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Journal for Geometry and Graphics 7 (2003), No. 1, 053--063
Copyright Heldermann Verlag 2003

Analagmatic Curves under the Isogonal Transformation

Ana Sliepcevic
Faculty of Civil Engineering, University Zagreb, Av. V. Holjevca 15, 10010 Zagreb, Croatia,

This paper treats plane curves of 3rd and 4th order generated under an isogonal transformation. It is shown by synthetic and constructive methods that there exists a variety of analagmatic curves, i.e., curves that are invariant under the isogonal transformation. Circular analagmatic curves of 3rd and 4th order are constructed as well. It is proved that there are pencils of such curves. Furthermore, for these pencils the curves of singular foci are determined.

Keywords: isogonal transformation, analagmatic curve, circular curve, singular focus.

MSC: 51N35.

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