geometry: Additional Information
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Assorted References
 axiomatic method
 fallacies and paradoxes
 foundations
 structure of coordination compounds
applications
 Earth measurement
 In geoid
 incommensurables
 physics
history
contribution of
 Archytas of Tarentum
 Blaschke
 Cayley
 Euclid
 Euclid’s “Elements”
 Eudoxus of Cnidus
 Fermat
 Gauss
 Monge
 Thales
 Theaetetus
 In Theaetetus
development in
 astronomy
 Babylonian mathematics
 Egyptian mathematics
 Greek mathematics
 Islamic mathematics
philosophical aspects
 logical empiricism
 Pythagoreanism
 rationalism
relationship to
 group theory
 trigonometry
Additional Reading
General history
The best overview in English of the history of geometry and its applications consists of the relevant chapters of Morris Kline, Mathematical Thought from Ancient to Modern Times (1972, reissued in 3 vol., 1990), which can be supplemented, for further applications, by Mathematics in Western Culture (1953, reissued 1987). Three other useful books of large scope are Petr Beckmann, A History of π, 4th ed. (1977, reissued 1993); Julian Lowell Coolidge, A History of Geometrical Methods (1940, reissued 1963); and David Wells, The Penguin Dictionary of Curious and Interesting Geometry (1991). A fine recent survey at a college level of the various branches of geometry, with much historical material, is David A. Brannan, Matthew F. Esplen, and Jeremy J. Gray, Geometry (1999).
Ancient Greek geometry
The standard English editions of the Greek geometers are those prepared by Thomas Little Heath beginning in the 1890s. They contain important historical and critical notes. Most exist in inexpensive reprints: Apollonius of Perga: Treatise on Conic Sections (1896, reissued 1961); The Works of Archimedes (1897, reissued 1953); Aristarchus of Samos, The Ancient Copernicus (1913, reprinted 1981); and The Thirteen Books of Euclid’s Elements, 2nd ed., rev. with additions, 3 vol. (1926, reissued 1956). The historical material has been shortened and simplified, and its coverage extended, in A History of Greek Mathematics, 2 vol. (1921, reprinted 1993).
Further information about technicalhistorical points—for example, the lunules of Hippocrates—may be found in Wilbur Richard Knorr, The Ancient Tradition of Geometric Problems (1986, reissued 1993). The epistemology of Greek geometry can be approached via the editor’s introduction to and the text of Proclus, A Commentary on the First Book of Euclid’s Elements, trans. and ed. by Glenn R. Morrow (1970, reprinted 1992).
Ancient nonGreek geometry
Other ancient geometrical traditions are covered in A.K. Bag, Mathematics in Ancient and Medieval India (1979); Richard J. Gillings, Mathematics in the Time of the Pharaohs (1972, reprinted 1982); Joseph Needham, Mathematics and the Sciences of the Heavens and the Earth (1959), vol. 3 of Science and Civilization in China; and B.L. van der Waerden, Science Awakening, 4th ed., 2 vol. (1975).
Geometry in Islam
Aspects of the extensive development of geometry by Islamic mathematicians can be studied in J.L. Berggren, Episodes in the Mathematics of Medieval Islam (1986). Otherwise, the best route to a survey is through the relevant chapters in vol. 2 of Roshdi Roshed (Rushdi Rashid) (ed.), Histoire des Sciences Arabes, 3 vol. (1997), and the articles on Arab mathematicians and astronomers in Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography, 18 vol. (1970–90).
Renaissance geometry and applications
J.L. Heilbron, Geometry Civilized: History, Culture, and Technique (1998, reissued 2000), considers examples of geometry from some modern cultures as well as from the ancient Mediterranean and gives examples of the development of Greek geometry in the Middle Ages and Renaissance. A more advanced book along similar lines, but with more restricted coverage, is Alistair Macintosh Wilson, The Infinite in the Finite (1995). James Evans, The History and Practice of Ancient Astronomy (1998), is by far the best introduction to the theoretical and instrumental methods of the old astronomers. Albert van Helden, Measuring the Universe (1985), describes the methods of the Greeks and their development to the time of Halley. John P. Snyder, Flattening the Earth: Two Thousand Years of Map Projections (1993, reissued 1997), gives the neophyte cartographer a start. J.V. Field, The Invention of Infinity: Mathematics and Art in the Renaissance (1997), contains an elegant account, in both words and pictures, of the theory of projection of Brunelleschi, Alberti, and their followers.
Geometry and the calculus
The transformation of mathematics in the 17th century can be followed in Carl B. Boyer, The Concepts of the Calculus: A Critical and Historical Discussion (1939, reissued 1949; also published as The History of the Calculus and Its Conceptual Development, 1949, reissued 1959), largely superseded by Margaret E. Baron, The Origins of the Infinitesimal Calculus (1969, reprinted 1987); Michael S. Mahoney, The Mathematical Career of Pierre de Fermat (1601–65) (1973); and René Descartes, Discourse on Method, Optics, Geometry, and Meteorology, trans. by Paul J. Olscamp (1965, reissued 1976). This last work, which ranks among the most important books on natural philosophy and mathematics ever written, repays the effort required to master its idiom.
Axiomatic Euclidean and nonEuclidean geometry
Roberto Bonola, NonEuclidean Geometry, 2nd rev. ed. (1938, reissued 1955), contains a thorough discussion of the work of Saccheri, Gauss, Bolyai, and Lobachevsky as well as a major text from each of the two founders of nonEuclidean geometry. David Hilbert, Foundations of Geometry, 2nd ed., trans. by Leo Unger and rev. and enlarged by Paul Bernays (1971, reissued 1992), is an excellent and accessible English translation.
Article Contributors
Primary Contributors

J.L. Heilbron
Senior Research Fellow at the University of Oxford, England. Author of Geometry Civilized and The Sun in the Church among others.
Other Contributors
 Briana Bierman
Other Encyclopedia Britannica Contributors
Article History
Type  Contributor  Date  

Modified title of Web site: NeoK12  Educational Videos and Games for School Kids  Geometry.  Feb 03, 2020  
Add new Web site: Kids Math Games  Have Fun Learning Online!  Geometry Facts.  Feb 20, 2019  
Add new Web site: Mr.Nussbaum  Geometry Games, Drills, and Videos for Kids.  Jan 09, 2017  
Add new Web site: University of Colorado at Boulder  Laboratory ofor Atmospheric and Space Physics  Basic Geometry.  Jan 09, 2017  
Media added.  May 10, 2016  
Add new Web site: Wolfram MathWorld  Geometry.  Feb 20, 2014  
In reference to Eratosthenes' estimate of Earth's circumference, changed "400,000" (stadia) to "250,000." 

Oct 22, 2013  
Add new Web site: Quatr.us  Geometry.  Apr 01, 2013  
Add new Web site: Kids Math Games  Geometry.  Mar 21, 2012  
Add new Web site: NeoK12  Educational Videos and Games for School Kids  Geometry.  Nov 04, 2011  
Added new Web site: Buzzle.com  Pipefish.  Apr 17, 2008  
Added new Web site: Maths Is Fun  Geometry.  Apr 17, 2008  
Added new Web site: Animal Planet  Sardine.  Mar 19, 2008  
Added new Web site: UNC Charlotte Mathematics Department  The Origins of Geometry.  Jan 09, 2008  
Added new Web site: Annenberg Media  Shape and Space in Geometry.  Sep 12, 2006  
Added new Web site: Wolfram MathWorld.  Jul 06, 2006  
Added new Web site: How the Greeks Used Geometry to Understand the Stars.  Jun 28, 2006  
Added new Web site: How the Greeks Used Geometry to Understand the Stars.  Jun 28, 2006  
Added new Web site: ThinkQuest  Geometry.  Jun 12, 2006  
Added new Web site: Neutral and NonEuclidean Geometry.  Jun 12, 2006  
Added new Web site: University of Minnesota  The Geometry Center.  Jun 01, 2006  
Added new Web site: MathsNet.  May 26, 2006  
Added new Web site: MathsNet.  May 26, 2006  
Added new Web site: The Geometry Section.  May 24, 2006  
Article revised.  Sep 12, 2003  
Article revised.  Nov 26, 2001  
New article added.  Sep 14, 2001 