2024/12/23 by Kanungo, Shihan
Engineering · #26-01 #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.2501.04705
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine space-filling curves, which are surjective continuous maps from [0,1] to some higher-dimensional space, usually the unit square [0,1]2. In particular, we define Peano's curve and Lebesgue's curve, and state some of their properties. We also discuss the Hahn-Mazurkiewicz theorem, which characterizes those subsets of ℝn that are the image of a space-filling curve. Finally, we discuss real-world applications of Hilbert curves, in particular Google's S2 Cells.