Open Problems from CCCG 2008
نویسندگان
چکیده
A swimmer falls overboard in an equilateral triangle lake in a fog. If the edge length of the triangle is 1, what is the shortest length swimming path that ensures the swimmer will reach the shore? Swimming one unit straight in any direction certainly reaches the shore. The problem was originally posed in 1963. Besicovitch showed shortly afterward that a 3-link chain of length 3 √ 21/14 = 0.98198 . . . suffices [Bes65].
منابع مشابه
Open Problems: Open Problems from CCCG 2005
Consider the following special case of planar point location: preprocess k sets of lines, where each set consists of parallel lines, to support queries of the form “given a point p, what is the line immediately above or below p?” What is the fastest possible query time as a function of k and the total number n of lines? In other words, the n given lines have k distinct orientations. See Figure ...
متن کاملOpen problems from cccg 2001
Refer to Figure 1. A monotone matching is a set of n segments, each the portion of a unique pseudoline, and each spanning a unique slab, such that the left endpoint of each segment is above the right endpoint of the segment in the previous slab. In addition, the point on the first vertical line is below the left endpoint of the first segment, and the point on the last vertical line is above the...
متن کاملOpen Problems from CCCG 2007
Imagine rolling a unit sphere on a plane without slipping or twisting, so that the point of contact follows a closed curve C. The south pole touches the plane at the start. What is the shortest length L = |C| that results in the north pole touching after one complete circuit of C? Figure 1 shows a curve achieving L = 3π. Also, C cannot be shorter than the geodesic distance between the poles: L ...
متن کاملPartitioning a Polygon into Two Mirror Congruent Pieces
Polygon decomposition problems are well studied in the literature [6], yet many variants of these problems remain open. In this paper, we are interested in partitioning a polygon into mirror congruent pieces. Symmetry detection algorithms solve problems of the same flavor by detecting all kinds of isometries in a polygon, a set of points, a set of line segments and some classes of polyhedra [2]...
متن کامل