Book Review
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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,
$49.95$
[Bis] Bishop, Errett, and Douglas Bridges, Constructive Analysis, New York: Springer-Verlag, 1985. MR 0804042
[Bor] Borsuk, Karol, and Wanda Szmielew, Foundations of geometry: Euclidean and Bolyai-Lobachevskian geometry. Projective geometry, New York: Interscience Publishers, 1960. MR 0143072
[CoWe] Cornish, Neil J., and Jeffrey R. Weeks, ``Measuring the Shape of the Universe", Notices of the AMS 45 (1998), 1463-1471. MR 1656892
[Efi] Efimov, N. V., ``Generation of singularities on surfaces of negative curvature" [Russian], Mat. Sb. (N.S.) 64 (106), pp. 286-320, 1964. MR 0167938
[EucPh] Euclid, Phaenomena, in Euclidis opera omnia, Heinrich Menge, ed., Lipsiae: B.G. Teubneri, 1883-1916.
[Hea] Heath, T.L., Mathematics in Aristotle, Oxford: Clarendon Press, 1949. MR 10:667d
[HenCr] Henderson, David W., and Daina Taimina, Crocheting the Hyperbolic Plane, The Mathematical Intelligencer, vol 23, no. 2, 2001, pp 17-28. MR 1843235
[HenDG] Henderson, David W., Differential Geometry: A Geometric Introduction, Upper Saddle River, NJ: Prentice Hall, 1998.
[HenEG] Henderson, David W., Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces, Upper Saddle River, NJ: Prentice Hall, 2001.
[Hil-a] Hilbert, David, Foundations of geometry (Grundlagen der Geometrie) (translated by Leo Unger), La Salle, IL: Open Court, 1971. MR 0275262
[Hil-b] Hilbert, David, Über Flächen von konstanter gausscher Krümmung, Transactions of the A.M.S., 1901, pp. 87-99.
[Kha] 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
[Kli] Kline, Morris, Mathematical Thought from Ancient to Modern Times, Oxford: Oxford University Press, 1972. MR 0472307
[Kui] Kuiper, Nicolas, On c1-isometric imbeddings II, Nederl. Akad. Wetensch. Proc. Ser. A58, 1955, pp. 683-689. MR 17:782c
[Mar] Martin, George E., Geometric Constructions, New York: Springer, 1998. MR 1483895
[McC] McCleary, John, Geometry from a Differentiable Viewpoint, Cambridge, UK: Cambridge University Press, 1994. MR 1314819
[MiPa] R.S. Millman and G.D. Parker, Elements of Differential Geometry, Englewood Cliffs, NJ: Prentice-Hall, 1977. MR 0442832
[PrTi] V.V. Prasolov & V.M. Tikhomirov, Geometry, Translations of Mathematical Monographs, Vol. 200, American Mathematical Society, 2001. MR 1833867
[Sul] Baudhayana, Sulbasutram, G. Thibaut, trans., S. Prakash & R. M. Sharma, ed., Bombay: Ram Swarup Sharma, 1968.
[Thu] Thurston, William, Three-Dimensional Geometry and Topology, Vol. 1, Princeton, NJ: Princeton University Press, 1997. MR 1435975
[Toth] Toth, Imre, Non-Euclidean Geometry before Euclid, Scientific American, 1969.
[Wee] Weeks, Jeffrey, The Shape of Space, Second Edition, New York: Marcel Dekker, 2002.
- [Bis]
- Bishop, Errett, and Douglas Bridges, Constructive Analysis, New York: Springer-Verlag, 1985. MR 0804042
- [Bor]
- Borsuk, Karol, and Wanda Szmielew, Foundations of geometry: Euclidean and Bolyai-Lobachevskian geometry. Projective geometry, New York: Interscience Publishers, 1960. MR 0143072
- [CoWe]
- Cornish, Neil J., and Jeffrey R. Weeks, ``Measuring the Shape of the Universe", Notices of the AMS 45 (1998), 1463-1471. MR 1656892
- [Efi]
- Efimov, N. V., ``Generation of singularities on surfaces of negative curvature" [Russian], Mat. Sb. (N.S.) 64 (106), pp. 286-320, 1964. MR 0167938
- [EucPh]
- Euclid, Phaenomena, in Euclidis opera omnia, Heinrich Menge, ed., Lipsiae: B.G. Teubneri, 1883-1916.
- [Hea]
- Heath, T.L., Mathematics in Aristotle, Oxford: Clarendon Press, 1949. MR 10:667d
- [HenCr]
- Henderson, David W., and Daina Taimina, Crocheting the Hyperbolic Plane, The Mathematical Intelligencer, vol 23, no. 2, 2001, pp 17-28. MR 1843235
- [HenDG]
- Henderson, David W., Differential Geometry: A Geometric Introduction, Upper Saddle River, NJ: Prentice Hall, 1998.
- [HenEG]
- Henderson, David W., Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces, Upper Saddle River, NJ: Prentice Hall, 2001.
- [Hil-a]
- Hilbert, David, Foundations of geometry (Grundlagen der Geometrie) (translated by Leo Unger), La Salle, IL: Open Court, 1971. MR 0275262
- [Hil-b]
- Hilbert, David, Über Flächen von konstanter gausscher Krümmung, Transactions of the A.M.S., 1901, pp. 87-99.
- [Kha]
- 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
- [Kli]
- Kline, Morris, Mathematical Thought from Ancient to Modern Times, Oxford: Oxford University Press, 1972. MR 0472307
- [Kui]
- Kuiper, Nicolas, On c1-isometric imbeddings II, Nederl. Akad. Wetensch. Proc. Ser. A58, 1955, pp. 683-689. MR 17:782c
- [Mar]
- Martin, George E., Geometric Constructions, New York: Springer, 1998. MR 1483895
- [McC]
- McCleary, John, Geometry from a Differentiable Viewpoint, Cambridge, UK: Cambridge University Press, 1994. MR 1314819
- [MiPa]
- R.S. Millman and G.D. Parker, Elements of Differential Geometry, Englewood Cliffs, NJ: Prentice-Hall, 1977. MR 0442832
- [PrTi]
- V.V. Prasolov & V.M. Tikhomirov, Geometry, Translations of Mathematical Monographs, Vol. 200, American Mathematical Society, 2001. MR 1833867
- [Sul]
- Baudhayana, Sulbasutram, G. Thibaut, trans., S. Prakash & R. M. Sharma, ed., Bombay: Ram Swarup Sharma, 1968.
- [Thu]
- Thurston, William, Three-Dimensional Geometry and Topology, Vol. 1, Princeton, NJ: Princeton University Press, 1997. MR 1435975
- [Toth]
- Toth, Imre, Non-Euclidean Geometry before Euclid, Scientific American, 1969.
- [Wee]
- Weeks, Jeffrey, The Shape of Space, Second Edition, New York: Marcel Dekker, 2002.
Review Information:
Reviewer:
David W. Henderson
Affiliation:
Cornell University
Email:
dwh2@cornell.edu
Journal:
Bull. Amer. Math. Soc.
39 (2002), 563-571
Published electronically:
July 9, 2002
Review copyright:
© Copyright 2002
American Mathematical Society
