Marden's theorem

The set of Marden (after Morris Marden ) is a mathematical theorem in the field of function theory. It describes a geometric relationship between the zeros of a polynomial of the third straight and the zeros of its derivative.

Although the set is now named after Morris Marden, his discovery does not go back to him. Marden described the result in 1945 in an article, and later in his book Geometry of Polynomials (1966 ) to use it without a special name. However, he indicates a number of previous publications, which began with a publication of Jörg Siebeck in Crelle Journal ( 1864) stands .. The representation of the sentence in an article in the American Mathematical Monthly by the mathematician Dan Kalman was in 2008 with the Lester Randolph Ford Award excellent.

Swell

  • Jörg Siebeck: About a new analytical treatment, the foci. In Journal of Pure and Applied Mathematics ( Crelle ), 1864, issue 64, pp. 175-182, ISSN 0075-4102
  • Dan Kalman: The Most Marvelous Theorem in Mathematics. In the Journal of Online Mathematics and its Applications (now loci - Online Journal of the MAA), April 2008
  • Dan Kalman: An Elementary Proof of Marden 's Theorem. The American Mathematical Monthly 115, pp. 330-338, ISSN 0002-9890
  • Morris Marden: A note on the zeroes of the sections of a partial fraction. In Bulletin of the American Mathematical Society 51 (12 ), pp. 935-940, 1945, doi: 10.1090/S0002-9904-1945-08470-5
Complex analysis Triangle Focus (geometry)
710418
de