ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXVI, (2007)
p. 241 - 246
On the Volume of the Trajectory Surfaces under the Homothetic Motions
M. Duldul and N. Kuruoglu
Abstract.
The volumes of the surfaces of 3-dimensional Euclidean Space
which are traced by a fixed point as a trajectory surface during 3-parametric
motions are given by H. R. Muller [3], [4], [5] and W. Blaschke [1].
In this paper, the volumes of the trajectory surfaces of fixed
points under 3-parametric homothetic motions are computed.
Also, using a certain pseudo-Euclidean metric we generalized
the well-known classical Holditch Theorem, [2], to the trajectory surfaces.
Keywords:
homothetic motion, Holditch theorem, volume of trajectory surface.
AMS Subject classification. Primary: 53A17.
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