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- W2222358822 abstract "Given a point (the spider) on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the fly - the reflection of the spider across the center of the box). Without loss of generality, we can assume that the box has dimensions $1times atimes b$ with the spider on one of the $1times a$ faces (with $aleq 1$). The shortest path between the points is always a line segment for some planar flattening of the box by cutting along edges. We then partition the $1times a$ face into regions, depending on which faces this path traverses. This choice of faces determines an algebraic distance formula in terms of $a$, $b$, and suitable coordinates imposed on the face. We then partition the set of pairs $(a,b)$ by homeomorphism of the borders of the $1times a$ face's regions and a labeling of these regions." @default.
- W2222358822 created "2016-06-24" @default.
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- W2222358822 creator A5071293587 @default.
- W2222358822 date "2015-02-03" @default.
- W2222358822 modified "2023-09-27" @default.
- W2222358822 title "The distance from a point to its opposite along the surface of a box" @default.
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- W2222358822 hasPublicationYear "2015" @default.
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