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A study on the rectangular coordinate system via comparing the interrelated influence between mathematical knowledge evolution and historical development of Cartography in Europe

Lee, Dong Won (Department of Mathematics, Teachers College, Kyungpook National University)

Publication Information

Journal for History of Mathematics / v.25, no.4, 2012 , pp. 37-51 More about this Journal

Abstract

By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.

Keywords

Cartography; Coordinate System; Rectangular Coordinate System; Analytic Geometry; Projection;

Citations & Related Records

Reference

1	J. L. Berggren and A. Jones, Ptolemy's Geography: An Annotated Translation of the Theoretical Chapters, Princeton University Press, 2000.
2	C. B. Boyer, A History of Mathematics (Second ed.), John Wiley and Sons, Inc., 1991.
3	F. Cajori, A History of Mathematical Notations, Dover Publications Inc., 1993.
4	M. Clagett, Oresme Nicole, in Dictionary of Scientific Biography, Vol. X, Ch. C. Gillispie (ed.), New York: Charles Scribner's Sons, 1974.
5	M. Clagett, Nicole Oresme and the Medieval Geometry of Qualities and Motions, Madison, Wisc, 1968.
6	R. Cooke, The History of Mathematics: A Brief Course, Wiley Interscience. 1997.
7	R. Descartes,La geometrie, In Discours de la Methode. Paris: Essellier (Appendix), 1637.
8	M. Friendly, Milestones in the history of thematic cartography, statistical graphics, and data visualization, Michael Friendly, 2009. http://datavis.ca/milestones/.
9	R. G. Frisius, Libellus de locorum describendorum ratione, Antwerp, 1533.
10	M. Jones, Tycho Brahe, Cartography and Landscape in 16th Century Scandinavia, in Hannes Palang (ed), European Rural Landscapes: Persistence and Change in a Globalising Environment, 2004.
11	M. Maor, Trigonometric Delights, Princeton University Press, 1998.
12	J. F. Moffitt, Medieval Mappaemundi and Ptolemy's Chorographia,Gesta 32 (1993), pp. 59-68 Published by: International Center of Medieval Art.
13	J. Napier, Mirifici logarithorum canonis descriptio, 1614. (English translation,A Description of the Admirable Table of Logarithms, published in 1616 by Edward Wright, London: Nicholas Okes).
14	J. Needham, Science and Civilization in China, Vol.3, Cambridge University Press, 1954.
15	I. Newton, Enumeration of Lines of the third Order, Generation of Curves by Shadows, Organic Description of Curves, and Construction, of Equations by Curves, 1760.
16	B. Otto, Linear Algebra with Applications, (3rd Edition ed.) Upper Saddle River NJ: Prentice Hall, 1995.
17	J. Stillwell, Mathematics and its History (Second Edition ed.). Springer verlag, 2004.
18	J. R. Stone, The Medieval Mappaemundi: Toward an Archaeology of Sacred Cartography, Religion 23(3) (1993), pp. 197-216. DOI ScienceOn
19	P. D. Thomas,Conformal Projections in Geodesy and Cartography, United States Government Printing Office, Washington, Special Publication No. 251, 1952.
20	L. da Vinci, Notebooks vol.M, Verso 40. Paris: Manuscripts of the Institute of France. 1500.
21	B. A. Rosenfeld, A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, Springer, 1988.
22	http://www.henry-davis.com/MAPS/AncientWebPages/AncientL.html, Mesopotamian City Plan, Nippur 1500 BC, 101.
23	http://www.henry-davis.com/MAPS/AncientWebPages/119.html, 119 Ptolemaic World Map, 12th-13th century.
24	http://www.henry-davis.com/MAPS/AncientWebPages/AncientL.html, World map according to Eratosthenes (194 B.C.), 112.
25	http://en.wikipedia.org/wiki/Marinus_of_Tyre.
26	http://www.henry-davis.com/MAPS/EMwebpages/EML.html, 226A Hereford mappa-mundi, Richard de Bello of Haldingham, 1290, color redrawing.
27	http://www.henry-davis.com/MAPS/EMwebpages/EML.html, 201F Macrobian world map, 9 th century.
28	http://www.henry-davis.com/MAPS/EMwebpages/EML.html, 205Z T-O map, unknown, from 12th century edition of Bede's De natura rerum (8.1 cm diameter).
29	http://en.wikipedia.org/wiki/Mercator_1569_world_map, The 1569 Mercator map of the world.