The theory of the surface area of plane polygons: some steps in the mathematization of a graphic concept. (Die Lehre vom Flächeninhalt ebener Polygone: Einige Schritte in der Mathematisierung eines anschaulichen Konzeptes.) (German) Zbl 0966.01005

The concepts of equidecomposability and equicomplementability for plane polygons and the relation to the concept of area measure are described in their historical development. Especially the work of Euclid, Legendre, Gerwien, Duhamel and Hilbert is discussed and, for the corresponding development in spherical, hyperbolic and absolute geometry, the work of Gérard, Liebmann and Finzel.
Reviewer: E.Heil (Darmstadt)


01A05 General histories, source books
51F20 Congruence and orthogonality in metric geometry
52-03 History of convex and discrete geometry
52A38 Length, area, volume and convex sets (aspects of convex geometry)
28A75 Length, area, volume, other geometric measure theory
00A35 Methodology of mathematics
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