1. Levi Ben Gerson - Mathematics And The Liberal Arts levi ben gerson Mathematics and the Liberal Arts. To expand search, seeJewishMedieval. Laterally related topic Rabbi ben Ezra. http://math.truman.edu/~thammond/history/LeviBenGerson.html

Levi ben Gerson - Mathematics and the Liberal Arts To expand search, see JewishMedieval . Laterally related topic: Rabbi ben Ezra The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Biggs, N. L. The roots of combinatorics. Historia Math. (1) As the author explains, the most ancient problem connected with combinatorics may be the house-cat-mice-wheat problem of the Rhind Papyrus (Problem 79), which occurs in a similar form in a problem of Fibonacci's Liber Abaci and in an English nursery rhyme. All are concerned with successive powers of 7. (2) The first occurrence of combinatorics per se may be in the 64 hexagrams of the

2. Levi Biographical article with links and bibliography, from the MacTutor History of Mathematics. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Levi.html

Levi ben Gerson Born: 1288 in Bagnols, Gard, France Died: Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Levi ben Gerson wrote Book of Numbers in 1321 dealing with arithmetical operations, including extraction of roots. Also, in 1342, he wrote On Sines, Chords and Arcs which examined trigonometry, in particular proving the sine theorem for plane triangles and giving 5 figure sine tables. One year later, at the request of the bishop of Meaux, he wrote The Harmony of Numbers which is a commentary on the first 5 books of Euclid He also invented Jacob's staff, an instrument to measure the angular distance between celestial objects. It is described as consisting ... of a staff of feet long and about one inch wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars. Levi observed a solar eclipse in 1337. After he had observed this event he proposed a new theory of the sun which he proceeded to test by further observations.

3. Levi Biography of levi ben gerson (12881344) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Comments On Levi Ben Gerson Comments on levi ben gerson. Comments http://math.truman.edu/cgi-bin/thammond/makebibcomment.pl?code=General&cat=LeviB

5. Linda_ellanna Astronomy Of Levi Ben Gerson 1288 - 1344 Studies In astronomy of levi ben gerson 1288 1344 studies in the history of mathematics physical science vol 11, but we have more than only Astronomy of http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Levi Biography of levi ben gerson (12881344) levi ben gerson wrote Book of Numbersin 1321 dealing with arithmetical operations, including extraction of http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Levi.html

Levi ben Gerson Born: 1288 in Bagnols, Gard, France Died: Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Levi ben Gerson wrote Book of Numbers in 1321 dealing with arithmetical operations, including extraction of roots. Also, in 1342, he wrote On Sines, Chords and Arcs which examined trigonometry, in particular proving the sine theorem for plane triangles and giving 5 figure sine tables. One year later, at the request of the bishop of Meaux, he wrote The Harmony of Numbers which is a commentary on the first 5 books of Euclid He also invented Jacob's staff, an instrument to measure the angular distance between celestial objects. It is described as consisting ... of a staff of feet long and about one inch wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars. Levi observed a solar eclipse in 1337. After he had observed this event he proposed a new theory of the sun which he proceeded to test by further observations.

7. The Astronomical Tables Of Levi Ben Gerson Infos Bernard R Goldstein The Astronomical Tables of levi ben gerson Book by Bernard R Goldstein ; review, summary, details http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. References For Levi References for the biography of levi ben gerson. BR Goldstein, Levi benGerson s analysis of precession, Journal for the History of Astronomy 6 (1975), http://www-groups.dcs.st-and.ac.uk/~history/Printref/Levi.html

References for Levi ben Gerson Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles: P H Espenshade, A text on trigonometry by Levi ben Gerson (1288-1344), Math. Teacher B R Goldstein, Preliminary Remarks on Levi ben Gerson's Contributions to Astronomy, Proc. Israel Acad. Sci. Humanities B R Goldstein, Levi ben Gerson's analysis of precession, Journal for the History of Astronomy B R Goldstein, Levi ben Gerson : On instrumental errors and the transversal scale, Journal for the History of Astronomy B R Goldstein, Astronomical and astrological themes in the philosophical works of Levi ben Gerson, Archives internationales d'histoire des sciences B R Goldstein, The physical astronomy of Levi ben Gerson, Perspect. Sci. B R Goldstein, Levi ben Gerson's theory of planetary distances, Centaurus B R Goldstein, The astronomy of Levi ben Gerson (1288-1344), Studies in the History of Mathematics and Physical Sciences (New York-Berlin, 1985). B R Goldstein, Levi ben Gerson's preliminary lunar model, Centaurus B R Goldstein, Levi ben Gerson's lunar model

9. Europe - Mathematics And The Liberal Arts Varahamihira, Brahmagupta, Bhaskara, The Islamic World, The Jewish Tradition, Rabbi ben Ezra, levi ben gerson, Magic Squares, Manuel http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Encyclopedia Of Astronomy And Astrophysics » Levi Ben Gerson (1288–1344) levi ben gerson (1288–1344). DOI 10.1888/0333750888/3812; Published November 2000.Icon Full text (PDF, 16K). Article summary http://eaa.iop.org/index.cfm?action=summary&doc=eaa/3812@eaa-xml

11. West Sea Co. Evolution Of The Sextant It was first described in 1342 by a Jewish scholar named levi ben gerson. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. Bibliography “R. levi ben gerson A Bibliographical Essay,” Studies in Bibliography and “levi ben gerson,” in Allgemeine Enzyklopaedie der Wissenschaften und Kuenste http://hcc.haifa.ac.il/Chairs/Wolfson/gersonideana/Bibliography5.htm

Gersonideana Bilbiographia V. Bibliography 1. Blumenkranz, Bernhard. Auteurs juifs en France m?di?vale: leur ?uvre imprim?e (Paris: Edouard Privat, 1975):65-69. Gersonides’ printed works. 2. Chazelas, Genevi?ve and Gilbert Dahan, “Bibliographie gersonidienne,” G. Dahan (ed.), Gersonide en son temps (Louvain: Peeters, 1991): 369-74. 3. Davidson, Israel. Parody in Jewish Literature (New York: Columbia University Press, 1907; 2nd. ed., 1966): 19, 23-28,115-34. On Gersonides’ two Purim parodies, Sefer ha-Baqbuq ha-Navi and Megillat Setarim. Touati (1973), p. 59f. mentions Megillat Setarim but is silent about Ha-Baqbuq ha-Navi. 4. Dienstag, Israel J. “The Relationship of Gersonides to the Philosophy of Maimonides An Annotated Bibliography,” Da`at 23 (1989): 5-13 (Hebrew). Partially annotated list of sixty-eight studies in which Gersonides and Maimonides are both mentioned. 5. Joel, Manuel. “Notizen zu Lewi ben Gerson,” MGWJ 9 Gersonides’ relation to Gershom ben Solomon, author of Sha`ar ha-Shamayim; the identity of the town of Ezov; a reference to the Orsini family in Gersonides; an implicit criticism of flagellation; Gersonides’ rejection of the heliocentric hypothesis. Moritz Steinschneider critically commented on this article in Hebraeishe Bibliographie 3 [no.16] (July-August, 1860), p. 71 (item 999).

13. Your Free Levi Ben Gerson Art History Online Reference And Guide Your Free levi ben gerson Art History Online Reference and Guide http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Wars Of The Lord - English translated by Bernard R. Goldstein in The Astronomy of levi ben gerson on levi ben gerson s Cosmology, David Novak and Norbert Samuelson (eds. http://hcc.haifa.ac.il/Chairs/Wolfson/gersonideana/wars_of_the_lord-english.htm

Gersonideana Bilbiographia ii. Wars of the Lord a. English 1. Treatise I, translated by Seymour Feldman in The Wars of the Lord, Vol. 1 (Philadelphia: Jewish Publication Society, 1984). Treatises II-IV, translated by Seymour Feldman in The Wars of the Lord, Vol. 2 (Philadelphia: Jewish Publication Society, 1987). 2. Treatise II, translated by David W. Silverman in "The Problem of Prophecy in Gersonides," Ph. D. Dissertation, Columbia University, 1974. 3. Treatise III, translated by Norbert M. Samuelson in Gersonides on God's Knowledge (Toronto: Pontifical Institute of Medieval Studies, 1977). 4. Treatise IV, translated by J. David Bleich in Providence in the Philosophy of Gersonides (New York, Yeshiva University Press, 1973). 5. Treatise V, Part 1, chapter 4, sections 1-4 translated from the Latin (De sinibus, chordis, et arcubus ) by Pamela Espenshade in " A Text on Trigonometry by Levi ben Gerson," The Mathematics Teacher 60 (1967): 628-37. 6. Treatise V, part i, chapters 1-20, translated by Bernard R. Goldstein in The Astronomy of Levi Ben Gerson (1288-1344): A Critical Edition of Chapters 1-20 with Translation and Commentary (New York: Springer-Verlag, 1985).

15. NodeWorks - Encyclopedia Levi Ben Gerson levi ben gerson http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. The Astronomy Of Levi Ben Gerson (1288-1344) (Goldstein)-Springer Mathematics (g I found The Astronomy of levi ben gerson (12881344) by Goldstein, BR atspringeronline.com and thought you would be interested in this title. http://www.springeronline.com/sgw/cda/frontpage/0,11855,5-10042-72-31221500-0,00

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17. LEVI BEN GERSON Translate this page levi ben gerson, auch Gersonides oder Rabbi L. ben Gerson (= RaLBaG), teils auchMeister Leo de Bagnols (= Magister Leo Hebraeus), jüdischer Philosoph, http://www.bautz.de/bbkl/l/Levi_b_g.shtml

18. Mathematics 245 Assignments It Is A Well-kept Secret That Doing levi ben gerson, from the Maasei Hoshev (Art of the Calculator) Does Leviben Gerson prove his theorems using the Principle of Mathematical Induction? http://newton.uor.edu/FacultyFolder/Beery/M245Assignments.html

Mathematics 245 Assignments It is a well-kept secret that doing mathematics really is fun-at least for mathematicians-and I am amazed at how often we use the word "beautiful" to describe work that satisfies us. I am reminded of a remark by a mathematician . . . who was talking with some anthropologists about early human experiments with fire. One anthropologist suggested that these humans were motivated by a desire for better cooking; another thought they were after a dependable source of heat. [The mathematician] said he believed fire came under human control because of their fascination with the flame. I believe that the best mathematicians are fascinated by the flame, and that this is a good thing . . . [b]ecause, fortunately for society, their fascination has, in the end, provided the good cooking and reliable heat we all need. - Phillip A. Griffiths, Director of Institute for Advanced Study Tuesday, Feb. 11 Read: Burton, Section 1.3, Early Number Theory (pages 13-15) Ore, Counting and Recording of Numbers (handout) Various authors on earliest evidences of counting; Egyptian, Mesopotamian, and Chinese mathematics, especially origins of Pythagorean Theorem (handout)

19. Math History - Middle Ages 1321, levi ben gerson (sometimes known as Gersonides) writes Book of Numbers dealing 1343, levi ben gerson (Gersonides) writes De harmonicis numeris http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MmiddleAges.htm

Math History Timeline Middle Ages 500 - 1400 A.D. Math History Prehistory and Ancient Times Middle Ages Renaissance Reformation ... 20th Century ... non-Math History Prehistory and Ancient Times Middle Ages Renaissance Reformation ... External Resources Varahamihira produces Pancasiddhantika (The Five Astronomical Canons). He makes important contributions to trigonometry. Decimal notation is used for numbers in India. This is the system on which our current notation is based. Brahmagupta writes Brahmasphutasiddanta (The Opening of the Universe), a work on astronomy; on mathematics. He uses zero and negative numbers, gives methods to solve quadratic equations, sum series, and compute square roots. About 700 Mathematicians in the Mayan civilization introduce a symbol for zero into their number system. About 810 Al-Khwarizmi writes important works on arithmetic, algebra, geography, and astronomy. In particular Hisab al-jabr w'al-muqabala (Calculation by Completion and Balancing)

20. MAA Student Paper Session I Spring 99 levi ben gerson is credited with inventing the Jacob Staff, I have constructeda Jacob Staff based upon levi ben gerson s method of construction. http://faculty.ssu.edu/~kmshanno/maa/student/session1.htm

MATHEMATICAL ASSOCIATION OF AMERICA Maryland-District of Columbia-Virginia Section MAA Student Chapters Conference Student Paper Session I 8:50 a.m. - 9:10a.m. Saturday April 10, 1999 Room: B31: Speaker: Devika Chawla, Georgetown University Title: The Secure Sockets Layer (SSL) Protocol Abstract: The talk will describe the key components of the SSL protocol. This protocol guarantees privacy by means of symmetric encryption of data, peer authentication using asymmetric cryptography, and connection reliability via message integrity checks. Speaker: Paul Dosart, James Madison University Title: Modeling Suspension Bridge Oscillations Using a Picard Iteration Technique . Abstract: A modified Picard iteration technique is used to solve equations involved with torsional oscillations in suspension bridges. Oscillations are modeled for different situations, and the different methods of solving these equations are discussed. The Picard iteration technique's accuracy is evaluated in comparison with other traditional methods. Room B34 Speaker: Melanie Hancock, St. Mary's College

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