Abstract
In an affine plane oriented distance d and oriented angle w (between non-oriented lines) are introduced as mapping into ℝ, fulfilling certain axioms. Examples show, that the use of w is of advantage in elementary geometry. Axiomatic consequences of generalizing d, w to mappings into ordered abelian groups are considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Birkhoff, G. D., ‘A set of postulates for plane geometry, based on scale and protractor’, Ann. Math. 33 (1933), 329–345.
Coxeter, H. S. M. und Greitzer, S. L., Zeitlose Geometrie, Stuttgart, 1983.
Freudenthal, H. und Baur, A., ‘Geometrie — phänomenologisch’, in Grundz.d.Math. (Hrsg.: Behnke u.a.) II, Göttingen, 1960.
Johnson, R. A., Advanced euclidean geometry (Modern Geometry), New York, 1960 (Nachdruck von Modern Geometry, 1929).
Hilbert, D., Grundlagen der Geometrie, Leipzig, 1903.
Kirsch, A. und Zech, F., Affine Geometrie der Ebene, Stuttgart, 1972.
Lambacher, Th. und Schweizer, W., Geometrie 1A, Stuttgart, 1968.
Pickert, G., Analytische Geometrie, Leipzig, 1952 (1976).
Pickert, G., Metrische Geometrie, Stuttgart, 1983.
Schupp, H., Kegelschnitte, Mannheim, 1988.
Steiner, H.-G., ‘Explizite Verwendung der reellen Zahlen in der Geometrie’, Der Mathematikunterricht, 1963, Heft 4, S.66–87 (Klett, Stuttgart).
Author information
Authors and Affiliations
Additional information
Herrn Helmut Salzmann zum 60. Geburtstag
Rights and permissions
About this article
Cite this article
Pickert, G. Winkelmessung und Orientierung. Geom Dedicata 36, 239–260 (1990). https://doi.org/10.1007/BF00150792
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00150792