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Journal for Geometry and Graphics 22 (2018), No. 2, 207--218
Copyright Heldermann Verlag 2018

A Study of Paths Formed by Directed Arcs and Line Segments

Jun Mitani
Faculty of Engineering, University of Tsukuba, 1-1-1 Tennohdai, Tsukuba City - Ibaraki 3058573, Japan

We study paths formed by directed arcs and line segments in the real plane R2. The central angle and radius of the arc that we consider are π/4 and 1, respectively, and the length of the line segments is 1. We are interested in the properties of the paths that are formed by these elements. We derive the conditions that determine which locations can be reached with these paths, and a method for constructing a path to an arbitrary location within a specified distance tolerance. We also show that the number of elements in a closed path is even. Further, we show that any open path can be closed by connecting eight or fewer identical paths.

Keywords: Path, arc, line segment.

MSC: 51M04; 68U05

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