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A new sequence of minima in the geometry of numbers

Published online by Cambridge University Press:  24 October 2008

A. M. Macbeath
A. M. Macbeath
Affiliation:
Clare CollegeCambridge
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Extract

The problem of evaluating the non-homogeneous critical determinant of the plane region |y − x2| ≤ 1 is solved as a particular case of a result concerning the non-homogeneous properties of convex regions proved in the author's thesis (not yet published). The search for an alternative method of proof led to a proof of the existence of an infinite sequence of minima analogous to the Markoff chain. This is the subject of the present paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 2 , April 1951 , pp. 266 - 273
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

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