Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T17:01:30.609Z Has data issue: false hasContentIssue false

The ‘odd’ number six

Published online by Cambridge University Press:  24 October 2008

J. A. Todd
Affiliation:
Trinity CollegeCambridge

Extract

1. A few months ago, in the course of teaching an elementary class. I had occasion to discuss problems of the familiar type, ‘if α, β, γ are the roots of the equation x3 + qx + r = 0, form the equation whose roots are α2 + βγ, β2 + γα, γ2 + αβ'. After I had explained the device of replacing βγ by αβγ/α = −r/α, so that the roots of the new equation are the same rational function of the separate roots of the original equation, I was asked ‘whether such a transformation was always possible’. On investigation the answer to the question proved to be a surprising one.

Type
Research Notes
Copyright
Copyright © Cambridge Philosophical Society 1945

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Burnside, , Theory of Groups of Finite Order, 2nd ed. (Cambridge, 1911), p. 209.Google Scholar

Sylvester, , Collected Papers, 1, p. 92Google Scholar. See, e.g., Baker, , Principles of Geometry, 2 (Cambridge, 1922), p. 221Google Scholar, and some remarks by Room, , Geometry of Determinantal Loci (Cambridge, 1938), p. 301.Google Scholar

Baker, loc. cit.