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Generalized Regularity and the Symmetry of Branches of ''Botanological'' Networks

2021
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KoG
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We derive the generalized regularity of convex quadrilaterals in R^2, which gives a new evolutionary class of convex quadrilaterals that we call generalized regular quadrilaterals in R^2. The property of generalized regularity states that the Simpson line defined by the two Steiner points passes through the corresponding Fermat-Torricelli point of the same convex quadrilateral. We prove that a class of generalized regular convex quadrilaterals consists of convex quadrilaterals, such that their

doi:10.31896/k.25.6
fatcat:sgmwmncsvzgvrhj7w53m45epza