Academic literature on the topic 'Archimedes. Mathematics, Greek'
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Journal articles on the topic "Archimedes. Mathematics, Greek"
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Bacelar Valente, Mario. "On Archimedes' statics." THEORIA. An International Journal for Theory, History and Foundations of Science 35, no. 2 (May 25, 2020): 235. http://dx.doi.org/10.1387/theoria.20482.
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Archimedes' statics is considered as an example of ancient Greek applied mathematics; it is even seen as the beginning of mechanics. Wilbur Knorr made the case regarding this work, as other works by him or other mathematicians from ancient Greece, that it lacks references to the physical phenomena it is supposed to address. According to Knorr, this is understandable if we consider the propositions of the treatise in terms of purely mathematical elaborations suggested by quantitative aspects of the phenomena. In this paper, we challenge Knorr's view, and address propositions of Archimedes' statics in their relation to physical phenomena.
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Pisano, Raffaele, and Paolo Bussotti. "NOTES ON MECHANICS AND MATHEMATICS IN TORRICELLI AS PHYSICS MATHEMATICS RELATIONSHIPS IN THE HISTORY OF SCIENCE." Problems of Education in the 21st Century 61, no. 1 (October 5, 2014): 88–97. http://dx.doi.org/10.33225/pec/14.61.88.
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In ancient Greece, the term “mechanics” was used when referring to machines and devices in general and intended to mean the study of simple machines (winch, lever, pulley, wedge, screw and inclined plane) with reference to motive powers and displacements of bodies. Historically, works considering these arguments were referred to as Mechanics (from Aristotle, Heron, Pappus to Galileo). None of the treatises entitled Mechanics avoided theoretical considerations on its object, particularly on the lever law. Moreover, there were treatises which exhausted their role in proving this law; important among them are the book on the balance by Euclid and On the Equilibrium of Planes by Archimedes. The Greek conception of mechanics is revived in the Renaissance, with a synthesis of Archimedean and Aristotelian routes. This is best represented by Mechanicorum liber by Guidobaldo dal Monte who reconsiders Mechanics by Pappus Alexandrinus, maintaining that the original purpose was to reduce simple machines to the lever. During the Renaissance, mechanics was a theoretical science and it was mathematical, although its object had a physical nature and had social utility. Texts in the Latin and Arabic Middle Ages diverted from the Greek and Renaissance texts mainly because they divide mechanics into two parts. In particular, al-Farabi (ca. 870-950) differentiates between mechanics in the science of weights and that in the science of devices. The science of weights refers to the movement and equilibrium of weights suspended from a balance and aims to formulate principles. The science of devices refers to applications of mathematics to practical use and to machine construction. In the Latin world, a process similar to that registered in the Arabic world occurred. Even here a science of movement of weights was constituted, namely Scientia de ponderibus. Besides this there was a branch of learning called mechanics, sometimes considered an activity of craftsmen, other times of engineers (Scientia de ingeniis). In the Latin Middle Ages various treatises on the Scientia de ponderibus circulated. Some were Latin translations from Greek or Arabic, a few were written directly in Latin. Among them, the most important are the treatises attributed to Jordanus De Nemore, Elementa Jordani super demonstratione ponderum (version E), Liber Jordani de ponderibus (cum commento) (version P), Liber Jordani de Nemore de ratione ponderis (version R). They were the object of comments up to the 16th century. The distribution of the original manuscript is not well known; what is certain is that Liber Jordani de Nemore de ratione ponderis (version R), finished in Tartaglia’s (1499-1557) hands, was published posthumously in 1565 by Curtio Troiano as Iordani Opvsculum de Ponderositate. In order to show a mechanical tradition dating back to Archimedes’ science, at least till the 40s of the 17th century, we present Archimede's influence on Torricelli’s mechanics upon the centre of gravity (Opera geometrica). Key words: Mechanics, Scientia de Ponderibus, Archimedes, Torricelli, Relationship physics and mathematics in the history of science.
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Mahesh, K., Aditya Kolachana, and K. Ramasubramanian. "An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere." Journal of the Indian Mathematical Society 85, no. 1-2 (January 4, 2018): 139. http://dx.doi.org/10.18311/jims/2018/18897.
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While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.
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Leventhal, Max. "COUNTING ON EPIC: MATHEMATICAL POETRY AND HOMERIC EPIC IN ARCHIMEDES' CATTLE PROBLEM." Ramus 44, no. 1-2 (November 27, 2015): 200–221. http://dx.doi.org/10.1017/rmu.2015.10.
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In 1773, the celebrated enlightenment thinker G.E. Lessing discovered in Wolfenbüttel's Herzog August Library a manuscript which contained a previously unknown Ancient Greek poem. The manuscript identified the author as Archimedes (c.287-212 BCE), and the work became known as the Cattle Problem (henceforth CP). On the surface, its twenty-two couplets capitalise on Homer's depiction of the ‘Cattle of the Sun’ in Book 12 of the Odyssey and its numerical aspect. A description of the related proportions of black, white, brown and dappled herds of cattle, which are then configured geometrically on Sicily, creates a strikingly colourful image. The author's decision to encode a number into the figure of the Cattle of the Sun styles the poem as a response to, and expansion of, Homer's scene. Reading through the work, though, it becomes clear that the mathematics is more complex than that of Homer's Odyssey.
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Hooper, Wyatte. "Archimedes of Syracuse and Sir Isaac Newton: On the Quadrature of a Parabola." Journal of Humanistic Mathematics 11, no. 2 (July 2021): 374–91. http://dx.doi.org/10.5642/jhummath.202102.21.
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Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that Archimedes solved the area problem for parabolas long before the use of algebraic expressions became mainstream. Archimedes used the geometry of the ancient Greeks, which gave him a vastly different perspective. In this paper we provide both Archimedes’ and Newton’s proofs involving the quadrature of the parabola, trying to remain true to their original texts as much as feasible.
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Grande, John Del. "The “Method” of Archimedes." Mathematics Teacher 86, no. 3 (March 1993): 240–43. http://dx.doi.org/10.5951/mt.86.3.0240.
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Many great developments of modern mathematics find their origin in the work done some two thousand years ago by the ancient Greeks. An eminent Harvard geometer, James Lowell Collidge, used to say, “There were giants in the land then.” The greatest of all these giants was the famous Archimedes. Some of his exploits and achievements can be appreciated by students who have had little exposure to physics. Archimedes, with the limited means at his disposal, found the volume of a sphere using a method that gave birth to integral calculus, which was finally perfected by such great mathematicians as Kepler, Leibniz, and Newton. We begin with some famous stories about the accomplishments of Archimedes.
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Moussas, Xenophon. "The Antikythera Mechanism: The oldest mechanical universe in its scientific milieu." Proceedings of the International Astronomical Union 5, S260 (January 2009): 135–48. http://dx.doi.org/10.1017/s1743921311002225.
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AbstractIn this review the oldest known advanced astronomical instrument and dedicated analogue computer is presented, in context. The Antikythera Mechanism a mysterious device, assumed to be ahead of its time, probably made around 150 to 100 BCE, has been found in a 1st century BCE shipwreck near the island of Antikythera in a huge ship full of Greek treasures that were on their way to Rome. The Antikythera Mechanism is a clock-like device made of bronze gears, which looks much more advanced than its contemporary technological achievements. It is based on mathematics attributed to the Hipparchus and possibly carries knowledge and tradition that goes back to Archimedes, who according to ancient texts constructed several automata, including astronomical devices, a mechanical planetarium and a celestial sphere. The Antikythera Mechanism probably had a beautiful and expensive box; looking possibly like a very elaborate miniature Greek Temple, perhaps decorated with golden ornaments, of an elegant Hellenistic style, even perhaps with automatic statuettes, ‘daemons’, functioning as pointers that performed some of its operations. Made out of appropriately tailored trains of gears that enable to perform specialised calculations, the mechanism carries concentric scales and pointers, in one side showing the position of the Sun in the ecliptic and the sky, possibly giving the time, hour of the day or night, like a clock. The position of the Moon and its phase is also shown during the month. On the other side of the Mechanism, having probably the size of a box (main part 32×20×6 cm), are two large spiral scales with two pointers showing the time in two different very long calendars, the first one concerning the eclipses, and lasting 18 years 11 days and 8 hours, the Saros period, repeating the solar and lunar eclipses, and enabling their prediction, and the 19 year cycle of Meton, that is the period the Moon reappears in the same place of the sky, with the same phase. An additional four-year dial shows the year of all Greek Festivities, the so-called ‘games’ (Olympic, Pythian, Isthmian etc). Two additional dials give the Exeligmos, the 54 year and 34 day cycle, which provides a more accurate prediction of eclipses. It is possible that the Mechanism was also equipped with a planetary show display, as three of the planets and their motion (stationary points) are mentioned many times in the manual of the instrument, so it was also a planetarium. From the manual we have hints that the mechanism was probably also an observational instrument, as having instructions concerning a viewfinder and possibly how to orient the viewfinder to pass a sunbeam through it, probably measuring the altitude of the Sun. There are fragmented sentences that probably give instructions on how to move the pointers to set the position of the Sun, the Moon and the planets in their initial places in the ecliptic, on a specific day, or how to measure angular distances between two celestial bodies or their coordinates. This mechanism is definitely not the first one of its kind. The fact that it is accompanied with instructions means that the constructor had in its mind to be used by somebody else and one posits that he made at least another similar instrument.
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Kaplan, Abram. "Analysis and demonstration: Wallis and Newton on mathematical presentation." Notes and Records: the Royal Society Journal of the History of Science 72, no. 4 (October 17, 2018): 447–68. http://dx.doi.org/10.1098/rsnr.2018.0025.
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Emulating the Greek geometers, Newton used synthetic demonstration to present the ground-breaking arguments of the Principia . This paper argues that we can better understand Newton's reasons for using geometry by considering John Wallis's interpretation of synthetic demonstration. Wallis condemned demonstration for failing to explain the mathematical truths it presented. He opposed to it a presentation that combined symbolic analysis with a documented account of discovery. In preferring symbols, Wallis was motivated both by the nascent tradition of symbolic analysis and by contemporary interest in artificial languages. Newton maintained Wallis's characterization of Greek demonstration as adapted to common understanding rather than as strictly elucidating, but he inverted the values Wallis associated with synthesis and analysis. In Newton's new account, synthetic demonstration was preferable precisely because it could address inexpert readers without exposing them to the complications of symbols-based analysis. Newton advanced his arguments on behalf of geometry through portraits of ancient mathematicians: Archimedes and Pythagoras.
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Ludkovsky, S. V. "Line antiderivations over local fields and their applications." International Journal of Mathematics and Mathematical Sciences 2005, no. 2 (2005): 263–309. http://dx.doi.org/10.1155/ijmms.2005.263.
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A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential forms such as the Cauchy-Green, Martinelli-Bochner, Leray, Koppelman, and Koppelman-Leray formulas are investigated. Applications to manifold and operator theories are studied.
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Smith, Russell. "Light Path." Journal of Early Modern Studies 8, no. 2 (2019): 43–79. http://dx.doi.org/10.5840/jems20198212.
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This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of diagrammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. Upon the atomistic conception of light, the optical interpretation of such geometrical principles entailed their mechanical generalisation to local motion; rectilinear motion via the physico-mathematics of reflection and the Mechanica’s parallelogram rule; circular motion via the physico-mathematics of reflection, the Archimedean squaring of the circle and the Mechanica’s extension of the parallelogram rule to centripetal motion. This appeal to the physico-mathematics of reflection forged a realist foundation for the mathematisation of motion. Whereas Aristotle’s physics rested on motions which had their source in the nature of the elements, early modern thinkers such as Harriot, Descartes, and Newton based their new principles of mechanical motion upon selected elements of the mechanics of light motion, projected upon the geometry of the parallelogram rule for rectilinear and, ultimately, circular motion.
Dissertations / Theses on the topic "Archimedes. Mathematics, Greek"
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McKinney, Colin Bryan Powell. "Conjugate diameters: Apollonius of Perga and Eutocius of Ascalon." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/711.
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The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions.
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DeSouza, Chelsea E. "The Greek Method of Exhaustion: Leading the Way to Modern Integration." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338326658.
Full textBooks on the topic "Archimedes. Mathematics, Greek"
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Sonneborn, Henry. Archimedes and the sands of space and time. Larchmont, N.Y: Eagle Press, 1994.
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Archimedes: What did he do besides cry eureka? Washington, D.C.: Mathematical Association of America, 1999.
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Heath, Thomas Little, Sir, 1861-1940, ed, ed. The works of Archimedes. Cambridge: Cambridge University Press, 2010.
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Heath, Thomas Little, Sir, 1861-1940., ed. The works of Archimedes. Mineola, N.Y: Dover Publications, 2002.
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Netz, Reviel. The Archimedes palimpsest. Cambridge: Cambridge University Press, 2011.
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The works of Archimedes: Translated into English, together with Eutocius' commentaries, with commentary, and critical edition of the diagrams. Cambridge: Cambridge University Press, 2004.
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Fichera, Teresa. Archimede: Precursore di secoli e millenni. [Palermo]: A. Lombardi, 2003.
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Gardies, Jean-Louis. L' organisation des mathématiques grecques de Théétète à Archimède. Paris: J. Vrin, 1997.
Find full textBook chapters on the topic "Archimedes. Mathematics, Greek"
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Katz, Victor J., and Karen Hunger Parshall. "The Ancient Greek World." In Taming the Unknown. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691149059.003.0003.
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This chapter focuses on the mathematicians of Ancient Greece; more specifically, on the elements of geometrical algebra present in the works of Euclid and Apollonius, as well as the propositions of perhaps the greatest of the ancient mathematicians—Archimedes. Only fragmentary documentation exists of the actual beginnings of mathematics in Greece, though the concept and necessity of proofs in mathematics might have come about due to the unique climate of argument and debate fostered in Ancient Greek society. In fact, most of these early developments took place in Athens, one of the richest of the Greek states at the time and one where public life was especially lively and discussion particularly vibrant.
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Bleakley, Chris. "Ever-Expanding Circles." In Poems That Solve Puzzles, 25–38. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198853732.003.0002.
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Chapter 2 looks at the development of algorithms for estimating the value of Pi and analysing waveforms. Early estimates for Pi – the ratio of a circle’s circumference to its diameter – were produced in Babylonia. The ancient Greek mathematian, Archimedes, produced improved estimates by means of a clever algorithm which used polygons to approximate the dimensions of a circle. Later, the Chinese mathematician Zu Chongzhi and his son used a similar method to produce an estimate that would stand as the most accurate for 900 years. With the decline of ancient Greece, Persia took on the mantel of leadership in mathematics from the 8th to 11th centuries. Al-Khawrzmi’s texts ultimately propagated knowledge of algorithms to the West. In 18th century France, Joseph Fourier proposed that waveforms could be decomposed into their constituent simple harmonics. The resulting algorithm became the key to signal analysis in today’s electronic communication systems.
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Heilbron, J. L. "3. Domestication in Europe." In The History of Physics: A Very Short Introduction, 48–68. Oxford University Press, 2018. http://dx.doi.org/10.1093/actrade/9780199684120.003.0004.
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Domestication of Greek and Arabic physica and mixed mathematics in the Latin West took c.400 years: from the 12th-century first translations to the 16th-century printing of Archimedes and Ptolemy, and the revitalization of Aristotle’s ancient rivals. With the generation of Copernicus, Galileo, Kepler, and Francis Bacon, physica’s place in the body of knowledge began to slip, although the Aristotelian world picture still hung securely, if awry, in universities and theological seminaries. ‘Domestication in Europe’ explains that the slippage owed much to social factors associated, as in Islamic times, with the needs of newly centralizing states, and with the discovery of new worlds on the Earth and in the heavens.