Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 34 No. 1 (2016): Revista Integración
Research and Innovation Articles

Peirce quincuncial projection

PDF HTML (Español (España))
  • Leonardo Solanilla,
  • Arnold Oostra,
  • Juan Pablo Yáñez
Leonardo Solanilla
Universidad del Tolima
Arnold Oostra
Universidad del Tolima
Juan Pablo Yáñez
Universidad del Tolima
DOI: https://doi.org/10.18273/revint.v34n1-2016002

Published 2016-05-06

Keywords

  • Peirce quincuncial projection,
  • elliptic functions,
  • geographic maps,
  • numerical conformal mapping,
  • tessellations

How to Cite

Solanilla, L., Oostra, A., & Yáñez, J. P. (2016). Peirce quincuncial projection. Revista Integración, Temas De matemáticas, 34(1), 23–38. https://doi.org/10.18273/revint.v34n1-2016002

Copyright (c) 2016 Leonardo Solanilla, Arnold Oostra, Juan Pablo Yáñez

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

We present the essential theoretical basis and prove concrete practical formulas to compute the image of a point on the terrestrial sphere under Peirce quincuncial projection. We also develop a numerical method to implement such formulas in a digital computer and illustrate this method with examples. Then, we briefly discuss the criticism of Pierponton the correctness of Peirce’s formula for the projection. Finally, we draw some conclusions regarding the generalization of Peirce’s original idea by means of Schwarz-Christoffel transformations.

To cite this article: L. Solanilla, A. Oostra, J.P. Yáñez, Peirce quincuncial projection, Rev. Integr. Temas Mat. 34 (2016), No. 1, 23–38.

PDF HTML (Español (España))

Downloads

Download data is not yet available.

References

  1. “Adams hemisphere-in-a-square projection”, https://en.wikipedia.org/wiki/Adams_hemisphere-in-a-square_projection, [accessed 14 June 2015].
  2. Bellacchi G., Introduzione storica alla teoria delle funzioni ellittiche, G. Barbèra, Firenze,1894.
  3. Bergonio P.P., “Schwarz-Christoffel Transformations”, Thesis (Master), The University of Georgia, Athens, 2007, 66 p.
  4. Durège H., Theorie der elliptischen Funktionen, Leipzig, Druck und Verlag von B.G. Teubner,1861.
  5. Frischauf I., “Bemerkungen zu C.S. Peirce Quincuncial Projection”, Amer. J. Math. 19(1897), No. 4, 381–382.
  6. “Guyou hemisphere-in-a-square projection”, https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a square_projection, [accessed 14 June 2015].
  7. Jacobi C.G.J., Fundamenta nova theoriae functionum ellipticarum, Regiomonti (Königsberg), Borntræger, 1829.
  8. Lee L.P., “Some Conformal Projections Based on Elliptic Functions”, Geographical Review 55 (1965), No. 4, 563–580.
  9. Liouville M.J., “Leçons sur les fonctions doublement périodiques faites en 1847 par M.J. Liouville”, J. Reine Angew. Math. 88 (1880), 277–310.
  10. Peirce C.S., “A Quincuncial Projection of the Sphere”, Amer. J. Math. 2 (1879), No. 4, 394–396.
  11. Pierpont J., “Note on C.S. Peirce’s Paper on ‘A Quincuncial Projection of the Sphere’ ”, Amer. J. Math. 18 (1896), No. 2, 145–152.
  12. Richelot F.J., “Darstellung einer beliebigen gegebenen Größe durch sin am(u + w, k)”, J. Reine Angew. Math. 45 (1853), 225–232.
  13. Solanilla L., Las transformaciones elípticas de Jacobi, Sello Editorial Universidad del Tolima, Ibagué, 2014.
  14. Solanilla L., Tamayo A.C. & Pareja G., Integrales elípticas con notas históricas, Sello Editorial Universidad de Medellín, Medellín, 2010.