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2 results

  • Kant on conic sections

  • Alison Laywine
  • Journal:
    Canadian Journal of Philosophy / Volume 44 / Issue 5-6 / December 2014
    Published online by Cambridge University Press:
    01 January 2020, pp. 719-758

  • This paper tries to make sense of Kant’s scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant’s attitude towards mathematics and the way he understood the cognitive resources available to us to do mathematics.

  • Slicing surfaces and the Fourier restriction conjecture

  • Part of
  • Fabio Nicola
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 2 / June 2009
    Published online by Cambridge University Press:
    28 May 2009, pp. 515-527
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  • We deal with the restriction phenomenon for the Fourier transform. We prove that each of the restriction conjectures for the sphere, the paraboloid and the elliptic hyperboloid in ℝn implies that for the cone in ℝn+1. We also prove a new restriction estimate for any surface in ℝ3 locally isometric to the plane and of finite type.