AWhat changed
Peano explicitly constructs a continuous mapping from the closed unit interval onto the whole unit square through ternary digits and parity-controlled complements, showing that continuity alone does not restrict a parametrized curve to an arbitrarily small enclosing area.
Scientific scope
Peano explicitly constructs a continuous mapping from the closed unit interval onto the whole unit square through ternary digits and parity-controlled complements, showing that continuity alone does not restrict a parametrized curve to an arbitrarily small enclosing area. Exact 1890 Mathematische Annalen 36(1),157-160 paper. formula glyphs were not visually certified. The mapping is continuous and onto, not a one-to-one continuous correspondence or a claim that dimension is preserved by arbitrary continuous maps. Parity-controlled digit complements and agreement at the two ternary representations of triadic rationals are essential; naive digit interleaving fails. The argument concerns continuous parametrizations: ordinary graphs and coordinates of bounded variation retain stronger restrictions. The final page also gives a cube construction. Original claims about nondifferentiability and exact preimage multiplicities were read but not independently reconstructed; no universal assertion about all space-filling curves is inferred. Cantor's earlier set-theoretic bijection, Netto's continuity obstruction for such a bijection, Hilbert's 1891 construction and Peano's 1908 visualizations remain distinct. This original paper is arithmetic and contains no curve illustration. Bounded exact rational representation checks illustrate the repair; they are not a full proof audit or a finite grid used as evidence of complete area coverage. January 1890 is the manuscript signature; publisher metadata gives March 1890. Later algorithms and applications keep separate credit.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Giuseppe Peano · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Peano, Sur une courbe, qui remplit toute une aire plane; exact 1890 original hosted by University of Edinburgh
- Crossref identity for the exact 1890 Peano space-filling paper
- University of Florence mathematical history entry: Giuseppe Peano and the 1890 space-filling note
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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