分组计数：如何分组？——可视化除法与乘法

GeoGebra 命令及参数

1. Element({11, 17, 25}, max) → boundary
2. Random(Element[{2, 20, 50}, max] + 1, Element[{20, 50, 120}, max]) → number
3. First(Shuffle[Flatten[Sequence[Sequence[Point[{i, j}], i, 0, boundary, 2], j, 0, boundary, 2]]], number) → origPoints
4. Sequence(Distance[(0, 0), Element[origPoints, i]], i, 1, number) → origPointsDist
5. Sort(origPoints, origPointsDist) → sortedOrig
6. If(groupSize > 0, Div[number, groupSize], 0) → groupsNeeded
7. If(groupSize ≟ 0 ∨ (¬Defined[groupSize]), {}, If[groupSize ≟ 5, {(0, 0), (1, 0), (2, 0), (3, 0), (4, 0)}, If[groupSize ≟ 10, {(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (0, 1), (1, 1), (2, 1), (3, 1), (4, 1)}, First[Flatten[Sequence[Sequence[Point[{i, j}], i, 0, ceil(groupSize^(0.5)) - 1], j, 0, ceil(groupSize^(0.5)) - 1]], groupSize]]]) → groupedSet
8. If(Defined[groupSize] ∧ groupSize > 0, Max[Zip[x(AAA), AAA, groupedSet]] + 1, 0) → groupX
9. If(groupSize > 0 ∧ Defined[groupSize], Max[Zip[y(AAA), AAA, groupedSet]] + 1, 0) → groupY
10. Div(boundary, groupX + 1) → horizontalGroups
11. Div(boundary, groupY + 1) → verticalGroups
12. If(groupSize ≥ 1, First[Flatten[Sequence[Sequence[groupedSet + ((i * (groupX + 1)), (j * (groupY + 1))), i, 0, horizontalGroups - 1], j, 0, verticalGroups]], (groupSize * groupsNeeded)], {}) → groupedAnchors
13. Zip(Distance[AAA, (0, 0)], AAA, groupedAnchors) → groupedDist
14. If(groupSize > 0 ∧ groupSize ≤ number, Max[Zip[y(AAA), AAA, groupedAnchors]] + 2, 0) → singlesStarter
15. Zip(Polygon[AAA, AAA + (1, 0), 4], AAA, movingPoints) → movingPolygons
16. Textfield(groupSize) → InputBox1
17. If(groupSize ≟ 0 ∨ groupSize ≟ 1 ∨ (¬Defined[groupSize]), {}, First[Flatten[Sequence[Sequence[Point[{i, j}], i, 0, boundary - 1, 2], j, singlesStarter, boundary - 1, 2]], number - (groupsNeeded * groupSize)]) → singles
18. If(¬Defined[groupSize], sortedOrig, If[groupSize > 0 ∧ groupSize ≤ number, Sort[groupedAnchors, groupedDist], {}]) → sortedGroup