journal article · cognizance · 2025

Quadralzahlen: A Rotation-Invariant Numeral System That Reduces Upside-Down Misreads in Real-World Displays

abstract

Introduces Quadralzahlen (QZ), a rotation-invariant numeral system for identifiers and state codes built to eliminate 180° misreads in rotation-rich contexts such as logistics, healthcare, and handheld UIs. QZ combines self-symmetric glyphs (0, 1, 8, X) with pairwise mappings (6–9, 3–E) plus typography and OCR guidance. In-silico evaluations show fewer upside-down confusions and flatter angle-time profiles than standard numerals, with OCR staying near ceiling at quarter turns.

@article{nguyen2025quadralzahlen,
  author = {Nguyen, Michel},
  title = {Quadralzahlen: A Rotation-Invariant Numeral System That Reduces Upside-Down Misreads in Real-World Displays},
  year = {2025},
  journal = {Cognizance},
  doi = {10.47760/cognizance.2025.v05i10.019},
  url = {https://doi.org/10.47760/cognizance.2025.v05i10.019}
}