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2 results

  • 3 - Anachronism and anachorism in the study of mathematics in India

  • Edited by Niccolò Guicciardini, Università degli Studi di Milano
  • Book:
    Anachronisms in the History of Mathematics
    Published online:
    19 July 2021
    Print publication:
    22 July 2021, pp 83-104

  • Summary

    The foremost historiographic challenge in interpreting pre-modern Indian mathematics is arguably not anachronism so much as anachorism, the blurring of geographical or cultural rather than chronological distinctions. For example, historians struggle constantly with ways to avoid or explain calling Indian analyses of right-triangle relations “Pythagorean”, or using the term “Diophantine equations” for the type of problems designated in Sanskrit as \kuttaka\ or \varga-\prakrti. Nonetheless, the combination of anachronism and anachorism provides the study of Indian mathematics with a powerful lens, which clarifies even as it distorts. This paper will address such trade-offs between popular misconceptions and deeper insights, especially in the application of concepts from the historiography of early modern European calculus to infinitesimal methods used in Sanskrit mathematics of the early to mid-second millennium.

  • Appendix - Mathematical details

  • Todd Timberlake, Berry College, Georgia, Paul Wallace
  • Book:
    Finding our Place in the Solar System
    Published online:
    18 March 2019
    Print publication:
    28 March 2019, pp 307-336

  • Summary

    This appendix provides mathematical details to supplement the ideas presented in the main text. Topic covered include: angular measurement, apparent diameter, trigonometry, finding the Sun’s altitude from the length of a shadow, determining the relative distances of the Sun and Moon, and finding the distance to an astronomical object using parallax measurements. In addition, this appendix shows how to calculate the sizes of epicycles in the Ptolemaic theory and the periods and sizes of planetary orbits in the Copernican theory. Mathematical details are also provided for Kepler’s Laws of Planetary Motion, Galileo’s measurement of mountains on the Moon, Galileo’s studies of falling bodies and projectiles, Newton’s universal gravitational force, and Bradley’s theory of the aberration of starlight.