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Division Decision

Division Decision
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2018-12-20 21:56
VectorSolid GeometryGeometric Construction
This example demonstrates the geometric representation of division and fractions in three-dimensional space, showcasing dynamic interactions between vectors and volume relationships. Core concepts include division, fractions, 3D vectors, geometric distribution, volume calculation, subtraction, and cone volume. GeoGebra commands and objects like If, First, Numerator, Denominator, Flatten, Sequence, Zip, Textfield, Length are utilized, with elements such as n1Text, n2Text, n1, n2, n1n2num. Suitable for high school and above learners to explore the integration of spatial geometry and algebraic operations.

GeoGebra Commands & Parameters

  1. If(n2Text ≠ "" ∧ floor(FromBase[n2Text, 10]) ≟ FromBase[n2Text, 10], FromBase[n2Text, 10], 1) → n2
  2. If(n1Text ≠ "" ∧ floor(FromBase[n1Text, 10]) ≟ FromBase[n1Text, 10], FromBase[n1Text, 10], 1) → n1
  3. If(n2 > n1, 1, n1^(0.5) / n2^(0.5)) → n2ArraySpacer
  4. If(n1 > n2, 1, n2^(0.5) / n1^(0.5)) → n1ArraySpacer
  5. First(Flatten[Sequence[Sequence[Point[{(i * n2ArraySpacer), (j * n2ArraySpacer)}], j, ((-(ceil(n2^(0.5)) - 1))) / 2, (ceil(n2^(0.5)) - 1) / 2], i, 1, ceil(n2^(0.5))]], n2) → n2Anchors
  6. Numerator(n1divn2) → n1n2num
  7. Denominator(n1divn2) → n1n2den
  8. First(Flatten[Sequence[Sequence[Point[{((-i) * n1ArraySpacer), (j * n1ArraySpacer)}], j, ((-(ceil(n1^(0.5)) - 1))) / 2, (ceil(n1^(0.5)) - 1) / 2], i, 1, ceil(n1^(0.5))]], n1) → n1Anchors
  9. Flatten(Sequence[Sequence[Element[n1Anchors, i], j, 1, n1n2den], i, 1, n1]) → n1n2StartingPoints
  10. Sequence(Sequence[Element[n2Anchors, j] + ((((1 - (0.8 * ceil(n1 / n2)^(-0.5))) * n2OrigCircleSize) * cos((i * π / π))), (((1 - (0.8 * ceil(n1 / n2)^(-0.5))) * n2OrigCircleSize) * sin((i * π / π)))), i, 0, (2 * π) - 1 / ceil(n1 / n2), (2 * π / ceil(n1 / n2))], j, 1, n2) → n1n2TargetHelper
  11. If(n1 > n2, Join[{Sequence[n1n2den, i, 1, n1divn2], {n1n2num - (n1n2den * floor(n1divn2))}}], {n1}) → n1n2BreakdownHelper
  12. Zip(Circle[AAA, n1OrigCircleSize], AAA, n1Anchors) → n1Circles
  13. Zip(Circle[AAA, n2OrigCircleSize], AAA, n2Anchors) → n2Circles
  14. Flatten(Sequence[Sequence[i, j, 1, Element[n1n2BreakdownHelper, i]], i, 1, Length[n1n2BreakdownHelper]]) → n1n2Breakdown
  15. If(n1 > n2, Flatten[Sequence[Sequence[Element[n1n2TargetHelper, i, Element[n1n2Breakdown, j]], j, 1, Length[n1n2Breakdown]], i, 1, Length[n1n2TargetHelper]]], Flatten[Sequence[Sequence[Element[n2Anchors, i], j, 1, n1n2num], i, 1, n2]]) → n1n2EndingPoints
  16. Denominator(n1divn2) → n2n1num
  17. Numerator(n1divn2) → n2n1den
  18. If(n2 > n1, Join[{Sequence[n2n1den, i, 1, n2divn1], {n2n1num - (n2n1den * floor(n2divn1))}}], {n2}) → n2n1BreakdownHelper
  19. Flatten(Sequence[Sequence[i, j, 1, Element[n2n1BreakdownHelper, i]], i, 1, Length[n2n1BreakdownHelper]]) → n2n1Breakdown
  20. Flatten(Sequence[Sequence[Element[n2Anchors, i], j, 1, n2n1den], i, 1, n2]) → n2n1StartingPoints
  21. Sequence(Sequence[Element[n1Anchors, j] + ((((1 - (0.8 * ceil(n2 / n1)^(-0.5))) * n1OrigCircleSize) * cos((i * π / π))), (((1 - (0.8 * ceil(n2 / n1)^(-0.5))) * n1OrigCircleSize) * sin((i * π / π)))), i, 0, (2 * π) - 1 / ceil(n2 / n1), (2 * π / ceil(n2 / n1))], j, 1, n1) → n2n1TargetHelper
  22. Textfield(n1Text) → InputBox1
  23. Textfield(n2Text) → InputBox2
  24. If(n2 > n1, Flatten[Sequence[Sequence[Element[n2n1TargetHelper, i, Element[n2n1Breakdown, j]], j, 1, Length[n2n1Breakdown]], i, 1, Length[n2n1TargetHelper]]], Flatten[Sequence[Sequence[Element[n1Anchors, i], j, 1, n2n1num], i, 1, n1]]) → n2n1EndingPoints
  25. Zip((AAA * (2 - Max[(-a), 1])) + (BBB * Max[(-a) - 1, 0]), AAA, n2n1StartingPoints, BBB, n2n1EndingPoints) → n2n1MovingPoints
  26. Flatten(Sequence[Sector[Circle[Element[n2n1MovingPoints, i], n2n1CircleSize], ((2 * π / n2n1den) * Mod[i, n2n1den]), ((2 * π / n2n1den) * (Mod[i, n2n1den] + 1))], i, 1, Length[n2n1MovingPoints]]) → n2n1Wedges
  27. Zip((AAA * (2 - Max[a, 1])) + (BBB * Max[a - 1, 0]), AAA, n1n2StartingPoints, BBB, n1n2EndingPoints) → n1n2MovingPoints
  28. Flatten(Sequence[Sector[Circle[Element[n1n2MovingPoints, i], n1n2CircleSize], ((2 * π / n1n2den) * Mod[i, n1n2den]), ((2 * π / n1n2den) * (Mod[i, n1n2den] + 1))], i, 1, Length[n1n2MovingPoints]]) → n1n2Wedges
  29. Length(n2n1EndingPoints) → b
  30. Length(n2n1StartingPoints) → c

AI Drawing Prompt Reference

Visualize a dynamic geometric representation in 3D space showing the geometric interpretation of fractions and division through vectors. Include two circles of different sizes with points on them connected by lines to form a grid. Adjust the grid size and distribution dynamically based on two input values, demonstrating the geometric meaning of fractions. Points in the grid move according to the fraction value, forming different shapes and ultimately illustrating the geometric relationship between fractions and division.
The prompt above was compiled from the original drawing commands and is for reference only.