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The Trigonometry of GF(22n) and Finite Hyperbolic Planes

Published online by Cambridge University Press:  26 February 2010

D. W. Crowe
D. W. Crowe
Affiliation:
The University of Wisconsin, Madison, Wisconsin
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Extract

In the present note we show that the elements of GF(q2) (q = 2n) can be represented in “polar form” in such a way that GF(q2) acts like an “Argand diagram” over its “real subfield” GF(q). From this polar representation it is easy to develop a trigonometry of the plane GF(q2), including definitions of circles and orthogonality. As an application of these ideas we show, in §4, that the circles and lines orthogonal to a given circle yield a new model satisfying Graves' axioms for finite homogeneous hyperbolic planes.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 83 - 88
Copyright
Copyright © University College London 1964

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References

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