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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Robin Hartshorne
Title: Geometry: Euclid and beyond
Additional book information: Springer-Verlag, New York, 2000, xi+526 pp., ISBN 0-387-98650-2, $49.95$

References [Enhancements On Off] (What's this?)

Bishop, Errett, and Douglas Bridges, Constructive Analysis, New York: Springer-Verlag, 1985. MR 0804042
Borsuk, Karol, and Wanda Szmielew, Foundations of geometry: Euclidean and Bolyai-Lobachevskian geometry. Projective geometry, New York: Interscience Publishers, 1960. MR 0143072
Cornish, Neil J., and Jeffrey R. Weeks, ``Measuring the Shape of the Universe", Notices of the AMS 45 (1998), 1463-1471. MR 1656892
Efimov, N. V., ``Generation of singularities on surfaces of negative curvature" [Russian], Mat. Sb. (N.S.) 64 (106), pp. 286-320, 1964. MR 0167938
Euclid, Phaenomena, in Euclidis opera omnia, Heinrich Menge, ed., Lipsiae: B.G. Teubneri, 1883-1916.
Heath, T.L., Mathematics in Aristotle, Oxford: Clarendon Press, 1949. MR 10:667d
Henderson, David W., and Daina Taimina, Crocheting the Hyperbolic Plane, The Mathematical Intelligencer, vol 23, no. 2, 2001, pp 17-28. MR 1843235
Henderson, David W., Differential Geometry: A Geometric Introduction, Upper Saddle River, NJ: Prentice Hall, 1998.
Henderson, David W., Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces, Upper Saddle River, NJ: Prentice Hall, 2001.
Hilbert, David, Foundations of geometry (Grundlagen der Geometrie) (translated by Leo Unger), La Salle, IL: Open Court, 1971. MR 0275262
Hilbert, David, Über Flächen von konstanter gausscher Krümmung, Transactions of the A.M.S., 1901, pp. 87-99.
Amir-Moez, A. R., ``Discussion of Difficulties in Euclid" by Omar ibn Abrahim al-Khayyami (Omar Khayyam), Scripta Mathematica, 24 (1958-59), pp. 275-303. MR 0114743
Kline, Morris, Mathematical Thought from Ancient to Modern Times, Oxford: Oxford University Press, 1972. MR 0472307
Kuiper, Nicolas, On c1-isometric imbeddings II, Nederl. Akad. Wetensch. Proc. Ser. A58, 1955, pp. 683-689. MR 17:782c
Martin, George E., Geometric Constructions, New York: Springer, 1998. MR 1483895
McCleary, John, Geometry from a Differentiable Viewpoint, Cambridge, UK: Cambridge University Press, 1994. MR 1314819
R.S. Millman and G.D. Parker, Elements of Differential Geometry, Englewood Cliffs, NJ: Prentice-Hall, 1977. MR 0442832
V.V. Prasolov & V.M. Tikhomirov, Geometry, Translations of Mathematical Monographs, Vol. 200, American Mathematical Society, 2001. MR 1833867
Baudhayana, Sulbasutram, G. Thibaut, trans., S. Prakash & R. M. Sharma, ed., Bombay: Ram Swarup Sharma, 1968.
Thurston, William, Three-Dimensional Geometry and Topology, Vol. 1, Princeton, NJ: Princeton University Press, 1997. MR 1435975
Toth, Imre, Non-Euclidean Geometry before Euclid, Scientific American, 1969.
Weeks, Jeffrey, The Shape of Space, Second Edition, New York: Marcel Dekker, 2002.

Review Information:

Reviewer: David W. Henderson
Affiliation: Cornell University
Journal: Bull. Amer. Math. Soc. 39 (2002), 563-571
Published electronically: July 9, 2002
Review copyright: © Copyright 2002 American Mathematical Society