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!
The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. CMJ publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.