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On seeing progressions of constant cross ratio. (English) Zbl 0851.40003
The author introduces the classes of geometric, artistic and melodic progressions. A progression is called artistic if every three successive terms $$a$$, $$b$$, $$c$$ have a common bias $$Q[a, b, c]= (ac- b^2)/ abc$$. Taking reciprocal values of terms of an artistic progression we obtain a melodic progression. Some properties and applications of artistic and melodic progressions are demonstrated.
##### MSC:
 40A05 Convergence and divergence of series and sequences
##### Keywords:
progressions; artistic progression; melodic progression
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