On Sylvester’s problem and Haar spaces

Peter B. Borwein

Vol. 109 (1983), No. 2, 275–278

DOI: 10.2140/pjm.1983.109.275

Abstract

Given a finite set of points in the plane (with distinct x coordinates) must there exist a polynomial of degree n that passes through exactly n + 1 of the points? Provided that the points do not all lie on the graph of a polynomial of degree n then the answer to this question is yes. This generalization of Sylvester’s Problem (the n = 1 case) is established as a corollary to a version of Sylvester’s Problem that holds for certain finite dimensional Haar spaces of continuous functions.

Mathematical Subject Classification 2000

Primary: 52A37

Milestones

Received: 15 June 1981

Published: 1 December 1983