, The Bernoulli family, Lewis Carroll, Georg Cantor, Christopher Clavius, Diophantes, Eratosthenes, Euclid, Pierre de Fermat, Leonard Pisano Fibonacci, Evaroste Galois, Carl Friedrich Gauss, Sophie Germain, Heron, Hypathia, Yang Hui, Felix Klein, Sofia Kovalevskaya, Leonardo da Vinci, Ada Byron Lovelace, August Mobius, Augustus de Morgan, John von Neumann, Emmy Noether, Pythagoras, Michael Stifel, Thales, Grace Chisolm Young, Zeno, Zhu Shi-jie. History of Mathematics this site links to information about several of the mathematicians including Archimedes, Georg Cantor, Euclid, Leonard of Pisa (Fibonacci), Emmy Noether, and Zeno. History of Mathematics this site hyperlinks to several sites related to the mathematicians on your list. Some of these links are: Zeno's Paradox of Motion, Archimedes and the Square Root of 3, Euclid's Plan and Proposition 6, Franklin's Magic Squares, and On Gauss's Mountains. Interactive Mathematics Miscellany and Puzzles examples of the theories put forth by many of the mathematicians can be located here. Some examples include: Apollonius, Archimedes, Cantor, Euclid, Heron, Moebius, and Pythagorius
GREEK MATHEMATICS
Because little original work of ancient greek mathematicians still exist, we cannotbe sure how much of mathematics in The Elements can be credited to Euclid.
http://www.fort-mill.k12.sc.us/fmhs/fosterc/greek_mathematics.htm

Extractions: GREEK MATHEMATICS SCAVENGER HUNT INTRODUCTION The Geometry we study is called Euclidean Geometry because Arabic and Latin translations of Euclid's 13 volume work, The Elements , are among the oldest known records of the formal study of mathematics. Because little original work of ancient Greek mathematicians still exist, we cannot be sure how much of mathematics in The Elements can be credited to Euclid. At the very least, Euclid arranged, perfected and provided rigorous proof for mathematics originated by his predecessors. Euclid and his followers were among the first mathematicians to recognize the importance of rigorous proof. They were not content to accept a rule just because it was true in a particular case. A few rules, called postulates, were accepted as true because they were obvious truths which could not be disproved. Other rules, called theorems, were proved using postulates and previously proved theorems. Thus the study of mathematics moved from discovery (inductive reasoning) to demonstration that those discoveries must be true (deductive reasoning.) By studying the history of Greek mathematics and Greek mathematicians, you will learn the basis for your study of Euclidean Geometry this semester. Later this will serve as a contrast to two non-Euclidean geometries, Elliptic and Hyperbolic.
The Shaping Of Deduction In Greek Mathematics - Cambridge University Press
4. Formulae; 5. The shaping of necessity; 6. The shaping of generality; 7. The historicalsetting; Appendix the main greek mathematicians cited in the book.
http://books.cambridge.org/0521622794.htm

Extractions: Philosophy Classical Studies A Study in Cognitive History In stock The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.Winner of the Runciman Award 2000. a necessary read for anyone interested in the history of Greek mathematics but will also be interesting to a wider audience, particularly philosophers of science and intellectual historians Netz has made an important contribution to intellectual history and has asked a diverse set of questions whose answers, while difficult, will broaden our understanding of the development of deductive practices.Bryn Maur Classical Review
Mathematical Masterpieces: Teaching With Original Sources
Offers insights on how to teach through original sources, such as Euclid's elements.Category Science Math Education Teaching Resources Lesson Plans After Babylonian and ancient greek mathematicians systematically solvedquadratic equations, progress passed to the medieval Arab world.
http://www.math.nmsu.edu/~history/masterpieces/masterpieces.html

Extractions: R. Calinger (ed.), MAA, Washington, 1996, pp. 257260] Our upper-level university honors course, entitled Great Theorems: The Art of Mathematics To achieve our aims we have selected mathematical masterpieces meeting the following criteria. First, sources must be original in the sense that new mathematics is captured in the words and notation of the inventor. Thus we assemble original works or English translations. When English translations are not available, we and our students read certain works in their original French, German, or Latin. In the case of ancient sources, we must often depend upon restored originals and probe the process of restoration. Texts selected also encompass a breadth of mathematical subjects from antiquity to the twentieth century, and include the work of men and women and of Western and non-Western mathematicians. Finally, our selection provides a broad view of mathematics building upon our students' background, and aims, in some cases, to reveal the development over time of strands of mathematical thought. At present the masterpieces are selected from the following. The Greek method of exhaustion for computing areas and volumes, pioneered by Eudoxus, reached its pinnacle in the work of Archimedes during the third century BC. A beautiful illustration of this method is Archimedes's determination of the area inside a spiral. [
Pythagoras - Geometrical Algebra
After the experience with the incommensurables, greek mathematicians considered workingwith number as unreliable, resulting in the development of algebra as a
http://www.mathgym.com.au/history/pythagoras/pythalg.htm

Extractions: Introduction: In the previous essay I concluded with the "logical scandal" of the incommensurables . The fact that all numbers were not Natural caused a major problem for the Pythagorean Order not only because their faith depended on it but also because their Theory of Proportions used at the time to solve equations, relied solely on Natural number. This "loss in confidence" with number caused Greek Mathematics to move away from numbers and to use measures in their place i.e. lengths, areas, volumes. Because geometrical properties could be physically constructed (with straight-edge and compass) and their accuracy "seen", geometry was considered to be verifiable and rigorous. After the experience with the incommensurables, Greek mathematicians considered working with number as unreliable, resulting in the development of algebra as a geometrical construct over the next few centuries. This confidence in the "tangibility" and rigour of geometry lasted through to the 17 century. Sir Isaac Newton is considered to be influential in the acceptance of algebraic procedures, though he would not publish his monumental "
Science
Archmede.tm. Euclid's Elements or alternative. Birthplaces of greek mathematicians(Univ. of St Andrew). Wonders of Ancient Greek Mathematics (Timothy Reluga).
http://pomoerium.com/links/science.htm

Extractions: Mesopotamian Mathematics History of Mathematics- Babylonia Egyptian Mathematics or alternate Archimedes Chris Rorres ) or alternate or alternate or alternate or alternate or alternate Archimedes page Works of Archimedes Archmede.tm ... Euclid's Elements or alternative Birthplaces of Greek Mathematicians (Univ. of St Andrew) Wonders of Ancient Greek Mathematics (Timothy Reluga) Roman Arithmetic Great mathematicians Library of Alexandria (Ellen N. Brundige) Greek Science History Greek Science (Gregory Crane) Cartography Lexicon of Ancient Geography Ptolemy's Geography Ptolemy's Geography (Library of Congress) Ptolemy (Bill Thayer) Ptolemaeus Weltkarte (Bayerische Staatsbibliothek) Orbis Latinus MapMachine (National Geographic) Fundamentals of Observational Astronomy in Babylonia Ancient Astrology Greek Astronomy Italy's volcanoes ... Fizyka dla wszystkich
Greek History - Greek Science And Its Influence On Western Civilization
Archimedes and Pythagoras are considered to be the greatest greek mathematicians,Archimedes was an early writer on the science of mechanics.
http://www.hellenism.net/eng/history-science.htm

Extractions: Greek civilization came to an end more than 2,000 years ago, when Greece became part of the Roman empire. Yet its influence on politics, philosophy, art, architecture, language and literature can still be felt today. Much of the language we use and many of our ideas about science and art come from ancient Greece. Greece has influenced the Western World in many ways. The Ancient Greeks especially contributed many things to the scientific world, from agriculture to astronomy. Many cultures have had innovative scientific developments and traditions of scientific thought. However, many of these cultures scientific histories have been swept away by the turbulent storms of time because their scientific foundations have been weak, resting on mythological superstitions. Greek science, on the other hand, has withstood time's tempests because of the strong foundations laid by earlier societies in mathematics, measurement, astronomy, and medicine. Greek science had its beginnings with mathematics. They were begun in Mesopotamia and Egypt, and then over the course of time were passed on to the Greeks. Archimedes and Pythagoras are considered to be the greatest Greek mathematicians, Archimedes was an early writer on the science of mechanics. Math and mechanics became extremely useful during the Golden Age of Greece (600 BC). Geometry played a large role in the development of Greek architecture, and was applied widely. Physics were used to construct buildings, as well as in war. Levers made moving large stones feasible. For war purposes, catapults were constructed to throw stones at the enemy.
Ivars Peterson's MathTrek - Ancient Infinities
The geometric diagrams, for example, suggest that greek mathematicians tendedto emphasize qualitative relationships over quantitative accuracy.
http://www.maa.org/mathland/mathtrek_11_25_02.html

Extractions: November 25, 2002 B.C. ) did his mathematical work more than 2,000 years ago. The manuscript, known as the Archimedes Palimpsest , is the only source of Archimedes' treatise on the "Method of Mechanical Theorems." As the oldest surviving Archimedes manuscript, it's the closest we can get to the mathematician himself, says science historian and classics professor Reviel Netz of Stanford University, who has been studying the relic. Dating from the 10 century, the Archimedes text survives as writing on parchment that 2 centuries later was cut apart, roughly scraped, and overwritten with a description of a church ritual. The document was first rediscovered in Constantinople in 1906 by the Danish scholar J.L. Heiberg. Aided only by a magnifying glass, however, he could not read every word of the text. The manuscript vanished from view in the 1920s before resurfacing in 1998 and being auctioned off for $2 million to an anonymous buyer. The buyer allowed the palimpsest (a scraped and overwritten parchment) to be conserved, photographed, and displayed at the Walters Art Gallery in Baltimore. "It has always been thought that modern mathematicians were the first to be able to handle infinitely large sets, and that this was something the Greek mathematicians never attempted to do," Netz wrote in the Nov. 1
Read This: The Shaping Of Deduction In Greek Mathematics
of Homeric repetitions. There are differences, though greek mathematicianswere not illiterate oral performers. RN gives a competent
http://www.maa.org/reviews/netz.html

Extractions: by Reviel Netz Reviel Netz has written an stimulating book about diagrams and mathematics, telling us facts that we all know, but hardly ever thought of. Thus he sets himself in the best of company, for isn't that what Euclid did from the very first proposition in the Elements? "The diagram is the metonym of mathematics" is RN's main claim. To understand what he means by that, think of two typical situations in the circus of conferences: if a philosopher or historian gives a talk, he will read aloud for half an hour, facing his audience without moving from his chair. If a mathematician gives a talk, he will dance around the platform talking to the blackboard while writing figures and letters on it, most of the time ignoring his audience and concentrating on his written deductions as they emerge out of sheer necessity. Years ago David Fowler (of Plato's Academy ) coined a motto: "Greek mathematics is to draw a figure and tell a story about it." RN has widened and deepened this into "Deductive mathematics grew out of the Greeks drawing lettered diagrams and telling stories by means of them, not only about them." The diagram and the argument live in such a close symbiosis that one cannot be understood without the other. The diagram is the metonym of mathematics.
Regular Polyhedra
Other sites with information about Greece and greek mathematicians. GreekMathematicians Images and information about greek mathematicians.
http://intranet.sgc.edu/people/faculty/bwyarbrough/regpoly.htm

Extractions: created by Suzanne Alejandre A polyhedron is a three-dimensional solid whose faces are polygons joined at their edges. A polyhedron is said to be regular if its faces are made up of regular polygons. A regular polygon is a polygon with equal sides and equal angles placed symmetrically around a common center. The word polyhedron is derived from the Greek poly (many) and the Indo-European hedron (seat). Five regular polyhedra comprise the convex Platonic solids: Applet by Multimedia Java Applications (MJA) Click on the five different buttons in the applet ( F=4, F=6, F=8, F=12, F=20 ). Can you name the five regular polyhedra? Look at the top of the chart. How many faces does each polyhedron have? How many vertices? Stop the rotation. Look at each of the polyhedra. What polygon do you see on the faces of the
Untitled
by researching the theories and formulas of the early greek mathematicians andusing them to explain their connections to modern science and technology;
http://www.bergen.org/ETTC/projects/AncientGreece/CurriculumStandards.htm

Extractions: Art - creating a collage of modern science and technology topics directly influenced by early Greek scientists and mathematicians; including photographs of the Greek individual they have selected in his or her report; creating fashionable ancient Greek clothing for the interviews or debates English - writing a dialogue between an ancient Greek scientist, mathematician, or philosopher (transported through time) and the student in which the student explains the connection between the early individual's work and modern science and technology, or by conducting a debate in which a group of "early Greek scientists, mathematicians, and philosophers" use early philosophy to defend a position on a modern topic against a group of "modern scientists" and their beliefs; writing of the culmination assignment Literature - by reading Greek mythology to understand its role in the attempts of the early Greek scientists and philosophers explanations of the world in which they lived History - by researching the early Greek scientists, mathematicians, and philosophers; the impact of ancient Greek culture and religion upon their efforts in explaining things from a scientific point of view; the role government played upon the lives of some of the Greek scientists
Resources For Students
to links of early Greek medicine and other related subjects, History of Mathematics links to areas of greek mathematicians and other sciences involving math.
http://www.bergen.org/ETTC/projects/AncientGreece/Resources.htm

Extractions: Greek Scientists, Mathematicians, and Philosophers Hippocrates Aristotle Theophrastus Discorides ... The Internet Encyclopedia of Philosophy - biographies of Greek philosophers listed alphabetically Science and Technology Greek Biology - brief description of Greek thoughts in biology and medicine Greek Scientific Thought - specific philosophies of Greek scientists and their impact on modern science Greek Science Resource Page - connects to specific links of individual scientists The Internet Guide to Greece - web page with various resources about Greece Greek Science and Technology - connects to website of links to Greek science, mathematics, and technology The Museum Exhibition Area - Museum of Thessaloniki Ancient Greek Technology Area - technology exhibitions in a museum in Greece Hippocrates on the Heart - description of the heart as perceived by Hippocrates, Aristotle, and Plato History of Science and Biographies of Scientists - connects to links of various aspects of science Jason's Website of Ancient Greek Science - influence of Greek science on Western Civilization Brief History of Ancient Greek Medicine - overview of early Greek medicine Medicine in Ancient Greece - links to Hippocrates and Temple Cures The Asclepion - study of ancient Greek medicine Dreams in Ancient Medicine - how dreams were interpreted in relation to illness Greek Civilization - The Coan School - thoughts on Greek beliefs about disease
Archimedes Scholar Finds Something To Holler 'Eureka!' About
Conventional wisdom has it that ancient greek mathematicians dislikeddealing with infinity. Now researchers have discovered that
http://www.eurekalert.org/pub_releases/2002-11/su-asf110802.php

Extractions: Stanford University Reviel Netz, an assistant professor of classics, might not have actually shouted "Eureka!" on a visit last year to the Walters Art Museum in Baltimore, but that's what he was thinking. A scholar of Greek mathematics, Netz was hanging out with one of his colleagues and frequent collaborators, Professor Ken Saito of the Osaka Prefecture University in Japan, when they flew together to Baltimore in January 2001 to look at a recently rediscovered codex of Archimedes treatises. "It was basically just tourism," Netz recalled. On a lark they examined a theretofore unread section of The Method of Mechanical Theorems, which is the book's biggest claim to fame; no other copy of the work is known to exist. What they discovered made their jaws drop. Missing The Archimedes Palimpsest, as the book is called, is in terrible shape. (A palimpsest is a manuscript that has been written on more than once; in this case, a 13th-century Greek prayer book overlays the 10th-century script of the treatises.) The pages have been battered, gouged, scorched by fire and blotched by fungus. Without the use of computer technology, they would be mostly unreadable. But when the palimpsest caught the attention of the great Danish philologist Johan Ludvig Heiberg in 1906, the underlying script was much more legible. At that time, the volume was in a library collection in Constantinople - present-day Istanbul - and, until Heiberg went to examine it, nobody seems to have realized its importance; the book contained the ancient Greek mathematician's previously unknown treatise on The Method of Mechanical Theorems.
Learning Family Studies Greek Science
work. Science in Ancient Greece (Science of the Past) by Kathlyn Gay.Harrison Learned about greek mathematicians. Guide Next . I
http://www.learningfamily.net/reiser/9901-act/021science.htm

Extractions: O ur modern science got its start in Ancient Greece, though it was much different than it is today. Without the curiosity and study of many Greek scholars, the advancements in medicine, technology, astronomy and mathematics that we benefit from today wouldn't exist. It's surprising to realize how advanced some of the concepts these men and women of science were even two thousand years ago. Things like atoms, the shape and size of the earth, the movement of planets and the purpose of the brain. We are so much better off because of their work. Pythagoras made a school for men and women where he and his "Pythagoreans" discussed mathematics. They made a theory that "all things are numbers". They may have gotten the idea by observing the patterns of music and nature. Pythagoras also found a mathematical fact about traingles now called the Pythagorean Theorem, which states: "The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse." Or, for any right traingle with legs a and b , and a hypotenuse c a b c ^2 ("^" means "raised to the power of")
Expression Calculator Mathematics
The use of logical reasoning, the methods of which were summarized by Aristotle,enabled greek mathematicians to make general statements instead of merely
http://excalc.vestris.com/docs/math.html

Extractions: Software Documentation Mathematics is the science of relationships between numbers, between spatial configurations, and abstract structures. The main divisions of pure mathematics include geometry, arithmetic, algebra, calculus, and trigonometry. Mechanics, statistics, numerical analysis, computing, the mathematical theories of astronomy, electricity, optics, thermodynamics, and atomic studies come under the heading of applied mathematics. Prehistoric humans probably learned to count at least up to ten on their fingers. The ancient Egyptians (3rd millennium BC), Sumerians (2000-1500 BC), and Chinese (1500 BC) had systems for writing down numbers and could perform calculations using various types of abacus. They used some fractions. Mathematicians in ancient Egypt could solve simple problems which involved finding a quantity that satisfied a given linear relationship. Sumerian mathematicians knew how to solve problems that involved quadratic equations. The fact that, in a right-angled triangle, the square of the longest side is equal to the sum of the squares of the other two sides (Pythagoras' theorem) was known in various forms in these cultures and also in Vedic India (1500 BC). The first theoretical mathematician is held to be Thales of Miletus (c. 580 BC) who is believed to have proposed the first theorems in plane geometry. His disciple Pythagoras established geometry as a recognized science among the Greeks. Pythagoras began to insist that mathematical statements must be proved using a logical chain of reasoning starting from acceptable assumptions. Undoubtedly the impetus for this demand for logical proof came from the discovery by this group of the surprising fact that the square root of 2 is a number which cannot be expressed as the ratio of two whole numbers. The use of logical reasoning, the methods of which were summarized by Aristotle, enabled Greek mathematicians to make general statements instead of merely solving individual problems as earlier mathematicians had done.

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