Winding Number and the Number of Real Zeroes of a Function


Lieven Smits and W. Kuyk (in real life, Willem Kuijk - here are a few of his many works)

Bibliographical Reference

Proceedings of the American Mathematical Society, volume 114, number 4 (April 1992), pages 981-987.


The theorem in this paper shows that the number of real simple zeros of a function of the form

f(x) = q(x) + ax + b, x R,
for not too wild q(x) can be obtained counting the winding number of a closed plane curve about the point (a, b).

AMS Subject Classifications (1985)

26C10, 12D10.


There are a few reprints left. If your library does not have this particular journal issue, ask for a reprint by emailing me your postal address. Remove "unwanted" from the address below.


  1. Kuyk, Willem and Smits, Lieven, On the Geometries of the Rational Unfoldings of ±Xk, Acta Applic. Math. 19 (1990), 77-86.

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