A Page on the Tschirnhausen Transformation

There are two papers here:

1. "A New Way To Derive The Bring-Jerrard Quintic In Radicals" by Titus Piezas III ABSTRACT: We derive, in radicals, the Bring-Jerrard quintic using a cubic Tschirnhausen transformation instead of the usual quartic transformation which is essentially the method employed by Erland Bring (1736-1798) and George Jerrard (1804-1863).  Certain limitations of the new method as applied to higher degrees will also be discussed. Mathematics Subject Classification: Primary: 12E12.

Tschirnhausen.html

Tschirhausen.pdf

2. "Deriving The Bring-Jerrard Quintic Using A Quadratic Transformation" ABSTRACT:  It can be shown that by passing through the Brioschi quintic form, a quadratic transformation can suffice to transform in radicals the general quintic to the Bring-Jerrard form.  This is in contrast to the quartic transformation found by Erland Bring and independently by George Jerrard, and the cubic one recently found by this author. A new one-parameter quintic form (z-5)(z^2+15)^2 + p = 0 which the general quintic can be reduced to in radicals will also be discussed.

Brioschi.html

Brioschi.pdf

See also: http://mathworld.wolfram.com/topics/Piezas.html

Brioschi Page

More Quintics Page

For an index of papers visit the Homepage

This webpage was born Mar. 20, 2006.