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Refereed Journal Articles and Conference Proceedings
"Aristarchus's On the
Sizes and Distances of the Sun and the Moon: Greek and Arabic Texts" (with
N. Sidoli). Arch. Hist. Exact.
Sci., Vol. 61, 2007, pp. 215 - 254.
"The Arabic Version of Ptolemy's Planispherium or Flattening the Surface of the Sphere:
Text, translation, commentary" (with N. Sidoli). SCIAMVS, Vol. 8, Dec. 2007, pp. 37 -
140.
"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 fuer 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 Matemematica
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 fuer 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.
"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.
"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.
"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.
"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.
"Mathematical Astronomy in the Fourth Century B.C. as found
in Euclid's Phaenomena" (with R.S.D. Thomas, Physis., Vol XXIX (1992), 7-33.
"Habash's Analemma
for Representing Azimuth Circles on the Astrolabe, Zeitschrift fur Geschichte der Arabisch-Islamischen Wissenschaften, (1992) 23-30.
"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.
"Ptolemy's Maps of Earth and the Heavens: A New
Interpretation", Archive for History
of Exact Sciences, Vol. 43, 2, 1991, pp. 133-144.
"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.
"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.
"Medieval Islamic Methods for Drawing
Azimuth Circles on the Astrolabe", Centaurus, (1991) Vol. 34: 309-344.
"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.
"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.
"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.
"Mathematical Methods in Ancient Science: Spherics"
in History in Mathematics Education,
ed. Ivor Grattan-Guinness, Belin, Paris 1987, pp.
14-32.
"Mathematical Methods in
Ancient Science: Astronomy" in History
in Mathematics Education, ed. Ivor Grattan-Guinness, Belin,
Paris 1987, pp. 33-49.
"Archimedes Among the
Ottomans" in From Ancient Omens to
Statistical Mechanics. Munksgaard, Copenhagen,
1987, pp. 101-109.
"The Origin of al-Biruni's Method of the Zijes in the
Theory of Sundials". Centaurus XXVIII, Vol. 28, (1985) 1 -16.
"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.
"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.
"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).
"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.
"Al-Biruni on Plane Maps of the
Sphere", J. for History of Arabic
Science, Vol. 6, 47-96 (1982).
"Al-Sijzi on
the Transversal Figure", J. for
History of Arabic Science, Vol. 5, Nos. 1 and 2, 23-36 (1981).
"An Anonymous Treatise on the Regular
Nonagon", J. for History of Arabic
Science, Vol. V, Nos. 1 and 2, 37-41 (1981).
"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).
"Medieval
Analemmas for Determining the Qibla",
J. for History of Arabic Science, IV,
69-80 (1980).
"The Barycentric
Theorems of Abu Sahl al-Kuhi,"
Proceedings of Second International
Symposium for History of Arabic Science, Aleppo, April 1979.
"A coincidence of Pappos'
Book VIII with al-Biruni's Tahdid",
J. for History of Arabic Science,
Vol. II, No. 1, 137-142 (May 1978).
"A Lacuna in Archimedes' Sphere and Cylinder Book I, Historia Mathematica,
4, 1-5 (1977).
"Spurious Theorems in Archimedes' Equilibrium of Planes
Book I", Archive for History of
Exact Sciences, Vol. 16, 2, 87-103 (1976).
"Some lessons for teachers from the history
of Mathematics," Vector, 11-21
(1974).
Polygons and Puzzles. Connecticut Mathematics Journal, Vol. 6,
no. 2, 3-7 (May 1974).
"On the determination of the maximum order
of the group of a tournament" (with B. R. Alspach). Can. Math. Bull., Vol. 16, no. 1, 11-14 (1973).
"An algebraic characterization of finite symmetric tournaments",
Bull. Australian Math. Soc., Vol. 6, 53-59 (1972.
"An algebraic characterization of symmetric graphs with a prime
number of vertices", Bull. Australian
Math. Soc., Vol. 7, no. 1, 131-134 (1972).
"Some remarks on Napier's conception of logarithms", Vector (Journal of the B.C. Mathematics
Teachers), Vol. 14, no. 1, 12-14 (1972).
"Solvable and supersolvable
groups in which every element is conjugate to its inverse", Pac. J. Math., Vol. 37, no. 1, 21-28
(1971).
"Finite groups in which every element is conjugate to its
inverse", Pac. J. Math., Vol. 28, no.
2, 289-293 (1969).
"Intervening opportunities and national park visitation rates", ( with W. Catton) Pac.
Soc. Review, Vol. 7, no. 2, 66-73 (1964).
Episodes in the Mathematics of Medieval Islam. Berlin, Heidelberg, New York: Springer-Verlag, 1986 (softcover ed'n
2003). A revised version of this work has been
published in German, in 2011, as Mathematik im mittelalterlichen Islam
(Springer Verlag).
From Ancient
Omens to Statistical Mechanics: Essays on the Exact Sciences Presented to Asger Aaboe (edited
jointly with B.R. Goldstein). Munksgaard: Copenhagen,
1987.
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.
Reprinted in 2006 in a softcover edition by the American
Mathematical Society and the London Mathematical Society as Vol. 29 in the
series History of Mathematics: Sources.
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.)
Pi: A Source Book (3rd
Edition - jointly with J. and P. Borwein). New York:
Springer-Verlag, 2004.
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.
Review of Mathematics in
Civilization by Resnikoff, H. and R. Wells, Jr.
in Historia Mathematica,
Vol. 1, no. 1, 1974, pp. 102-106.
Review of Diocles On Burning Mirrors (Arabic Text with
English Translation), by G.J. Toomer, in Historia Mathematica,
Vol. 4, No. 3, 1977, pp. 360-363.
Review of 'The Astrolabe Kit' in Technology
and Culture, 151-153, (January 1977).
Review of Ivo Schneider's Archimedes,
in Isis, Vol. 72, No. 4, 1981,
674-675.
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.
Review of E.S. Kennedy et al, Studies in the Islamic Exact Sciences. Beirut,
Lebanon: AUB Press, 1983 in J. for Archaeoastronomy.
Review of J. Sesiano, Books
IV to VII of Diophantus Arithmetica
in the Arabic Translation Attributed to Qusta ibn Luqa, in Centaurus, 1983.
Review of A. Allard, Maxime Planude: Le grand calcul
selon les Indiens in Isis, vol. 74, No. 271, 126-127 (1983).
Review of A. Djebbar, Enseignment et Recherche Mathematiques dans le Maghreb des XIIIe - XIVe Siecles in Isis, vol. 74, no. 273, Sept. 1983.
Review of A.D. Naini, Geschichte der Zahlentheorie
im Orient, in Isis,
Vol. 75, No. 278, 611-612 (1984).
Review of R. Rashed and A. Djebbar, L'Oeuvre Algebrique d' al-Khayyam, in Math. Reviews, 84a: 01008.
Review of Helmuth
Gericke, Mathematik in Antike und Orient, in 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.
Review of Al-'ulum 'ind al-muslimin,
by Kuwait Foundation for the Advancement of Sciences, MESA Bulletin, 19, 1985, 266-267.
Review of Pierre Souffrin, Trois Etudes sur L'oeuvre d'Archimede, in Ganita Bharati, Vol.
7, Nos. 1-4 (1985), pp. 41-43.
Review of J.P. Hogendijk, Ibn al-Haytham's Completion of the Conics in Isis, 77:2:287 (1986), 365-367.
Review of R. Rashed,
Diophante: Les Arithmetiques
(Vols. III and V). Paris: Les Belles Lettres, 1984, in Historia Mathematica, Vol.14
(1987), 386-389.
Review of Roshdi Rashed,
Entre arithmetique
et algebra: Recherches sur l'histoire des mathematiques arabes in 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 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 G. Toomer, The Arabic text of Apollonius's Conics Books
V - VII: The Arabic Translation of the Lost Greek Original in the version of
the Banu Musa, in Mathematical Reviews (1992), Review No. 92e:01017.
Review of W.R. Knorr, Textual
Studies in Ancient and Medieval Geometry in Ancient Philosophy, Vol. XII No.2, 1992, pp.522-528.
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, in American Historical Review, October 1994, pp. 1286-87.
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 W. S. Anglin. Mathematics: A Concise History and
Philosophy in Philosophia Mathematica
(Series III) 4(1996) No. 2, pp. 196-198.
Review of Geometrical Landscapes: The
Voyages of Discovery etc., by A. R. Alexander, in Science and Public Policy. Volume 32, No. 2, 2005, pp. 167 - 168.
Review of The Archimedes
Codex, by R. Netz and W. Noel, in Notices of the Amer. Math. Soc. Volume 55, No. 8, 2008, pp. 943 - 947.
Review of Hypatia
of Alexandria: Mathematician and Martyr, by Michael B. Deakin,
in Metascience: Volume 18, Issue1, 2009.
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 . (Subsequently
incorporated into Encarta.)
Review of Mathematics
articles in 1986 ed. of Encyclopaedia Britannica and article "Arabic
Mathematics" in Encyclopaedia Britannica (Macropaedia),
1986.
Articles "Abu Sahl al-Quhi", "Ibrahim ibn Sinan" and "Sharaf al-Din al-Tusi" in New Dictionary of Scientific Biography, (Noretta
Koertge, editor) Detroit: Charles Scribner's Sons,
2008.
Publications by J.L. Berggren
Table of Contents