==> pickover/pickover.06.p <== Title: Cliff Puzzle 6: Star Chambers From: cliff@watson.ibm.com If you respond to this puzzle, if possible please send me your name, address, affiliation, e-mail address. If you like, tell me a little bit about yourself so I can cite you appropriately if you provide unique information. PLEASE ALSO directly mail me a copy of your response in addition to any responding you do in the newsgroup. I will assume it is OK to describe your answer in any article or publication I may write in the future, with attribution to you, unless you state otherwise. Thanks, Cliff Pickover * * * As many of you probably know, 5-sided stars produced by drawing a continuous line with your pencil can nest inside each other. (One star can sit inside the pentagon produced by the larger star. Each of the 5 points of the small star coincide with the 5 points of the internal pentagon of the large star.) Start with a five sided star formed with 5 line segments, each 1 inch long. Continually nest stars so that the assembly of stars gets bigger and bigger. Questions: 1. How many nestings N are required to make star N have an edge-length equal to the diameter of the sun (4.5E9 feet)? 2. How many nestings N are required to make the cumulative length of lines of all the nested stars equal to the diameter of the sun?