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Exploring Division with Geometry

Exploring Division with Geometry
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2016-09-02 00:14
Probability & Statistics
In collections Multiplication and Division - Visuals Multiplication and Division - Visuals
This example uses geometric shapes to illustrate the concept of division. It involves core concepts from geometry and probability & statistics. Using GeoGebra commands such as If, Sequence, Flatten, etc., dynamic geometric figures can be constructed. Suitable for middle school and above students or teachers for teaching or self-study.

GeoGebra Commands & Parameters

  1. If(a1 / a2 < 6, 1, If[a1 / a2 < 11, 2, 3]) → groupLayoutSizes2
  2. First(Flatten[Sequence[Sequence[Point[{i, j}], i, (0.5 * a1 / quotativeGPR), a1, a1 / quotativeGPR], j, ((-0.5 * a1)) / quotativeGPR - 1, ((-0.5 * a1)) / quotativeGPR - 1 - (a1 / quotativeGPR * (groupLayoutSizes2 - 1)), ((-a1)) / quotativeGPR]], q) → quotativeGroupCenters
  3. If(a2 > 2 ∧ q > 2, 0.5, 0.4) → polySize
  4. Sequence(Point[{i, 0}], i, 0, a1 - 1) → arrayPoints
  5. If(a2 < 6, 1, If[a2 < 11, 2, 3]) → groupLayoutSizes1
  6. Flatten(Sequence[Sequence[Point[{i, j}], i, (0.5 * a1 / partitiveGPR), a1, a1 / partitiveGPR], j, ((-0.5 * a1)) / partitiveGPR - 1, ((-0.5 * a1)) / partitiveGPR - 1 - (a1 / partitiveGPR * (groupLayoutSizes1 - 1)), ((-a1)) / partitiveGPR]) → partitiveGroupCenters
  7. Textfield(a1text) → InputBox0
  8. Textfield(a2text) → InputBox1
  9. Max(a1, a2) → arraySize
  10. Flatten(Sequence[Sequence[Element[partitiveGroupCenters, i] - (polySize / 2, polySize / 2) + (((1 - q) / q * (0.4 * a1 / partitiveGPR)) * (cos(((2 * π / q) * j)), sin(((2 * π / q) * j)))), j, 0, q - 1], i, 1, Length[partitiveGroupCenters]]) → partitiveGroupDots
  11. Min((-0.1 * a1), -2) → left
  12. If(c, (((-a1)) / partitiveGPR * groupLayoutSizes1) - 1, If[a, (((-a1)) / quotativeGPR * groupLayoutSizes2) - 1, 0]) → bottom
  13. Flatten(Sequence[Sequence[Element[quotativeGroupCenters, i] - (polySize / 2, polySize / 2) + (quotativeDistance * (cos(((2 * π / a2) * j) + π), sin(((2 * π / a2) * j) + π))), j, 0, a2 - 1], i, 1, Length[quotativeGroupCenters]]) → quotativeGroupDots
  14. Max((1.1 * a1), 2) → right
  15. Sequence((Element[arrayPoints, i] * (1 - timer2)) + (Element[quotativeGroupDots, i] * timer2), i, ((test - 1) * a2) + 1, (test * a2)) → movingQuotativeDots
  16. Sequence(Polygon[Element[arrayPoints, i], Element[arrayPoints, i] + (polySize, 0), 4], i, 1, a1) → fixedArrayPolys
  17. Last(fixedArrayPolys, a1 - (test * a2)) → quotativeRemainingPolys
  18. Last(fixedArrayPolys, a1 - (ms * a2)) → partitiveRemainingPolys
  19. If(a, quotativeDistance + 1 / 2, (0.5 * a1 / partitiveGPR) - 1 / 5) → PCS
  20. If(ms > 0, Sequence[Polygon[Element[movingPartitiveDots, i], Element[movingPartitiveDots, i] + (polySize, 0), 4], i, 1, Length[movingPartitiveDots]], {}) → movingPartitiveArrays
  21. Sequence(Sequence[Polygon[Element[partitiveGroupDots, i], Element[partitiveGroupDots, i] + (polySize, 0), 4], i, k, a1, q], k, 1, ms - 1) → partitiveGroupedPolys
  22. First(Sequence[Circle[Element[partitiveGroupCenters, i], PCS], i, 1, Length[partitiveGroupCenters]], circleTimer) → partitiveGroupCircles
  23. First(Sequence[Polygon[Element[quotativeGroupDots, i], Element[quotativeGroupDots, i] + (polySize, 0), 4], i, 1, (a2 * q)], (a2 * circleTimer)) → quotativeGroupedPolys
  24. If(ms > 0, Sequence[Polygon[Element[movingQuotativeDots, i], Element[movingQuotativeDots, i] + (polySize, 0), 4], i, 1, Length[movingQuotativeDots]], {}) → movingQuotativeArrays
  25. First(Sequence[Circle[Element[quotativeGroupCenters, i], PCS], i, 1, Length[quotativeGroupCenters]], circleTimer) → quotativeGroupCircles

AI Drawing Prompt Reference

Illustrate division using geometric shapes with two dynamic point grids, one distributed proportionally and the other equally partitioned. The centers of the grids have circular markers with lines connecting the points. Include a grid background with scale marks on the left and bottom. The point grids change over time, some disappear, demonstrating the concept dynamically.
The prompt above was compiled from the original drawing commands and is for reference only.