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Positive Cartesian Integers V1.1

Positive Cartesian Integers V1.1
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2019-08-19 21:09
Coordinate GeometryOptimization
This example demonstrates the construction of positive Cartesian integers. Key mathematical concepts include integers, equations, arithmetic, and optimization. Using GeoGebra commands such as Segment, Join, and Flatten, the example provides a visual understanding of these concepts. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → seg_{real025}
  2. Segment(C, D) → seg_{real075}
  3. Join(Sequence[Sequence[Sequence[If[true, Text["(" + (k) + " + " + (j) + " + " + (i) + ") = " + (k + j + i) + " ", (k + xp, j + yp, i + zp), true, true]], i, sv, ev, inc], j, sv, ev, inc], k, sv, ev, inc]) → L_3b
  4. Join(Sequence[Sequence[Sequence[If[k + j + i ∈ List_{Odd-Ints}, Vector[Origin, (k + xp, j + yp, i + zp)]], i, sv, ev, inc], j, sv, ev, inc], k, sv, ev, inc]) → L_1c
  5. Join(Sequence[Sequence[Sequence[If[k + j + i ∈ List_{Odd-Ints}, Sphere[(k + xp, j + yp, i + zp), abs(ps_{01})]], i, sv, ev, inc], j, sv, ev, inc], k, sv, ev, inc]) → L_1a
  6. Flatten(Join[Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Odd-Ints}, k + j + i], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]]) → L_1w
  7. Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Odd-Ints} ≠ 0, Text["(" + (k) + " + " + (j) + " + " + (i) + ") = " + (k + j + i) + " ", (ps_{01} + k + xp, ps_{01} + j + yp, ps_{01} + i + zp), true, true]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_1b
  8. Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Odd-Ints} ≠ 1, Text["(" + (k) + " + " + (j) + " + " + (i) + ") = " + (k + j + i) + " ", (ps_{01} + k + xp, ps_{01} + j + yp, ps_{01} + i + zp), true, true]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_2b
  9. Point(zAxis) → E
  10. Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ≟ 0, Sphere[(k, j, i), abs(ps_{02} - 0.009)]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_{zeros}
  11. Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Even-Ints} ≠ 0, Sphere[(k, j, i), abs(ps_{02} - 0.01)]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_2a