Science & Education

, Volume 16, Issue 6, pp 625–636 | Cite as

Fiatland: An Analogy between Mathematics and Physics

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Abstract

Before the 19th century the idea of more than three dimensions was exceptional. During the 19th century, however, geometry was revolutionized and new branches were developed. This revolution also created the idea of the possibility of a n-dimensional geometry or space; flatland, i.e. n = 2, was a consequence of this new thinking. In 1884 the clergyman Edwin Abbott and the mathematician Charles Hinton published their still-famous flatland stories. In the 20th century authors also included modern physics as well as computer science in flatland stories.

Key words

computer science geometry physics space 

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References

  1. Abbott, E.A.: 1984, Flatland: A Romance of Many Dimensions. With an introduction by A.K. Dewdney. New York.Google Scholar
  2. Abbott, E.A.: 2002, The Annotated Flatland: A Romance of Many Dimensions. Introduction and notes by Ian Stewart. Reading/Mass.Google Scholar
  3. Breitenberger, E.: 1993, Gauß und Listing. Topologie und Freundschaft. Mitteilungen der Gauß-Gesellschaft 30, pp. 3–56, especially p. 30f.Google Scholar
  4. Burger, D.: 1965, Sphereland: A Fantasy about Curved Spaces and an Expanding Universe. Translated by Cornelie J. Rheinboldt, New York. Reprint with a foreword by Isaac Asimov New York 1983.Google Scholar
  5. Burger, D.: 2001, Silvestergespräche eines Sechsecks: ein phantastischer Roman von gekrümmten Räumen und dem sich ausdehnenden Weltall. Köln.Google Scholar
  6. Busch, W.: 1891, Eduards Traum. Munich.Google Scholar
  7. Gauss, C.F.: 1861, Heinrich Christian Schumacher Briefwechsel, Vol. 3, Altona, p. 104f (31.7.1836).Google Scholar
  8. Gauss, C.F.: 1862, Heinrich Christian Schumacher Briefwechsel, Vol. 4, Altona, p. 83f (3.9.1842).Google Scholar
  9. Gauss, K.F.: 1902, General Investigations of Curved Surfaces of 1827 and 1825, Translated with notes and a bibliography by J.C. Morehead and A.M. Hiltebeitel, Princeton, p. 21.Google Scholar
  10. Henderson, L.D.: 1983, The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton, p. 15f.Google Scholar
  11. Kippenhahn, R.: 1984, Licht vom Rande der Welt. Stuttgart, p. 158.Google Scholar
  12. Miller, A.: 2001, Einstein-Picasso. Space, Time and the Beauty that Causes Havoc. New York, pp. 89–125.Google Scholar
  13. Dr. Mises: 1846, [Gustav Theodor Fechner]: Vier Paradoxa. Leipzig, p. 17.Google Scholar
  14. Oresme, N.: 1961, Quaestiones Super Geometriam Euclidis. in H.L.L. Busard (ed.), Leiden, S.27 (= Questio 10).Google Scholar
  15. Peano, G.: 1888, Calcolo geometrico secondo VAusdehnungslehre di H.Gr assmann. Torino, pp. 49–55, 63–65, 97–106.Google Scholar
  16. Poincare, H.: 1891/2, ‘Non-Euclidean Geometry’, Nature 45, 404–407.Google Scholar
  17. Riemann, B.: 1882, ‘On the Hypotheses which Lie at the Bases of Geometry’, Transl. by W.K. Clifford. Nature 8, 1873, pp. 14-17, 36f. in W. K. Clifford (ed.), Mathematical Papers by Robert Tucker, London, pp. 55–71Google Scholar
  18. Riemann, B.: 1959, On the Hypotheses which Lie at the Foundations of Geometry, in D.E. Smith (ed.),, A Source Book in Mathematics 2, Dover Publ., New York, pp. 411–425.Google Scholar
  19. Riemann, B.: 1970, ‘On the Hypotheses which lie at the Foundations of Geometry’, in M. Spivak (ed.), A Comprehensive Introduction to Differential Geometry, Vol. 2, Boston, pp. 4A–4 to 4A-20.Google Scholar
  20. Rucker, R.v.B.: 1980a, ‘Introduction’, in C. Hinton (ed.), Speculations on the Fourth Dimension, New York, pp. V–XVIII.Google Scholar
  21. Rucker, R.v.B.: 1980b, ‘Introduction’, in C. Hinton (ed.), Speculations on the Fourth Dimension, New York, p. VII.Google Scholar
  22. Stifel, M.: 1544, Arithmetica Integra, Nürnberg, fol. 31r-33v.Google Scholar
  23. Thiele, R.: 2003, ‘Fechner und Zöllner. Die Einschränkung der realen Welt auf Mathematik und ihre Erweiterung in eine Geisterwelt. Ein Vergleich zweier Raumauffassungen’, in U. Fix and I. Altmann (eds.), Fechner und die Folgen außerhalb der Naturwissenschaften, Tübingen, pp. 67–111.Google Scholar
  24. von Waltershausen, W.S.: 1856, Gauss zum Gedächtniss. Leipzig, p. 81. Reprint Wiesbaden 1965, Vaduz 1980.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department MathematikUniversität HamburgHamburgGermany

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