Abstract
One of the most interesting and less known two-dimensional transformations is the so-called circle inversion. This paper presents a new Mathematica package, CircleInversion, for computing and displaying the images of two-dimensional objects (such as curves, polygons, etc.) by the circle inversion transformation. Those objects can be described symbolically in either parametric or implicit form. The output obtained is consistent with Mathematica’s notation and results. The performance of the package is discussed by means of several illustrative and interesting examples.
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References
Casey, J.: Theory of Inversion. In: A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th edn., pp. 95–112. Hodges, Figgis & Co., Dublin (1888)
Coolidge, J.L.: Inversion. In: A Treatise on the Geometry of the Circle and Sphere, pp. 21–30. Chelsea, New York (1971)
Courant, R., Robbins, H.: Geometrical Transformations. Inversion. In: What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd edn., pp. 140–146. Oxford University Press, Oxford (1996)
Coxeter, H.S.M., Greitzer, S.L.: An Introduction to Inversive Geometry. In: Geometry Revisited. Math. Assoc. Amer., Washington, pp. 103–131 (1967)
Coxeter, H.S.M.: Inversion in a Circle and Inversion of Lines and Circles. In: Introduction to Geometry, 2nd edn., pp. 77–83. John Wiley and Sons, New York (1969)
Darboux, G.: Lecons sur les systemes orthogonaux et les coordonnées curvilignes. Gauthier-Villars, Paris (1910)
Dixon, R.: Inverse Points and Mid-Circles. In: Mathographics, pp. 62–73. Dover, New York (1991)
Durell, C.V.: Inversion. In: Modern Geometry: The Straight Line and Circle, pp. 105–120. Macmillan, London (1928)
Fukagawa, H., Pedoe, D.: Problems Soluble by Inversion. In: Japanese Temple Geometry Problems, pp. 17–22, 93–99. Charles Babbage Research Foundation, Winnipeg (1989)
Gardner, M.: The Sixth Book of Mathematical Games from Scientific American. University of Chicago Press, Chicago (1984)
Greenberg, M.: Euclidean and Non-Euclidean Geometries: Development and History, 3rd edn. W.H. Freeman and Company, New York (1993)
Johnson, R.A.: Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle, pp. 43–57. Houghton Mifflin, Boston (1929)
Lachlan, R.: The Theory of Inversion. In: An Elementary Treatise on Modern Pure Geometry, pp. 218–236. Macmillian, London (1893)
Lockwood, E.H.: Inversion. In: A Book of Curves, pp. 176–181. Cambridge University Press, Cambridge (1967)
Maeder, R.: Programming in Mathematica, 2nd edn. Addison-Wesley, Redwood City (1991)
Wells, D.: The Penguin Dictionary of Curious and Interesting Geometry, pp. 119–121. Penguin, London (1991)
Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media, Champaign, IL & Cambridge University Press, Cambridge (1999)
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Urbina, R.T., Iglesias, A. (2005). Circle Inversion of Two-Dimensional Objects with Mathematica. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_58
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DOI: https://doi.org/10.1007/11424857_58
Publisher Name: Springer, Berlin, Heidelberg
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