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Visualizing Divisibility

Visualizing Divisibility
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2016-08-17 23:43
FunctionCoordinate GeometryCalculusParametric EquationGeometric Construction
In collections CBSE Class VI Maths Multiplication and Division - Visuals Multiplication and Division - Visuals Multiplication and Division - Visuals
This example demonstrates integer division and remainder through dynamic geometry, involving logarithmic functions, indefinite integrals, exponentials, polynomials, and parametric equations. It uses GeoGebra commands like Textfield, If, Sequence, and objects such as n and divisor to create interactive visualizations. Suitable for high school and above, helping learners grasp geometric interpretations of division and parametric equations.

GeoGebra Commands & Parameters

  1. Textfield(nText) → InputBox1
  2. If(n / divisor ≟ floor(n / divisor), false, true) → hasR
  3. Sequence(((-columns)) / 2 + i - 1 / 2, i, 1, columns) → xValues
  4. Sequence(((-divisor) - 1) / 2 + i, i, 1, divisor) → yValues
  5. First(Flatten[Sequence[Sequence[Point[{xValues(i), yValues(j)}], j, 1, Length[yValues]], i, 1, columns]], n) → list2
  6. If(hasR, First[list2, (divisor * Div[n, divisor])], list2) → dividendList
  7. Last(list2, n - (divisor * Div[n, divisor])) → remainderList
  8. Min(xValues) → left
  9. Max(xValues) → right
  10. Min(yValues) → bottom
  11. Max(yValues) → top
  12. Sequence(Circle[Element[dividendList, i], 0.4], i, 1, Length[dividendList]) → dividendCircles
  13. Sequence(Circle[Element[remainderList, i], 0.4], i, 1, Length[remainderList]) → remainderCircles
  14. Segment((left, bottom) + (-1 / 2, -1 / 2), (right, bottom) + (1 / 2, -1 / 2)) → i
  15. Segment((left, top) + (-1 / 2, 1 / 2), (right, top) + (1 / 2, 1 / 2)) → j
  16. Sequence(Segment[(left + i, bottom) + (-1 / 2, -1 / 2), (left + i, top) + (-1 / 2, 1 / 2)], i, 0, Length[xValues]) → dividendBoxes
  17. Text(If[hasR, " + " + (Mod[n, divisor]), ""]) → text4
  18. Sequence(Circle[Element[moving, i], 0.4], i, 1, Length[moving]) → movingCircles