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The sequence of generalized median triangles and a new shape function

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Abstract

Starting with a triangle ABC and a real number s, we let AA s , BB s , CC s be the cevians that divide the sides BC, CA, AB, respectively, in the ratio s : 1 − s, and we let \({\mathcal{H}_s(ABC)}\) be the triangle whose side lengths are equal to those of AA s , BB s , CC s . We investigate the sequence of (the shapes of) triangles \({\mathcal{H}_s^n(ABC)}\) , n = 1, 2, ... by introducing a new shape function that suits this sequence. We also use this shape function to prove a theorem of C. F. Parry concerning automedian triangles.

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Authors and Affiliations

  1. Mathematics Department, Yarmouk University, Irbid, Jordan

    Mowaffaq Hajja

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  1. Mowaffaq Hajja
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Correspondence to Mowaffaq Hajja.

Additional information

This work was supported by a research grant from Yarmouk University.

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Hajja, M. The sequence of generalized median triangles and a new shape function. J. Geom. 96, 71–79 (2009). https://doi.org/10.1007/s00022-010-0036-0

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  • DOI: https://doi.org/10.1007/s00022-010-0036-0

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