41. Math 300 Guidelines For Papers ibn Qurra Gerbert d'Aurillac Ibn alHaytham Mohammad al-Biruni Omar Khayyam Nasiral-Din al-Tusi Leonardo of Pisa Qin Jiushao levi ben gerson Nicole Oresme http://cerebro.cs.xu.edu/math/math300/02s/papers.html

Math 300 Great Moments in Mathematics Spring 2002 Guidelines for papers You will prepare two research papers for this course: a biographical paper, due February 21 , that relates the mathematical career of a noted historical figure born before 1700; and a paper due April 18 that performs a critical reading of an original source of importance in the history of mathematics. Your biographical paper should conform to the following guidelines, listed in order of importance, and will be evaluated against them: The paper should present a comprehensively researched discussion of the life history of your chosen mathematician; this person's significant mathematical accomplishments must be thoroughly discussed. (35%) It should be presented in a clear and coherent writing style , using correct spelling, proper pronunciation and good grammar. (25%) It should contain a bibliography with at least three sources including at least three print-published (not Web) sources, it should make appropriate use of direct quotations , and should include in-text citations (as either footnotes or endnotes). (25%)

42. BSHM: Abstracts -- M Mancha, JL, ‘Heuristic reasoning approximation procedures in levi ben gerson’sastronomy’, Archive for history of exact sciences 52 (1998), 1350 An http://www.dcs.warwick.ac.uk/bshm/abstracts/M.html

The British Society for the History of Mathematics HOME About BSHM BSHM Council Join BSHM ... Search BSHM Abstracts A B C D ... Z These listings contain all abstracts that have appeared in BSHM Newsletters up to Newsletter 46. BSHM Abstracts - M Maanen, Jan van, ‘Seventeenth century instruments for drawing conic sections’, Mathematical gazette A consequence of Descartes’ new approach to geometry (1637) was an increased interest in instruments for drawing conic sections. This article sketches the background to this growing interest and describes some of the instruments designed by the Dutch mathematician Van Schooten (1615/6-1660). Maanen, Jan van, ‘The ‘double-meaning’ method for dating mathematical texts’, M. Folkerts and J.P. Hogendijk (eds), Vestigia mathematica , Rodopi 1993, pp. 253-263 A mathematical text may contain numerical data concealing information about the text or its author. Questions of dating and authorship of certain texts can be resolved by decoding such information. Notices of the AMS MacKenzie, Donald, ‘Slaying the Kraken: the sociohistory of a mathematical proof’

43. BSHM: Abstracts -- L found in two Hebrew mathematical treatises. The reconstruction of thequadrature by levi ben gerson (12881344) is wholly original. http://www.dcs.warwick.ac.uk/bshm/abstracts/L.html

The British Society for the History of Mathematics HOME About BSHM BSHM Council Join BSHM ... Search BSHM Abstracts A B C D ... Z These listings contain all abstracts that have appeared in BSHM Newsletters up to Newsletter 46. BSHM Abstracts - L Lacki, Jan, ‘The early axiomatizations of quantum mechanics: Jordan, von Neumann and the continuation of Hilbert’s program’, Archive for history of exact sciences When Hilbert’s axiomatization of physical theories faced the rise of quantum mechanics, the novelty of the mathematics was matched by its lack of physical interpretation. Von Neumann, the most outstanding of Hilbert’s heirs, continued his programme and pushed it to the limit, blending axiomatic rigour with interpretative commitment. Lam Lay Yong, ‘Jiu zhang suanshu (Nine chapters on the mathematical art): an overview’, Archive for history of exact sciences Jiu zhang suanshu is one of the earliest and most important Chinese texts, and is built on a rod-numeral system with conceptually the same decimal place-value structure (albeit with alternating orientation) as our own. It encompassedprobably most of Chinese mathematical knowledge at the beginning of the second century AD, and had a great influence. Archive for history of exact sciences Langermann, Y. Tzvi, ‘Mediaeval hebrew texts on the quadrature of the lune’

44. Rabbi JOSEPH CARLEBACH Das Heilige Land. (The Holy Land). 1909. levi ben gerson Als Mathematiker. (Leviben Gerson mathematician). 1910. Liberales Judentum u. Judische Tradition. http://www.jct.ac.il/judaica/ashkenaz/carlebj.html

Rabbi JOSEPH CARLEBACH (Son of Salomon Carlebach b. Lubeck 1883; deported to Riga, November, 1941; murdered by the Nazis with his wife and three of his children in March, 1942. Educated at Berlin Rabbinical Seminary and Berlin University, where he graduated. Rabbi Joseph Carlebach began his career as a teacher at the Laemel Teachers' Seminary, Jerusalem (1905-1908). During the first World War he was called to Kovno (Lithuania) to serve as educational adviser to the German military government and was entrusted with the task of organising a Jewish Secondary School, becoming its headmaster (1916-1919). Further appointments: Rabbi of Lubeck 1919-1924 Headmaster of " Talmud Thora" Secondary School , Hamburg, 1924-1927 Chief Rabbi of Altona 1927-1937 Chief Rabbi of Hamburg (and the last incumbent of this office before the Nazi holocause) 1937-1941. Rabbi Joseph Carlebach was a great orator and a writer of distinction. Although he would have saved his life by leaving Germany in time, he stayed at his post to comfort and support his brethren. Publications: Das Heilige Land. (The Holy Land). 1909.

45. ThinkQuest Library Of Entries levi ben gerson worked on plane trigonometry, particularly the lawsof sines and cosines. He expanded on levi ben gerson's work. http://library.thinkquest.org/C0110248/trigonometry/history2.htm

Welcome to the ThinkQuest Internet Challenge of Entries The web site you have requested, , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to click here Back to the Previous Page The Site you have Requested ... click here to view this site A ThinkQuest Internet Challenge 2001 Entry Click image for the Site Awards Received Achievement Award Site Desciption Want to learn more about the world of mathematics? Then go forth, and enter the wildest math adventure you've ever been! Learn new math concepts and refresh your knowledge for those you've already known. Understand how the formulae you use were derived from. Or, you can take a step back into the past and read about how mathematics and its concepts originated. Go forth and multiply! Students Teow Lim Raffles Junior College Singapore Vee San Raffles Girls' School (Secondary) Singapore Coaches Poh Kheng Pioneer Junior College Singapore Jee Wah Raffles Girls' School (Sec) Singapore

46. Manuscript Detail His astronomy was derived mainly from alBatt?n? (Albategnius) and levi ben gerson;that is, it was Greek-Arabic astronomy, as it had been gradually corrected http://dewey.library.upenn.edu/sceti/ljs/PageLevel/view.cfm?option=view&ManID=lj

47. Olivier's Opinion #006 If we come back to Rabbi levi ben gerson, I agree with Doron that probably, likemany of us, he was fascinated by the plays of these charming entities that http://web.ccr.jussieu.fr/gmpib/oliver/opinions/Opinion006.html

About Doron Zeilberger's Opinion #36 While I am very sympathetic with Doron Zeilberger's frank and direct way of expressing his ideas and while most of the mathematics he does with his companion Shalosh B. Ekhad has a strong appeal to me, I am far to agree with it on many minor aspects of his opinions. (It is better to have read Doron Zeilberger's text before reading this. See: and for the feedback he received from various people go to As english is not my mother tongue, any comment on the spelling, grammar or style of this text is welcome. Please mail it to me Mathematician=programmer ? No, a Ph. D. in math does not warrant at all the ability to learn programming, even when one has removed those very common psychological blocks DZ refers to. There is a lot to unlearn, there is the whole social implication of a researcher in the academic system. Moreover, we all now math Ph. D. who aren't smart *at all* and especially about mathematics. Introducing this kind of public to even mathematically-minded computer macro-languages like TeX is sometimes worth Hercules' works. Part of the trouble with any academic system is that there are areas, times and circonstances were you can be dubbed "researcher" or "professor" by only being a good schoolboy, no need to be smart or creative about the subject. In fact, the mathematics researchers I know who program well had most of the time a keen interest in programming or computers before they graduated. It makes me appreciate even more the senior mathematicians who are good with these tools or who switched successfully at a late stage in their career.

48. The Hyperbolic Geometry Exhibit alHaytham's proof and Umar Khayyam's resulting criticism. Medievil scholarsVitello (Poland, 1230-1275?); levi ben gerson (South France, 1288-1344); http://www.math.ubc.ca/~robles/hyperbolic/eucl/prll/struggle.html

49. Philosophische Buecherei - Philosophen G Translate this page Georg von Trapezunt (1395-1472/1473). Gerbert von Aurillac (ca. 950-1003). JeanGerson (Johannes Gersonius) (1363-1429). levi ben gerson (Gersonides) (gest. http://buecherei.philo.at/philg.htm

zum Inhaltsverzeichnis (Home) Philosophen Philosophinnen: G ... besondere Empfehlung D ... deutschsprachige Seite ... neu aufgenommene Seite Salomo ben Jehuda ibn Gabirol (Avicebron, Avencebrol) (ca. 1020-1058 od. ca. 1070) D Avicebron (auch Avencebrol; eigentlich Salomon ben Jehuda ibn Gabirol) (BBKL) Hans Georg Gadamer (1900-2002) D Hans Georg Gadamer (Etsuro Makita / Gadamer Homepage) D Philosophie Hans-Georg Gadamer ist tot (Spiegel online, 14.3.2002) Nachruf auf Hans Georg Gadamer The Hans Georg Gadamer Homepage (Kris Murray) D Festakt zu Ehren des 100. Geburtstages von Hans Georg Gadamer (Universität Heidelberg) Nicht nur eine Dokumentation des Festaktes am 11.2.2000, sondern auch eine profunde Einführung in Gadamers Biographie und Werk von Dieter Borchmeyer D Hans-Georg Gadamer: Aus: Wahrheit und Methode (Axel W. Bauer) D Jens Kertscher: Wahrheit mit Methode - Gadamer zum 100. Galenos (Galen) (129-210) Galileo Galilei (1564-1642) The Galileo Project (Rice University) Umfassende Informationen zu Galilei und seiner Zeit Galileo Galilei (The Catholic Encyclopedia) The Art of Renaissance Science: Galileo and Perspective Einführung in Galileos Leben und Wirken Galileo Galilei´s Notes on Motion (Biblioteca Nazionale Centrale, Firenze; Istituto e Museo di Storia della Scienza, Firenze; Max Planck Institut für Wissenschaftsgeschichte, Berlin)

50. Faculty Professor Goldstein has written extensively on medieval Jewish sciencewith special attention to the work of levi ben gerson Gersonides. http://www.pitt.edu/~jsp/faculty.html

FACULTY ASSOCIATED WITH THE JEWISH STUDIES PROGRAM Core faculty Alexander Orbach is associate professor of Modern Jewish History in the Department of Religious Studies and the Department of History at the University of Pittsburgh. He teaches a variety of courses focused on the Jewish experience in the modern age including courses on Russian Jewry, Zionism, the State of Israel, and the Holocaust. Mr. Orbach has written on each of these themes and is currently working on a study of Jewish politics in Tsarist Russia in the period 1900-1914. Alexander Orbach is the Director of the Jewish Studies Program and may be reached at (412) 624-2279 or by e-mail orbach@pitt.edu Adam Shear is instructor in Medieval and Early Modern Judaism in the Department of Religious Studies. Mr. Shear offers courses examining medieval and early modern Jewish life in Europe including an introduction to Jewish-Christian relations. In his written work, Mr. Shear has studied the reception by Jews in the Renaissance and early modern periods of Judah HaLevi's twelfth century work Book of the Kuzari. Mr. Shear may be reached at (412) 624-2280 or by e-mail ashear@pitt.edu

51. History Of Astronomy: Persons (G) astronomy); Links to WWW sources. Gersonides see levi ben gerson (12881344);Getaldic Ghetaldi, Marin Marino (1568-1626) Biographical http://www.astro.uni-bonn.de/~pbrosche/persons/pers_g.html

History of Astronomy Persons History of Astronomy: Persons (G) Deutsche Fassung Gabir ben Aflah: see Jabir ibn Aflah Gabor, Dennis (1900-1979) The Nobel Prize in Physics 1971 Including an autobiography. Very short biographical data and links Gagarin, Yuri Alekseyevich (1934-1968) Very short biography Gale, Walter Frederick (1865-1945) Short biographical data and archival sources Galilei, Galileo Galle, Johann Gottfried (1812-1910) Very short biography Very short biography Very short biography Galois, Evariste (1811-1832) Short biography and references (MacTutor Hist. Math.) Crater Galois (lunar feature) Links to WWW sources Gamow, George (1904-1968) Short biography and references Very short biography (Eric Weisstein's Treasure Trove) Very short biography Ganesa (1507-after 1564) Very short biography Gaposchkin, Cecilia Payne: see Payne-Gaposchkin, Cecilia (1900-1979) Gascoigne, Sidney Charles (b. 1915) Short biographical data Short biography Gascoigne, William (1621-1644) Biographical data and references Gassendi [Gassend; Gassendy], Pierre (1592-1655)

52. History Of Astronomy: What's New At This Site On May 29, 2000 Joseph (18111877) Very short biography. levi ben gerson Gersonides(1288-1344) Very short biography. Levi-Civita, Tullio (1873 http://www.astro.uni-bonn.de/~pbrosche/new/new000529.html

History of Astronomy What's new History of Astronomy: What's new at this site on May 29, 2000 Some URLs have been updated. Welcome / About Site map (complete Table of Contents) updated History of astronomy Persons A Finding List of Obituary Notes of Astronomers (1900 - 1997) , compiled by Hilmar W. Duerbeck and Beatrix Ott, with contributions by Wolfgang R. Dick Contains more than 9000 bibliographical entries for obituaries and short obituary notes. A Abbon de Fleury [Abbo of Fleury; Abbo von Fleury; Albo; Albon Floriacensis] (c. 945-1004) Short biography and references (in German) Adam von Bremen [Adam of Bremen] (?-c.1085) Wrote also on the shape of the Earth. Short biography and references (in German) Very short biography Agrippa, Heinrich Cornelius [Agrippa von Nettesheim] (1486-1535) Short biography and references (in German) Ahmad Khan, Sir Sayyid (1817-1898) Biography and extended bibliography (in German) Ailly, Pierre d' [Aliacensis; Petrus de Allaco] (1350-c.1420) Short biography and references (in German) al-Farabi, Mohammed [Abu Nasr; Abu al-Nasr; Ablufarabius; Avennasar] (c. 870-950)

53. American Philosophical Society Publications Transactions 787. Goldstein, Bernard R., levi ben gerson's Prognosticationfor the Conjunction of 1345, Transactions 80-6. Goldstine, Herman http://www.aps-pub.com/subjects.htm

Your browser does not support script Current Catalogs APS Publications In Print APS Publications, By Subject Proceedings on-line ... Order On Line Publications In Print, By Subject The following inventory includes all available APS publications, arranged by broad subject area, with links (when available) to more complete descriptions. Click here to order on line AfricaHistory Aaboe, Asger et al, Saros Cycle Dates and Related Babylonian Astronomical Texts , Transactions 81-6 Feinberg, Harvey M., Africans and Europeans in West Africa , Transactions 79-7 Lambrecht, Frank L., In the Shade of an Acacia Tree: Memoirs of a Health Officer in Africa, 1945-1959 , Memoir 194 Moser, Gerald M., Changing Africa: The First Literary Generation of Independent Cape Verde , Transactions 82-4 AgricultureHistory Berman, Constance H., Medieval Agriculture, the Southern French Countryside, and the Early Cistercians , Transactions 76-5 Klingelhofer, Eric, Settlement and Land Use in Micheldever Hundred, Hampshire, 700-1100 , Transactions 81-3 American Philosophical Society Bell, Whitfield J., Patriot-Improvers: Members of the American Philosophical Society, Volume Two: 1768

54. CIDICSEF - Centro De Investigación Y Difusión De La Cultura Sefaradí Translate this page Vale también recordar que la empresa del Descubrimiento se nutrió con variosaportes de estudiosos judíos como el astrónomo levi ben gerson (de Provenza http://www.cidicsef.org.ar/home04.html

INFORMATIVO Año 2 N° 4 Actividades Abril/Junio 1999 Actividades Abril/Junio 2000 NUEVA SEDE DEL CIDICSEF PRESENTACIONES EN LA FERIA INTERNACIONAL DEL LIBRO DE BUENOS AIRES EL PROFESOR MORDECHAI ARBELL EN BUENOS AIRES SEMINARIO AÑO 2000 Caracteres de la muestra Aniversario Otros motivos En 1996 se cumplen asimismo dos importantes aniversarios: ORIGENES Y OBJETIVOS MOMENTOS DESTACADOS PUBLICACIONES ACTIVIDADES ... E-MAIL Desarrollado por KehilaNet.com www.kehilanet.com correo@kehilanet.com

55. Biographien - Archiv Levihttp//www.bautz.de/bbkl/l/Levi.shtml levi ben gerson (1288-1345) http//www http://www.biografien-im-netz.de/archiv.php?Letter=L&Page=800

56. Islamic Philosophy: Transmission Into Western Europe several scholars in the south of France, Catalonia and Italy, including Moses ibnTibbon, Shem Tov Ibn Falaquera, levi ben gerson (see Gersonides) and Moses of http://www.muslimphilosophy.com/rep/H056.htm

Islamic philosophy: transmission into Western Europe Early translations: twelfth century Thirteenth-century translations The contribution of Jewish scholars The beginnings of Arabic scholarship 1. Early translations: twelfth century Some seventy works were translated from Arabic by Gerard of Cremona , nicknamed 'the Master' ( dictus magister ), at the cathedral of Toledo. These included Aristotle's Posterior Analytics Physics On Generation and Corruption and Meteorology I-III (see Aristotle ), as well as four short tracts on natural science by Alexander of Aphrodisias . To these originally Greek works, Gerard added four philosophical letters of al-Kindi , a letter on proof by the Ikhwan al-Safa' and al-Farabi's Kitab ihsa' al-'ulum (On the Classification of the Sciences) (see al-Farabi Also at this time, the importance of the al-Shifa' (Healing) of Avicenna (Ibn Sina) was brought to the notice of Archbishop John of Toledo by a Jewish scholar called 'Avendauth' (perhaps the same as Abraham Ibn Daud , the author of al-'Aqida al-rafi'a (The Exalted Faith) ). Portions of the text, including those on universals, physics (in part), the soul and metaphysics, were translated by Avendauth, Dominicus Gundissalinus (an archdeacon in the cathedral

57. Kleine Publicaties Nr. 5 - Titel Translate this page Tabulae de mansionibus lunae. - Tractatus astronomici II. - levi ben gerson Leonisde Bagnolo Tabulae astronomicae. - Ioannae d'Estutoville Horoscopium. http://bc.leidenuniv.nl/whs/catalogi/catcomp1/09.htm

Westerse handschriften IX CODICES SCALIGERANI (SCA) Conf. P.C. Molhuysen, Bibliothecae Universitatis Leidensis Codices Manuscripti, Pars II, Codices Scaligerani praeter orientales (1910). Tabula SCA 1 Adelardi Bathensis Reguli abaci. SCA 2 Eusebii Pamphili Historia ecclesiastica ex recensione Rufini. - Didymus Alexandrinus de Spiritu sancto ex versione Hieronymi. - Series episcoporum. - Henrici Huntindonensis Historiae. SCA 3 Pappi Alexandrini Collectionis lbb. II-VIII. SCA 4 Apollonii Pergaei Conica. SCA 5 Procopii Historiarum libri VIII. SCA 6 Agrimensorum Romanorum fragmenta. SCA 7 Georgii Chrysococcae Expositio in Syntaxin Persarum. SCA 8 Tabulae astronomicae. SCA 9 Procopius de Aedificiis Iustiniani. SCA 10 I.I. Scaligeri Excerpta ex scriptoribus graecis historicis et chronographicis. SCA 11 I.I. Scaligeri Index in I. Gruteri Inscriptiones antiquas. SCA 12 Heronis Alexandrini Opera geometrica et stereometrica. - Michael Psellus de Corporibus coelestibus eorumque motibus.

58. The Newberry Library: Smith Center: Mapline 84/85 Feature of Aragon. His work in turn was based on the observations and tablesof levi ben gerson and Abraham bar Hiyya. The Jewish Catalan http://www.newberry.org/nl/smith/mapline84feature.html

Issue 84/85, Fall 1998 ASTROLABES AND MAPS Some time during the Middle Ages people began to make measured maps designed for practical use in navigation. The oldest surviving example is the Pisan chart, now in the Bibliotheque Nationale in Paris. It dates from the late 13th century, but there is no reason to believe that it was the first of its kind. Unlike the mappamundi, which co-existed with the portolan charts for a long time, the new maps emphasized purely geographical features with little of the historical, religious, and fabulous information so prominently displayed on the mappamundi. Among the many questions raised by the portolan charts, one of the most vexing is that of their construction. What kind of instruments were used to make their meticulously drawn coastlines? No written evidence survives from the earliest period of their existence. However, we do know that two tools, useful for making measured maps, were introduced into Europe in the Middle Ages. These were the astrolabes, which appeared in the tenth century, and the compass in the twelfth. The possible use of the compass in making the charts, which are marked by compass roses and rhumb lines, has been widely discussed, though no firm conclusions have been drawn. The use of the astrolabe has been treated very little. The next oldest dates from the 14th century, though it is possible that Western Europeans were using astrolabes of Islamic manufacture imported through Spain.

59. A History Of Mediaeval Jewish Philosophy of the main arguments and teachings of Moses Maimonides, Isaac Israeli, Judah Halevi,Abraham Ibn Daud, Hillel ben Samuel, levi ben gerson, Joseph Albo, and http://store.doverpublications.com/0486422372.html

American History, American...... American Indians Anthropology, Folklore, My...... Antiques Architecture Art Bridge and Other Card Game...... Chess Children Cookbooks, Nutrition Crafts Detective Stories, Science...... Ethnic Interest Gift Certificates Gift Ideas History, Political Science...... Holidays Humor Languages And Linguistics Literature Magic, Legerdemain Military History, Weapons ...... Music Nature Performing Arts, Drama, Fi...... Philosophy And Religion Photography Puzzles, Amusement, Recrea...... Reference Science and Mathematics Sports, Out-of-door Activi...... Stationery, Gift Sets Summer Fun Shop Travel and Adventure Women's Studies By Subject Philosophy And Religion Western Philosophy and Religion A History of Mediaeval Jewish Philosophy Isaac Husik Our Price Availability: In Stock (Usually ships in 24 to 48 hours) Format: Book ISBN: Page Count: Dimensions: 5 3/8 x 8 1/2 In this enlightening study, a noted scholar elucidates the distinguishing characteristics of the works of several Jewish thinkers of the Middle Ages. In addition to summaries of the main arguments and teachings of Moses Maimonides, Isaac Israeli, Judah Halevi, Abraham Ibn Daud, Hillel ben Samuel, Levi ben Gerson, Joseph Albo, and many others, the author offers insightful analyses and commentary. Of particular value to beginners, this volume is also an ever-relevant resource for many issues of scholarly debate. Buy Now!

60. MathTrek: Zeroing In On Catalan's Conjecture, Science News Online, Dec. 2, 2000 Around 1320, levi ben gerson (1288–1344) proved that if powers of 2 and 3 areconsecutive, they must be 8 and 9 (see Medieval Harmony, January 23, 1999). http://www.sciencenews.org/20001202/mathtrek.asp

Home page. Math Trek Zeroing in on Catalan's Conjecture Food for Thought Soy Land, Soy Land Science Safari Undersea Mountain Descent TimeLine 70 Years Ago in Science News Week of Dec. 2, 2000; Vol. 158, No. 23 Zeroing In on Catalan's Conjecture Fermat's last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat's scribbled conjecture, for instance. Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to a solution of Catalan's conjecture, another venerable problem involving relationships among whole numbers. He presents his result in a paper to be published in the Journal of Number Theory "This is a very important contribution," says mathematician Andrew Granville of the University of Georgia in Athens. Mihailescu's work probably puts the resolution of Catalan's conjecture into the foreseeable future, he notes. Named for Belgian mathematician Eugène Charles Catalan, the conjecture concerns powers of whole numbers. For example, the sequence of all squares and cubes of whole numbers begins with the integers 4, 8, 9, 16, 25, 27, and 36. In this sequence, 8 (the cube of 2) and 9 (the square of 3) are not only powers but also consecutive whole numbers. In 1844, Catalan asserted that, among all powers of whole numbers, the only pair of consecutive numbers that arises is 8 and 9. His conjecture amounts to a search for whole-number solutions to the equation

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