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Cubes Demonstration

Cubes Demonstration
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2018-12-19 07:45
SequenceCoordinate GeometrySolid GeometryCalculus
This example demonstrates the construction and properties of cubes, involving core math concepts like solid geometry, sequences, and coordinate geometry. It uses commands such as Sequence, Sort, Remove, and objects like n, originPoints, and keepTheseCubes. Suitable for high school and above to understand 3D shapes and Riemann Sum in calculus.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Sequence[Point[{i, j, k}], i, ((-n)) / 2, n / 2 - 1], j, ((-n)) / 2, n / 2 - 1], k, ((-n)) / 2, n / 2 - 1) → originPoints
  2. Sort(Flatten[Join[{{{Sequence[{(n * i) + 1, (n * (i + 1))}, i, 1, n - 2], Sequence[n^(3) + 1 - {(n * i) + 1, (n * (i + 1))}, i, 1, n - 2]}, Sequence[Sequence[i, i, Element[threeFaces, k] + 1, Element[threeFaces, k + 1] - 1], k, 1, Length[threeFaces], 2]}, Sequence[{(i * n^(2)) + 1, (i * n^(2)) + n, ((i + 1) * n^(2)) - n + 1, ((i + 1) * n^(2))}, i, 1, n - 2]}]]) → twoFaces
  3. Sort(Flatten[Sequence[Sequence[Sequence[{(k * n^(2)) + (i * n) + j}, k, 1, n - 2], i, 1, n - 2], j, 2, n - 1]]) → noFaces
  4. Remove(Sequence[i, i, 1, n^(3)], Flatten[Join[{noFaces, twoFaces, threeFaces}]]) → oneFace
  5. Element({noFaces, oneFace, twoFaces, threeFaces, Sequence[i, i, 1, n^(3)]}, i + 1) → keepTheseCubes
  6. Element({{}, KeepIf[x ≤ n^(2), oneFace], KeepIf[x ≤ n^(2), twoFaces], KeepIf[x ≤ n^(2), threeFaces], Sequence[i, i, 1, n^(2)]}, i + 1) → keepTheseColors
  7. RemoveUndefined(Flatten[Sequence[Sequence[Element[spacedPoints, i + j], i, 1, n], j, 0, Length[spacedPoints], n^(2)]]) → frontPoints
  8. Sequence(Element[Sequence[Polygon[Element[backPoints, i], Element[backPoints, i] + (1, 0, 0), Element[backPoints, i] + (1, 0, 1), Element[backPoints, i] + (0, 0, 1)], i, 1, Length[backPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → back
  9. Sequence(Element[spacedPoints, i], i, 1, n^(3), n) → leftPoints
  10. Flatten(First[spacedPoints, n^(2)]) → bottomPoints
  11. Sequence(Element[Sequence[Polygon[Element[frontPoints, i], Element[frontPoints, i] + (1, 0, 0), Element[frontPoints, i] + (1, 0, 1), Element[frontPoints, i] + (0, 0, 1)], i, 1, Length[frontPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → front
  12. Sequence(Element[Sequence[Polygon[Element[rightPoints, i], Element[rightPoints, i] + (0, 1, 0), Element[rightPoints, i] + (0, 1, 1), Element[rightPoints, i] + (0, 0, 1)], i, 1, Length[rightPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → right
  13. Sequence(Element[Sequence[Polygon[Element[topPoints, i], Element[topPoints, i] + (1, 0, 0), Element[topPoints, i] + (1, 1, 0), Element[topPoints, i] + (0, 1, 0)], i, 1, Length[topPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → top
  14. Sequence(Element[Sequence[Polygon[Element[bottomPoints, i], Element[bottomPoints, i] + (1, 0, 0), Element[bottomPoints, i] + (1, 1, 0), Element[bottomPoints, i] + (0, 1, 0)], i, 1, Length[bottomPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → bottom
  15. Sequence(Element[Sequence[Polygon[Element[leftPoints, i], Element[leftPoints, i] + (0, 1, 0), Element[leftPoints, i] + (0, 1, 1), Element[leftPoints, i] + (0, 0, 1)], i, 1, Length[leftPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → left
  16. Sequence(Element[Sequence[Cube[Element[spacedPoints, i], Element[spacedPoints, i] + (1, 0, 0), Element[spacedPoints, i] + (1, 1, 0)], i, 1, Length[spacedPoints]], Element[keepTheseCubes, j]], j, 1, Length[keepTheseCubes]) → allSmallCubes

AI Drawing Prompt Reference

Create a demonstration of cubes, showing their construction and properties. Generate a grid of cube vertices first. Then, draw the faces of the cubes based on visibility, distinguishing single, double, triple, and fully visible faces. Use different colors to mark these faces and ensure each small face of the cubes is correctly displayed. Finally, combine all the small cubes to form a complete set of cubes, demonstrating solid geometry and sequence concepts.
The prompt above was compiled from the original drawing commands and is for reference only.