On Sphere-Filling Ropes
نویسندگان
چکیده
What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope’s thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others exhibit a striking resemblance to Turing patterns in chemistry, or to ordered phases of long elastic rods stuffed into spherical shells. Mathematics Subject Classification (2000): 49Q10, 51M15, 51M25, 52C15, 53A04
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 118 شماره
صفحات -
تاریخ انتشار 2011