Archimedes Scholar Finds Something To Holler 'Eureka!' About the book contained the ancient Greek mathematician s previously unknown and that this was something the greek mathematicians never attempted to do http://www.light-science.com/stanfordmath.html
Untitled Document It has always been thought that modern mathematicians were the first to be and that this was something the greek mathematicians never attempted to do http://www.sas.org/E-Bulletin/2002-11-15/features/body.html
Extractions: Reprinted from The Stanford Report, November 6, 2002 R eviel 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. A section from The Archimedes Palimpsest, which classics Professor Reviel Netz stumbled on during a visit to the Walters Art Museum in Baltimore. Closer examination showed the Greeks understood the concept of infinity. 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.
Archimedes Scholar Finds Something To Holler 'Eureka!' About Conventional wisdom has it that ancient greek mathematicians disliked dealingwith infinity. Now researchers have discovered that Archimedes used infinitely 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.
Geometry History Books Archimedes is considered the greatest of greek mathematicians. Archimedes isregarded as the greatest of the greek mathematicians and physicists. http://geometryalgorithms.com/books_history.shtml
The Classical Greek Problems The greek mathematicians thus needed to find a way to construct this quantity The ancient greek mathematicians also could not find a proof for angle http://www.math.rutgers.edu/courses/436/Honors02/classical.html
Extractions: The Classical Greek Problems Patricia DiJoseph There were three problems that the ancient Greeks (600BC to 400AD) tried unsuccssfully to solve by Euclidean methods, all of which were proven unsolvable by these means as much as two thousand years later, as a result of progress in algebra, and the idea of analytic geometry in the sense of Descartes. The Greeks wanted to solve these problems using only a Euclidean constructions, or as they themselves called them, "plane" methods. Though they were never able to do so ( as they cannot be done this way, they did find a series of remarkably clever constructions using more powerful techniques, involving so-called "solid" and "mechanical" methods, as well as a technique called "verging". Then, in the 19th century, the impossibility of finding purely Euclidean constructions for these problems was finally proved. The three classical Greek problems were problems of geometry: doubling the cube, angle trisection, and squaring a circle. Duplication of the cube is the problem of determining the length of the sides of a cube whose volume is double that of a given c ube. A cube by definition is a three dimensional shape comprised of a height, width, and depth all of the same magnitude s. To find its volume, one multiplies the length (s) by the width (s) and then by the depth (s): the volume is s(s(s or s3. Diagram not converted, here and below
Greek.htm greek mathematicians. Pythagoras (500 BC). He developed the first general proofof the Pythagorean theorem. The square of the longest side of the right http://www.germantownacademy.org/academics/US/Math/Geometry/stwk98/RYANMS/Greek.
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.
MSN Encarta - Mathematics About 300 bc Euclid, a Greek mathematician who taught in Alexandria, Egypt,organized the work of many greek mathematicians in a masterful work called the http://encarta.msn.com/encyclopedia_761578291_6/Mathematics.html
Extractions: Search for books and more related to Mathematics Encarta Search Search Encarta about Mathematics Editors' Picks Great books about your topic, Mathematics ... Click here Advertisement document.write(' Page 6 of 12 Encyclopedia Article Multimedia 45 items Article Outline Introduction Mathematics: The Language of Science Branches of Mathematics History of Mathematics a Number System The Greek number system was based on the alphabet. The Attic system, in use from 600 bc to 200 bc , used a stroke for 1 and the initial letters of the words for 5, 10, 100, 1,000, and 10,000ânamely, the initials of pente deka hekaton khilioi , and myrioi âto represent the respective numbers. A later system assigned number values to the 24 letters of the Greek alphabet and to 3 other letters that were no longer used. The letters could be combined to form numbers through 999. For higher numbers, a stroke preceding the initial letter (1 through 9) indicated a multiple of 1,000 (1,000 through 9,000). For 10,000 and above, the symbol M indicated that the numeral below should be multiplied by 10,000. See also Numerals b Pythagoras and the Pythagoreans Pythagoras taught the importance of studying numbers in order to understand the world. We know of his achievements only from his disciples, the Pythagoreans, who made important discoveries about number theory and geometry. The Pythagoreans represented whole numbers by using arrangements of dots or pebbles, and classified these numbers according to the shapes produced. (The English word
Four Problems Of Antiquity Three geometric questions raised by the early greek mathematicians attained thestatus of classical problems in Mathematics. These are http://www.cut-the-knot.com/arithmetic/antiquity.shtml
Extractions: Construct a square whose area equals that of a given circle. Often another problem is attached to the list: Construct a regular heptagon (a polygon with 7 sides.) The problems are legendary not because they did not have solutions, or the solutions they had were unusually hard. No, numerous simple solutions have been found yet by Greek mathematicians. The problem was in that all known solutions violated an important condition for this kind of problems, one condition imposed by the Greek mathematicians themselves: Valid solutions to the construction problems are assumed to consist of a finite number of steps of only two kinds: drawing a straight line with a ruler (or rather a straightedge as no marks are allowed on the ruler) and drawing a circle. You are referred to solutions of problems and as examples of existent solutions. That no solution exists subject to the self-imposed constraints have been proven only in the 19th century.
Alphabet Greek Astronomy Greek number systems greek mathematicians sources Greekmathematics - sources Harriot s manuscripts Hirst s diary comments http://www.chaffey.edu/MathWeb/html/alpha.html
History Of Mathematics, Math History University of North Carolina, Chapel Hill Greek Mathematics Information Guide Greek Mathematics here via data on the works of greek mathematicians and http://www.buzzle.com/chapters/education-and-higher-learning_primary-and-seconda
Extractions: Throughout history, the goal of mathematics education has been to develop accurate and logical thinking in individuals so they can apply their newly gained knowledge to solving all kinds of problems. Math is therefore an important course of educational study, especially in preparing college students for careers in business, engineering, medicine, psychology and the various sciences. This section provides math history resources that focus on the history of mathematics and the individuals and groups that have made contributions to this area of study. Advanced Network and Services: Library: Mathematics Historical Time Periods Guide
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.
Chapter 1: Mathematical Preliminaries greek mathematicians associated magnitude with the lengths of lines or the areaof surfaces and so developed methods of computation which went a step beyond http://research.opt.indiana.edu/Library/FourierBook/ch01.html
Extractions: Table of Contents 1.A Introduction These ancients understood how to figure the area of the polygon, but they were never convinced that the area of the polygon would ever exactly match that of the circle, regardless of how large N grew. This conceptual hurdle was so high that it stood as a barrier for 2,000 years before it was cleared by the great minds of the 17th century who invented the concept of limits which is fundamental to the Calculus (Boyer, 1949) . My teaching experience suggests there are still a great many ancient Greeks in our midst, and they usually show their colors first in Fourier analysis when attempting to make the transition from discretely sampled functions to continuous functions. When geometrical intuition fails, analytical reasoning may come to the rescue. If the location of a point in 3-dimensional space is just a list of three numbers (x,y,z), then to locate a point in 4-dimensional space we only need to extend the list (w,x,y,z) by starting a bit earlier in the alphabet! Similarly, we may get around some conceptual difficulties by replacing geometrical objects and manipulations with analytical equations and computations. For these reasons, the early chapters of these coursenotes will carry a dual presentation of ideas, one geometrical and the other analytical. It is hoped that the redundancy of this approach will help the student achieve a depth of understanding beyond that obtained by either method alone.
Mathematics Term Papers...Research Papers About Mathematics... paper gives a brief overview of the Greek mathematician, Euclid. He was the chiefarchitect A 12 page comprehensive study of early greek mathematicians http://www.researchpapers.net/papers_on_mathematics2.htm
PSIgate - Physical Sciences Information Gateway Search/Browse Results How do we know about greek mathematicians? Ancient Greek index History TopicsIndex Version for printing There are two separate articles How do we know http://www.psigate.ac.uk/roads/cgi-bin/search_webcatalogue2.pl?limit=3100&term1=
When Is A Triangle Not A Triangle During the third century BCE, greek mathematicians and astronomers developed Triangles were central to Greek mathematical thinking, beginning with the http://www.cityu.edu.hk/ccs/Newsletter/newsletter5/Triangle.htm
Extractions: When is a Triangle Not a Triangle? Lisa Raphals and celestial distances, including the distance to the ¡§ends of the earth¡¨ and the ¡§height of heaven.¡¨ They incorrectly assumed that the earth was flat, but correctly assumed that the sun was a finite, and measurable, distance from the earth. Their calculations were less accurate than Eratosthenes¡¦, but no less mathematically well reasoned. Similar Triangles in Greek Astronomy During the third century B.C.E., Greek mathematicians and astronomers developed hypotheses and calculations regarding the motion and sizes and distance of the sun, moon and earth. Aristarchus of Samos (310-230 B.C.E.) is best known as the first Greek exponent of a heliocentric theory, a view that his contemporaries rejected because it conflicted with the commonsense view that the earth did not move. In his one surviving work, he used assumptions and the properties of similar triangles to ¡§demonstrate¡¨ ratios between the diameters of the earth, sun and moon and their distances from each other. For example: ¡§The distance of the sun from the earth is greater than 18 times, but less than 20 times the distance of the moon from the earth.¡¨ The Greek text is a list of procedures for naming points and drawing lines and circles between them, with no visual representation. (Modern editions and translations typically add an illustrative diagram.) The Greek text has the look and feel of a proof by deduction from the properties of similar triangles, rather than calculation from actual measurements.
BSHM: Abstracts -- N Netz, Reviel, Greek mathematical diagrams their use and their meaning, Before writing down a proof, greek mathematicians would have outlined it http://www.dcs.warwick.ac.uk/bshm/abstracts/N.html
Extractions: In the early 19th century, local theory of geodesics was well known as an application of infinitesimal calculus to geometry, although equations for geodesics were generally hard to solve. With the work of Jacobi, Sturm and Liouville, a global qualitative treatment of geodesics emerged, through study of the conjugate locus, the cut locus and examination of global topological conditions. Mathematical intelligencer At the close of the nineteenth century, philosophical discussions about geometry and space strongly influenced both the concepts and development of geometry. Both Poincaré and Russell in their discussions about the axioms of geometry used mathematics to support their philosophical arguments, and their respective philosophies in turn influenced their thoughts about geometry. Nagel, Fritz, A catalogue of the works of Jacob Hermann (1678-1733)
Untitled Document geometrical formulations of greek mathematicians such as Euclid, one ofthe Vedic texts predating Euclid and the greek mathematicians by at least a http://www.infinityfoundation.com/ECITmathframe.html
Extractions: 1. Math and Ethnocentrism The study of mathematics in the West has long been characterized by a certain ethnocentric bias, a bias which most often manifests not in explicit racism, but in a tendency toward undermining or eliding the real contributions made by non-Western civilizations. The debt owed by the West to other civilizations, and to India in particular, go back to the earliest epoch of the "Western" scientific tradition, the age of the classical Greeks, and continued up until the dawn of the modern era, the renaissance, when Europe was awakening from its dark ages. This awakening was in part made possible by the rediscovery of mathematics and other sciences and technologies through the medium of the Arabs, who transmitted to Europe both their own lost heritage as well as the advanced mathematical traditions formulated in India. George Ghevarughese Joseph, in an important article entitled "Foundations of Eurocentrism in Mathematics," argued that "the standard treatment of the history of non-European mathematics is a product of historiographical bias (conscious or otherwise) in the selection and interpretation of facts, which, as a consequence, results in ignoring, devaluing or distorting contributions arising outside European mathematical traditions." (1987:14) Due to the legacy of colonialism, the exploitation of which was ideologically justified through a doctrine of racial superiority, the contributions of non-European civilizations were often ignored, or, as Joseph argued, even distorted, in that they were often misattributed as European, i.e. Greek, contributions, and when their contributions were so great as to resist such treatment, they were typically devalued, considered inferior or irrelevant to Western mathematical traditions.
Scholars Decode Ancient Text, Shake Up Pre-calculus History: 11/02 the book contained the ancient Greek mathematician s previously unknown and that this was something the greek mathematicians never attempted to do, http://news-service.stanford.edu/news/november6/archimedes-116.html
Extractions: Stanford Report, November 6, 2002 Scholars decode ancient text, shake up pre-calculus history BY JOHN SANFORD 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. A section from The Archimedes Palimpsest, which classics Professor Reviel Netz stumbled on during a visit to the Walters Art Museum in Baltimore. Closer examination showed the Greeks understood the concept of infinity. ROCHESTER INSTITUTE OF TECHNOLOGY, WALTERS ART MUSEUM, JOHNS HOPKINS UNIVERSITY
Arabic Mathematics Explains contributions of Arabian mathematicians by translating early greek texts, developing early algebraic ideas, number theory and astronomical calculations. Includes information about key people during this time period. http://www-history.mcs.st-and.ac.uk/history/HistTopics/Arabic_mathematics.html
Extractions: Version for printing Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks. There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century. That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in [3]:-
