Geometrical redundancy of street patterns based on threshold of isoperimetric ratio
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Tokyo, Japan
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Tokyo, Japan GREE, Inc., Tokyo, Japan
ABSTRACT: The isoperimetric ratio of a given planar closed curve is the ratio of the square of the perimeter to the area. We show the following theorem: (1) Any convex quadrilateral is affine-equivalent to a quadrilateral whose isoperimetric ratio is less than 20.784. (2) The above result is optimal. And, we propose to use 20.784 as a threshold when we judge that a given polygon is not a succinct quadrilateral. In particular, ...
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