Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-11T09:18:10.954Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Representation of Circles by means of Points in Space of Three Dimensions

Published online by Cambridge University Press:  03 November 2016

D. Pedoe
Get access Rights & Permissions [Opens in a new window]

Extract

The idea of the representation of a linear system of plane curves by means of a flat space is of fundamental importance in algebraic geometry. In this paper some details of the representation of circles are worked out, and an attempt is made to give a three-dimensional picture of certain parts of circle geometry The theorems given in italics are thought to be new, although in a subject with such an enormous literature it might almost be said that no theorem can be a new one.

Type
Research Article
Information
The Mathematical Gazette , Volume 21 , Issue 244 , July 1937 , pp. 210 - 215
Copyright
Copyright © Mathematical Association 1937

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

Page no 213 note * See remark at end of paper.

Page no 214 note * This point is on the locus, for one circle of the coaxal system is orthogonal to D, and the inverse of D in this circle is D itself.

Page no 215 note * The reader may verify, that if the fixed circle be taken as

x 2+y 2+2gx+2fy+d=0,

and the coaxal system as x 2+y 2+2λx+c 2=0, the enveope is

(x 2+y 2+2λy−c 2)(x 2+y 2+2μy−c2)=0,

When λ, μ are the roots of

4t 2(d−g 2)−4ft(d−c 2)+(c 2+d)2−4c 2(f 2+g 2)=0.