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Two and three dimensional regions from homothetic motions. (English) Zbl 1222.53011

The area of the swept region obtained by 1-parametric planar homothetic motions and the volume of the region swept under spatial homothetic motions are studied. The polar moment of inertia of a planar region swept by a line segment under a Frenet motion is given. In the last section, the author obtains a volume formula of the region swept by a fixed rectangle under 1-parametric homothetic motions in Euclidean 3-space.

MSC:

53A17 Differential geometric aspects in kinematics
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