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The Tracing of Cubic Curves

Published online by Cambridge University Press:  03 November 2016

E. H. Neville
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Extract

1. We all know that if we wish to sketch a cubic curve such as

xy (x + 2y − 1 ) = 2x − 3y + 4,

the first thing to do is to draw the three asymptotes and the satellite. These divide the plane into eleven compartments, and the simple consideration that there can be no points of the curve in a compartment throughout which xy (x + 2y − 1 ) and 2x − 3y + 4 have different signs enables us at once to rule out six of the compartments, and so to see how the curve goes to infinity.

Type
Research Article
Information
The Mathematical Gazette , Volume 18 , Issue 230 , October 1934 , pp. 258 - 266
Copyright
Copyright © Mathematical Association 1934

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References

Page 259 of note * With reference to one of his own examples (Pl. 10, Fig. 2), a curve of degree six, Frost can say only “I find no isolated oval, after trying several search-lights”.