Abstract
The formal properties of orbits in a plane are explored by elementary topology. The notions developed from first principles include: convex and polygonal orbits; convexity; orientation, winding number and interior; convex and star-shaped regions. It is shown that an orbit that is convex with respect to each of its interior points bounds a convex region. Also, an orbit that is convex with respect to a fixed point bounds a star-shaped region.
Biological considerations that directed interest to these patterns are indicated, and the implications of the prospect of higher orders of star-shapedness mentioned.
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Berger, K.R., Murphy, E.A. Angular homeostasis: III. The formalism of discrete orbits in ontogeny. Theor Med Bioeth 10, 339–353 (1989). https://doi.org/10.1007/BF00489654
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DOI: https://doi.org/10.1007/BF00489654