Learn
Read the rule.
A short introduction to rows, columns, modular wrapping and phase, with a worked example.
Learn the constructionFinite rules. Open questions.
Naglich Squares
Modular arithmetic, symmetry, phase, and structure.
Explore arithmetic grids. Follow the rule, change a parameter, and see what happens.
Open the explorerA(r,c,k,N) · a notation for exploration
01 / BEGINStart with
Start with
something exact.
A grid becomes easier to understand when its size, indexing and arithmetic rule are explicit. Start small, then compare.
Explore
Change one thing.
Choose a grid size, move through phases and inspect the arithmetic behind a cell.
Try the TLF explorerInvestigate
Ask a better question.
Separate the construction you can specify from a pattern you observe and a statement you can prove.
Results and open questions02 / THE INSTRUMENTSOne rule.
One rule.
More ways to see.
Read a plane, compare an orientation or separate the phases in space. Each view keeps its construction in reach.
03 / PERSPECTIVEA pattern starts
A pattern starts
a question.
It does not finish the argument. Definitions, finite checks and mathematical proofs answer different questions.
Research with a clear scope.
The tools state their arithmetic and indexing. An attractive image is an invitation to investigate, not evidence for a physical or computational application.
From small hand-drawn grids to interactive instruments: follow the development of Naglich Squares, with mathematical questions and exploratory interpretations kept distinct.
Learn the notation, inspect the formulas and read the story here.