Advertisement

The Mathematical Intelligencer

, Volume 19, Issue 3, pp 33–40 | Cite as

The Geometry of Piero della Francesca

  • Mark A. Peterson
Department

Conclusion

Piero’s books are a mass of detail—detailed arithmetic, detailed instructions. In the case ofDe Prospectiva Pingendi, though, we have another medium, the paintings, to reveal what it is really about. We see that a simplistic reading would completely miss the point. With the mathematical treatises we are not so fortunate—there is no other medium. If we want to know the real meaning, we have to construct it from the treatises alone by getting behind the superficial details and discovering the mathematical thought. Beneath the surface, the thought is surprisingly deep. Piero was a real mathematician—one can say it without apology.

Keywords

Mathematical Intelligencer Fifteenth Century Regular Polyhedron Archimedean Solid Pythagoras Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M.A. Lavin, “The Piero Project,” inPiero della Francesca and His Legacy, ed. by M.A. Lavin, University Press of New England, Hanover, NH (1995), 315–523.Google Scholar
  2. [2]
    G. Vasari, LeOpere, ed. G. Milanesi, vol. 2, Florence (1878), 490.Google Scholar
  3. [3]
    Piero della Francesca, DeProspectiva Pingendi, ed. G. Nicco Fasola, 2 vols., Florence (1942).Google Scholar
  4. [4]
    Piero della Francesca,Trattato d’Abaco, ed. G. Arrighi, Pisa (1970).Google Scholar
  5. [5]
    Piero della Francesca,L’opéra “De corporibus regularibus” di Pietro Franceschi detto della Francesca usurpata da Fra Luca Pacioli, ed. G. Mancini, Rome, (1916).Google Scholar
  6. [6]
    M. Clagett,Archimedes in the Middle Ages, University of Wisconsin Press, 1971.Google Scholar
  7. [7]
    T.L. Heath,The Thirteen Books of Euclid’s Elements, Cambridge University Press (1908), 97.Google Scholar
  8. [8]
    T.L. Heath,The Works of Archimedes, Cambridge University Press (1897), xxix.Google Scholar
  9. [9]
    M. Clagett, op. cit. vol 3, pp. 383-415.Google Scholar
  10. [10]
    P. Grendler, “What Piero Learned in School: Fifteenth-Century Vernacular Education,” inPiero della Francesca and His Legacy, ed. M.A. Lavin, University Press of New England (1995), 161–176.Google Scholar
  11. [11]
    Leon Battista Albert!,On Painting, ed. Martin Kemp, trans. Cecil Grayson, London-New York (1991).Google Scholar
  12. [12]
    M. Kemp, “Piero and the Idiots: The EarlyFortuna of His Theories of Perspective,” inPiero della Francesca and His Legacy, ed. M.A. Lavin, University Press of New England (1995), 199–212.Google Scholar
  13. [13]
    J.V. Field, “A Mathematician’s Art,” inPiero della Francesca and His Legacy, ed. M.A. Lavin, University Press of New England (1995), 177–198.Google Scholar
  14. [14]
    J. Elkins, “Piero della Francesca and the Renaissance Proof of Linear Perspective,”Art Bulletin 69 (1987), 220–230.CrossRefGoogle Scholar
  15. [15]
    M.D. Davis,Piero della Francesca’s Mathematical Treatises, Longo Editore, Ravenna (1971).Google Scholar
  16. [16]
    S.A. Jayawardene, ‘The Trattato d’abaco’ of Piero della Francesca,” inCultural Aspects of the Italian Renaissance, Essays in Honour of Paul Oskar Kristeller, ed C. Clough, Manchester (1976).Google Scholar
  17. [17]
    L. Pacioli,Summa Arithmetica, Venice (1494) Book II, fol. 72r, Problem 36.Google Scholar
  18. [18]
    L. Pacioli, DeDivina Proportione, Venice (1509).Google Scholar
  19. [19]
    J.J. Sylvester, “On Staudt’s Theorems Concerning the Contents of Polygons and Polyhedrons, with a Note on a New and Resembling Class of Theorems,’Philosophical Magazine IV (1852), 335–345.Google Scholar
  20. [20]
    T.L. Heath,The Method of Archimedes, Recently Discovered by Heiberg, Cambridge University Press (1912).Google Scholar
  21. [21]
    P.R. Cromwell, “Kepler’s Work on Polyhedra”,The Mathematical Intelligencer Vol. 17, No. 3, New York (1995), 23–33.CrossRefzbMATHMathSciNetGoogle Scholar
  22. [22]
    Nicolo Tartaglia,Trattato Generate di Numeri e Misure, Venice (1559).Google Scholar
  23. [23]
    Nicolo Tartaglia, op. cit., Part IV Book 2, and Part V Book 2.Google Scholar
  24. [24]
    Nicolo Tartaglia, op. cit., Part I Book 13, fol. 107r.Google Scholar
  25. [25]
    In this paragraph I paraphrase arguments culled from 18th century sources by Gino Arrighi and quoted by him in the introduction to Ref. [4].Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Mark A. Peterson
    • 1
  1. 1.Department of MathematicsMount Holyoke CollegeSouth BadleyMA 01075USA

Personalised recommendations