MathPlotAI Logo MathPlotAI

Synergistic Cartesian Prime Integers V1.1

Synergistic Cartesian Prime Integers V1.1
Loading the math board and drawing, please wait…
2019-08-13 18:50
TrigonometryCoordinate GeometryProbability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates the synergistic distribution and visualization of prime integers in Cartesian coordinates. Core math concepts include prime number identification, Cartesian coordinate systems, random experiments, subtraction operations, and scatter plots. Construction highlights involve commands like Segment, Join, Flatten, Point, with objects such as sv, ev, xp, yp, zp, inc, fine, ps_{01}, a, c, text1, A, B, seg_{real025}, C, D, seg_{real075}, text3, button1, L_{Fib}, Origin, List_{Prime-Ints}, b, d, L_3b, L_1c, L_1a, L_1w, L_1b, L_2b, ps_{02}, L_2a, text4, E, L_{zeros}, View_1. Ideal for high school mathematics instruction and number theory enthusiasts.

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_{Prime-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_{Prime-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_{Prime-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_{Prime-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_{Prime-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. Join(Sequence[Sequence[RemoveUndefined[Sequence[If[k + j + i ∈ List_{Prime-Ints} ≠ 1, Sphere[(k, j, i), abs(ps_{02} - 0.01)]], i, sv, ev, inc]], j, sv, ev, inc], k, sv, ev, inc]) → L_2a
  10. Point(zAxis) → E
  11. 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}