Spiral Mapping Natural Numbers to Integer Coordinates
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This applet demonstrates a spiral that visits every integer lattice point in order, providing a visual bijection between the set of natural numbers and the 2D integer grid. Core concepts include natural numbers, integer lattice points, bijective mappings, parametric spiral equations, and the interplay of sequences with coordinate geometry. Construction highlights: a parameter t indexes the natural numbers; points a, p, q represent the current lattice point, previous point, and spiral center; the Sequence command generates the point list, while Locus or Slider animates the spiral trajectory. Suitable for high‑school sequences and analytic geometry, university discrete mathematics or computer science courses on countable sets, and as an introductory modeling example.
GeoGebra Commands & Parameters
Numeric a(747.0)floor(sqrt(4 * a + 1))a - floor(p^(2) / 4)q * ί^(p) + (floor((p + 2) / 4) - floor((p + 1) / 4) * ί) * ί^(p - 1)
AI Drawing Prompt Reference
Draw a spiral that visits every integer lattice point in order. The spiral is indexed by natural numbers and follows a specific sequence. Include the current point, the previous point, and the spiral center. Ensure the spiral covers the entire integer grid to show the correspondence between natural numbers and integer coordinates.
The prompt above was compiled from the original drawing commands and is for reference only.