Marden's theorem [SEP] named after
Marden's theorem
In mathematics, Marden's theorem, named after Morris Marden but proved much earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative. See also Geometry of roots of real polynomials.
Statement of the theorem.
A cubic polynomial has three zeroes in the complex number plane, which in general form a triangle, and the Gauss–Lucas theorem states that the roots of its derivative lie within this triangle. Marden
Bernoulli since l'Hôpital, a nobleman, paid Bernoulli a retainer of 300 francs per year to keep him updated on developments in calculus and to solve problems he had. See L'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes and reference therein.
- Maclaurin series. The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published this special case of the Taylor series in 1742, but never claimed to have discovered it.
- Marden's theorem. This theorem relating the location of the zeros of a