Len Berggren

Journal Articles and Conference Proceedings

"Tenth-Century Mathematics Through the Eyes of Abu Sahl al-Kuhi" in The Enterprise of Science in Islam: New Perspectives (ed. Jan P. Hogendijk and Abelhamid I. Sabra). Cambridge, Mass. and London: The MIT Press, 2003, pp. 177 - 196.

"From Euclid to Apollonius: Al-Kuhi's Lemmas to the Conics" (jointly with Glen Van Brummelen). Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, Vol. 15, 2003, pp. 165 - 174.

"Ptolemy's Maps as an Introduction to Ancient Science" in Science and Mathematics in Ancient Greek Culture. (C.J. Tuplin and T.E. Rihll, ed's). Oxford, New York, etc.: Oxford University Press (2002), pp. 36 - 55.

"Some Ancient and Medieval Approximations to Irrational Numbers and Their Transmission" in From China to Paris: 2000 Years Transmission of Mathematical Ideas. (Boethius Texte Abh. Gesch. Math. Wiss). Stuttgart:Franz Steiner Verlag (2002), pp. 31 - 44.

"Medieval Arithmetic: Arabic Texts and European Motivations" in Word, Image, and Number: Communication in the Middle Ages (ed. John J. Contreni and Santa Casciani). Sismel - Edizioni del Galluzzo (2002), pp. 351 - 365 + 8 pp. of plates.

'The Transmission of Greek Geometry to Medieval Islam.' Cubo Matemématica Educacional, Vol. 4, No. 2, June 2002, pp. 1 - 13.

Abu Sahl al-Kuhi's "On Drawing two lines from a given point to a given line by the method of analysis." (jointly with Glen Van Brummelen) Suhayl, Vol. 2 (2001), pp. 161 - 198.

Abu Sahl al-Kuhi on the Distance to the Shooting Stars (jointly with Glen Van Brummelen). Journal for the History of Astronomy xxxii (2001), 137 - 151.

Abu Sahl al-Kuhi on Rising Times (jointly with Glen Van Brummelen). SCIAMVS, Vol. 2, April 2001, pp. 31 - 46.

Abu Sahl al-Kuhi's On the Ratio of the Segments of a Single Line That Falls on Three Lines, (jointly with Glen Van Brummelen). Suhayl , Vol. I, 2000, pp. 1 - 56.

Abu Sahl al-Kuhi on "Two Geometrical Questions." (jointly with G. Van Brummelen). Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften. Vol. 13 (1999-2000), pp. 165 - 187.

"Numbers at Work in Medieval Islam." Journal for the History of Arabic Science. Aleppo, Syria: Institute for the History of Arabic Science, 1998.

Berggren, J.L., "Mathematics and her Sisters in Medieval Islam: A Selective Review of Work Done from 1985 - 1995", Historia Mathematica, vol. 24, Dec. 1997, pp. 407-440

Berggren, J. L., "Al-Kuhi's `Filling a Lacuna in Book II of Archimedes' On the Sphere and Cylinder in the Version of Nasir al-Din al-Tusi", Centaurus, 38 (1996), 140- 207.

'Didactical and Other Remarks on Some Theorems of Archimedes (jointly with A. Aaboe), Centaurus, XXI (1996), 1 - 23.

Berggren, J.L., "Abu Sahl Al-Kuhi's Treatise on the Construction of the Astrolabe with Proof: Text, Translation and Commentary." Physis, Vol. XXXI, Nuova Serie Fasc. 1, (1994) 142-252.

Berggren, J.L., "Historical Reflections of Scientific Knowlege: The Case of Medieval Islam" published in Knowledge Across Cultures, Universities East and West. Hubei Education Press & OISE Press, 139-153 (1994). Reprinted in Knowledge Across Cultures: A Contribution to Dialogue Among Civilizations (Ruth Hayhoe and Julia Pan, ed's.) by Comparative Education Research Centre: The University of Hong Kong (2001), 127 - 138.

Berggren, J.L., Thomas, R.S.D., "Mathematical Astronomy in the Fourth Century B.C. as found in Euclid's Phaenomena", Physis., Vol XXIX (1992), 7-33.

Berggren, J.L., "Habash's Analemma for Representing Azimuth Circles on the Astrolabe, Zeitschrift fur Geschichte der Arabisch-Islamischen Wissenschaften, (1992) 23-30.

Berggren, J.L., "Islamic Acquisition of Foreign Sciences: A Cultural Perspective" Amer.J. of Isl. Soc. Sci. 9, 3 (Fall, 1992), 310-324. Reprinted, with minor changes, in Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-modern Science held at the University of Oklahoma (F. J. Ragep and S.P. Ragep, ed's.) Leiden: E.J. Brill, 1996, pp. 263-283.

Berggren, J.L., "Ptolemy's Maps of Earth and the Heavens: A New Interpretation", Archive for History of Exact Sciences, Vol. 43, 2, 1991, 133-144.

Berggren, J.L., "The Relation of Greek Spherics to Early Greek Astronomy" in Science and Philosophy in Ancient Greece (ed. Alan C. Bowen), Garland Publishing, 1991, 227-248.

Berggren, J.L., "Greek and Islamic Elements in Arabic Mathematics" in a special number of Apeiron ("Peri ta mathemata", ed.Ian Mueller) 24, No. 4 (1991), 701-23.

Berggren, J.L., "Medieval Islamic Methods for Drawing Azimuth Circles on the Astrolabe", Centaurus, (1991) Vol. 34: 309-344.

Berggren, J.L., "Geometric Methods in Medieval Islam: The Case of the Azimuth Circles", Proceedings of the Second Maghrib Colloq. for History of Arabic Mathematics, Algeria (1991).

Berggren, J.L. "Innovation and Tradition in Sharaf-al-Din al-Tusi's Al-Mucadalat", Journal of the American Oriental Society, 110, 2, 1990, 304-309.

Berggren, J.L., "Proof and Pedagogy in Medieval Islamic Mathematics". Interchange (A special issue titled Creativity, Thought and Mathematical Proof (Gila Hanna and Ian Winchester, eds.) 21, 1, Spring 1990, 36-48.

Berggren, J.L., A study of the spherical trigonometry in Kushyar ibn Labban's al-Zij al-Jami", in From Deferent to Equant (ed. D. King and G. Saliba). New York Acad. of Sciences, 1987, 15-34.

Berggren, J.L., Mathematical Methods in Ancient Science: Spherics, in History in Mathematics Education, ed. Ivor Grattan-Guinness, Belin, Paris 1987, pp. 14-32.

Berggren, J.L., Mathematical Methods in Ancient Science: Astronomy" in History in Mathematics Education, ed. Ivor Grattan-Guinness, Belin, Paris 1987, pp. 33-49.

Berggren, J.L., "Archimedes Among the Ottomans" in From Ancient Omens to Statistical Mechanics. Munksgaard, Copenhagen, 1987, pp. 101-109.

Berggren, J.L., "The Origin of al-Biruni's Method of the Zijes in the Theory of Sundials". Centaurus XXVIII, Vol. 28, (1985) 1-16.

Berggren, J.L., "History of Mathematics in the Islamic World: The Present State of the Art". Bull. Middle East Studies Assoc., Vol. 19, No. 1, (1985) 9-33.

Berggren, J.L., "Greek Mathematics: An annotated Bibliography", as a chapter in History of Mathematics from Antiquity to the Present: A Selective Bibliography (ed. J.W. Dauben). Garfield: U.S.A. (1984), pp. 25-64.

Berggren, J.L., "History of Greek Mathematics: A Survey of Recent Research", Historia Mathematica, Vol. 11 (1984) 394-410.

"Episodes from the History of Arabic Mathematics: Spherics", Vector, Vol. 24, No. 2, 26-34 (1983).

Berggren, J.L., "The Correspondence of Abu Sahl al-Kuhi and Abu Ishaq al-Sabi: A translation with commentaries". Journal for History of Arabic Science, Vol. 7, Nos. 1 & 2 (1983) 39-123.

Berggren, J.L., "Al-Biruni on Plane Maps of the Sphere", J. for History of Arabic Science, Vol. 6, 47-96 (1982).

Berggren, J.L., "Al-Sijzi on the Transversal Figure", J. for History of Arabic Science, Vol. 5, Nos. 1 and 2, 23-36 (1981).

Berggren, J.L., "An Anonymous Treatise on the Regular Nonagon", J. for History of Arabic Science, Vol. V, Nos. 1 and 2, 37-41 (1981).

Berggren, J.L., "On al-Biruni's 'Method of the Zijes' for the Qibla," Proceedings of the XVth International Congress of the History of Science, Bucharest, Romania 237-245 (1981).

Berggren, J.L., "Medieval Analemmas for Determining the Qibla", J. for History of Arabic Science, IV, 69-80 (1980).

Berggren, J.L., The Barycentric Theorems of Abu Sahl al-Kuhi. Proceedings of Second International Symposium for History of Arabic Science, Aleppo, April 1979.

Berggren, J.L., A coincidence of Pappos' Book VIII with al-Biruni's Tahdid. Journal of History of Arabic Science, Vol. II, No. 1, 137-142 (May 1978).

Berggren, J.L., A Lacuna in Archimedes' Sphere and Cylinder Book I, Historia Mathematica, 4, 1-5 (1977).

Berggren, J.L., "Spurious Theorems in Archimedes' Equilibrium of Planes Book I", Archive for History of Exact Sciences, Vol. 16, 2, 87-103 (1976).

Berggren, J.L., Some lessons for teachers from the history of Mathematics, Vector, 11-21 (1974).

Berggren, J.L., Polygons and Puzzles. Connecticut Mathematics Journal, Vol. 6, no. 2, 3-7 (May 1974).

Alspach, B.R., and Berggren, J.L., On the determination of the maximum order of the group of a tournament. Can. Math. Bull., Vol. 16, no. 1, 11-14 (1973).

Berggren, J.L., An algebraic characterization of finite symmetric tournaments. Bull. Australian Math. Soc., Vol. 6, 53-59 (1972).

Berggren, J.L., An algebraic characterization of symmetric graphs with a prime number of vertices. Bull. Australian Math. Soc., Vol. 7, no. 1, 131-134 (1972).

Berggren, J.L., Some remarks on Napier's conception of logarithms. Vector, Journal of the B.C. Mathematics Teachers, Vol. 14, no. 1, 12-14 (1972).

Berggren, J.L., Solvable and supersolvable groups in which every element is conjugate to its inverse. Pac. J. Math., Vol. 37, no. 1, 21-28 (1971).

Berggren, J.L., Finite groups in which every element is conjugate to its inverse. Pac. J. Math., Vol. 28, no. 2, 289-293 (1969).

Berggren, J.L. and Catton, W., Intervening opportunities and national park visitation rates. Pac. Soc. Review, Vol. 7, no. 2, 66-73 (1964).

Books

Pi: A Source Book (3rd Edition - jointly with J. and P. Borwein). New York: Springer-Verlag, 2004.

Ptolemy's Geography: An annotated translation of the theoretical chapters (jointly with Alexander Jones). Princeton and Oxford: Princeton University Press (Hardcover edition: 2000; softcover edition 2002.)

Euclid's Phaenomena: A Translation and Study of a Hellenistic Work in Spherical Astronomy. (jointly with R.S.D. Thomas), in the series Sources and Studies in Hellenistic Exact Sciences New York: Garland Publishing, 1996.

From Ancient Omens to Statistical Mechanics (edited jointly with B.R. Goldstein). Munksgaard: Copenhagen, 1987.

Episodes in the Mathematics of Medieval Islam. Berlin, Heidelberg, New York: Springer-Verlag, 1986 (softcover ed'n 2003).

Invited Articles

J. L. Berggren and Jan P. Hogendijk, "The Fragments of Abu Sahl al-Kuhi's Lost Geometrical Works in the Writings of al-Sijzi" in Studies in the History of the Exact Sciences in Honour of David Pingree (C. Burnett, Jan P. Hogendijk, Kim Plofker and Michio Yano, ed's). Leiden-Boston: Brill (2004), pp. 609 - 665.

Essay on "Islamic Mathematics" in Supplement to the Dictionary of the Middle Ages (Sponsored by the American Council of Learned Societies and published in 2004 by Charles Scribner's Sons.

"Le sfere celesti e le origini della trigonometria" in Storia della scienza, editor-in-chief Sandro Petruccioli, Roma, Istituto della Encicplopedia Italiana, v. I, 2001, pages 840 - 848.

Article "The Mathematical Sciences" in History of Civilizations of Central Asia Vol. 4 (The Age of Achievement: A.D. 750 to the End of the Fifteenth Century), Part Two (The Achievements) (ed. C.E. Bosworth and the late M.S. Asimov.) Paris: UNESCO, pp. 182 - 193.

"Scholarly work of E.S. Kennedy" in From Deferent to Equant: Essays in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy pp. xxv - xxix, (ed. D. King and G. Saliba) New York Academy of Sciences (1987).

"Life and Work of Asger Aaboe" in From Ancient Omens to Statistical Mechanics, pp. xi-xv, Munksgaard, Copenhagen (1987).

"Mathematics in Medieval Islam", Hikmat, Vol. II, No. 5 (Mar. 1985) pp. 12-16.

"Nine Sages of Medieval Islam", Hikmat, Vol. I, No. 9 (Oct. 1979), pp. 13-16, p. 35.

Reviews to 1996

Review of W. S. Anglin. Mathematics: A Concise History and Philosophy. Philosophia Mathematica (Series III) 4(1996) No. 2, pp. 196-198.

Essay review of The Optics of Ibn al-Haytham: Books I-III On Direct Vision. (Parts I and II: Translated with Introduction and Commentary by A. I. Sabra.) in Physis xxxii N.S. Fasc. 1(1995), 143-153.

Review of J. B. Harley and David Woodward, editors. The History of Cartography. Vol. 2, Book 1, Cartography in the Traditional Islamic and South Asian Societies. Assisted by Joseph E. Schwartzberg et al. Chicago: University of Chicago Press. 1992. p xxiv, 579; 395 plates. American Historical Review, October 1994, pp. 1286-87.

Review of G. Toomer, The The Arabic text of of Apollonius's Conics Books V - VII: The Arabic Translation of the Lost Greek Original in the version of the Banu Musa, Mathematical Reviews, Review No. 92e:01017.

Review of W.R. Knorr's Textual Studies in Ancient and Medieval Geometry, Ancient Philosophy, pp.522-528, Vol. XII No.2, 1992.

Review of Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages (E. Grant and J.E. Murdoch, eds.), Cambridge U.Press 1987 in Journal of Interdisciplinary History, Vol. 20, No. 1 (Summer, 1989), pp. 132 - 135.

Review of R. Rashed Diophante: Les Arithmetiques (Vols. III and V). Paris: Les Belles Lettres, 1984, in Historia Mathematica., 14 (1987), 386-389.

Review of Entre arithmetique et algebra: Recherches sur l'histoire des mathematiques arabes by Rishda Rashed. Middle East Journal 41 (2) 1987.

Review of O. Neugebauer's Astronomy and History: Selected Essays in Ancient Philosophy 6, 202-204 (1987).

Review of Ibn al-Haytham's Completion of the Conics by J.P. Hogendijk in Isis, 77:2:287 (1986), 365-367.

Review of Helmuth Gericke, Mathematik in Antike und Orient. Isis, 76:4:284 (1985).

Review of Anton M. Heinen, Islamic Cosmology: A Study of al-Suyuti's "ilm al-hay'a as-saniya fi l-hay'a al-sunniya". MESA Bulletin, 19, 1985, 248-249.

Short review of Al-'ulum 'ind al-muslimin, by Kuwait Foundation for the Advancement of Sciences, MESA Bulletin, 19, 1985, 266-267.

Review of Trois Etudes sur L'oeuvre d'Archimede by Pierre Souffrin in Ganita Bharati, Vol. 7, Nos. 1-4 (1985), 41-43.

Berggren, J.L., Review of R. Rashed and A. Djebbar's L'Oeuvre Algebrique d' al-Khayyam, inMath. Reviews, 84a: 01008.

Review of B.L. Van der Waerden, Geometry and Algebra in Ancient Civilizations. New York/Berlin: Springer-Verlag, 1983, in Ancient Philosophy, 5, 305-307.

Berggren, J.L., Review of A.D. Naini's Geschichte der Zahlentheorie im Orient, in Isis, Vol. 75, No. 278, 611-612 (1984).

Review of E.S. Kennedy et al, Studies in the Islamic Exact Sciences. Beirut, Lebanon: AUB Press, 1983 in J. for Archaeoastronomy.

Berggren, J.L., Review of J. Sesiano's Books IV to VII of Diophantus Arithmetica in the Arabic Translation Attributed to Qusta ibn Luqa, in Centaurus, 1983.

Berggren, J.L., Review of A. Allard's Maxime Planude: Le grand calcul selon les Indiens, Isis, vol. 74, No. 271, 126-127 (1983).

Berggren, J.L., Review of A. Djebbar's Enseignment et Recherche Mathematiques dans le Maghreb des XIIIe - XIVe Siecles, Isis, vol. 74, no. 273, Sept. 1983.

Berggren, J.L., Review of Ivo Schneider's Archimedes, in Isis, Vol. 72, No. 4, 1981, 674-675.

Berggren, J.L., The Astrolabe Kit. Technology and Culture, 151-153, (January 1977).

Berggren, J.L., Review of Diocles On Burning Mirrors (Arabic Text with English Translation), by G.J. Toomer, in Historia Mathematica, Vol. 4, No. 3, 360-363.

Berggren, J.L., Review of Mathematics in Civilization, Historia Mathematica, Vol. 1, no. 1, 102-106 (1974).

Encyclopedia Articles

Berggren, J.L., Five articles: Calculus, Integral Calculus, Differential Calculus, Number Theory, Numerical Analysis, totalling 8000 words in Academic American Encyclopedia (pub. Grollier, Inc.)

Articles "Calculus", "Vectors", Trigonometry", "Sequences and Series", "Mathematics (History)" for Funk and Wagnalls Encyclopedia . (Now incorporated into Encarta.) Review of Math. articles in 1986 ed.

Article "Arabic Mathematics" in Encyclopaedia Britannica (Macropaedia), 1986.