Eighty-eight Thousand, Four Hundred and Eighteen (More) Ways to Fill Space

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After Peano gave an arithmetic construction, Hilbert developed a geometric construction for space-filling curves. This paper describes the key idea of Hilbert's construction, here called 'the nested-squares criterion,' implicit in Hilbert's writing but, once explicated, generalizes to a whole class of space-filling curves that correspond to a special class of rook's walks enumerated by Mobius 150 years ago!

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/193113409X469541

Publication date: March 1, 2009

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