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Point Set Subsets Distance Demo

Point Set Subsets Distance Demo
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2016-12-16 21:28
FunctionCoordinate GeometryOptimizationInequalityGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates how to construct subsets of a point set where each point is at least r distance from its first point. The core mathematical concepts involved include distance calculation, set construction, and inequality representation. The construction uses GeoGebra commands and objects such as Point, Length, Sequence, RemoveUndefined, Element, Zip, and TableText to create points, calculate distances, generate sequences, and display text information. Suitable for high school students learning coordinate geometry and inequalities.

GeoGebra Commands & Parameters

  1. Point(yAxis) → U
  2. Point(xAxis) → S
  3. Length(l1t) → lä
  4. Sequence(Join[{{i}, RemoveUndefined[Sequence[If[Segment[Element[l1t, i], Element[l1t, j]] > r, NaN, j], j, i + 1, Length[l1t]]]}], i, 1, lä) → l2t
  5. RemoveUndefined(Sequence[If[Sum[Sequence[If[Length[Intersection[Element[l2t, j], Element[l2t, i]]] ≟ Length[Element[l2t, i]], 1, 0], j, 1, lä]] ≟ 1, i, NaN], i, 1, lä]) → l3t
  6. Length(l3t) → lä1
  7. Element(l1t, i) → P
  8. Sequence(Element[l2t, Element[l3t, i]], i, 1, lä1) → l4t
  9. Zip(Element[l1t, a], a, Element[l4t, c]) → l6t2
  10. Sequence(Zip[Element[l1t, a], a, Element[l4t, i]], i, 1, lä1) → l5t
  11. Element(l5t, c) → l6t1
  12. TableText({Join[{{"N"}, Sequence[i, i, 1, lä]}], Join[{{"l2t:"}, l2t}]}, "vr") → text4
  13. TableText({Join[{{"N"}, l3t}], Join[{{""}, Sequence["→", i, 1, c]}], Join[{{"l4t:"}, l4t}]}, "vr") → text5