Digital Services        F A Q


The Spiral of Theodorus, Numerical Analysis, and Special Functions

Dept. of Computer Science (March 14, 2014)

SEMINAR SERIES : Distinguished lecture

MAJOR SPEAKER : Gautschi, Walter
LENGTH : 61 min.
ACCESS : Open to all
SUMMARY : Theodorus of Cyrene (ca. 460399 B.C.), teacher of Plato und Theaetetus, is known for his proof of the irrationality of √n, n = 2, 3, 5, ..., 17. He may have known also a discrete spiral, today named after him, whose construction is based on the square roots of the numbers n = 1, 2, 3,.... The subject of this lecture is the problem of interpolating this discrete, angular spiral by a smooth, if possible analytic, spiral. An interesting solution has been proposed twenty years ago by P.J. Davis, which is based on an infinite product. The computation of this product gives rise to problems of numerical analysis, in particular the summation of slowly convergent series, and the identification of the product to questions regarding special functions. The former are solved by a method of integration, in particular Gaussian integration, the latter by means of Dawson's integral and the BoseEinstein distribution. Number-theoretic questions also loom behind this work.  [Go to the full record in the library's catalogue]

  ●  Persistent link:
  ●  XML Dublin Core code for metadata harvesting

Recommended for You

This video is presented here with the permission of the speakers. Any downloading, storage, reproduction, and redistribution are strictly prohibited without the prior permission of the respective speakers. Go to Full Disclaimer.

  For enquiries, please contact Digital and Multimedia Services Section

© 2009-2023 All rights reserved