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, we illustrate which shapes have larger isoperimetric ratio than the threshold 20.784, with real street patterns. Finally, we discuss possible application to measuring redundancy of street patterns.
