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Deciding whether the frontier of a regular tree is scattered

Bloom S.L., Esik Z.

Fundamenta Informaticae

2003

Vol. 55, nr 1

1-21

Geometrical aspects of a relation ordering the field of complex numbers

Kaczmarek J.

Zeszyty Naukowe. Geometria / Politechnika Poznańska

2002

Nr XXII

39-52

In the paper the properties of a relation that linearly ordered the set of complex numbers, are discussed. Further, the notions of imaginary vector direction, orientation of the space and the distance between imaginary points are introduced too. It's shown that a real, non-degenerate conic section, defined by the use of focuses, is identical to that one, defined by a second order equation if the conic is a circle, a parabola or if the points in discussion are real points only. The opportunity of using the imaginary elements causes that for an ellipse and hyperbola the two definitions are note equivalent.