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A Property of Linear Cyclic Transformations

Published online by Cambridge University Press:  03 November 2016

J.H. Cadwell
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Extract

The mid-points of the sides of any quadrilateral form a parallelogram. Repeated applications of this inscription process will lead to two families of similar and similarly situated figures. It is proved below that the general n-sided polygon lying in space of h dimensions gives rise to similar sequences in the limit. If the initial polygon is not re-entrant convergence is rapid, as will be seen from Figures 1 and 5. The parallelogram is replaced by the affine transformation of a regular polygon lying in a plane.

Type
Research Article
Information
The Mathematical Gazette , Volume 37 , Issue 320 , May 1953 , pp. 85 - 89
Copyright
Copyright © The Mathematical Association 1953

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