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估算两位数乘积的几何探索

估算两位数乘积的几何探索
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2023-02-08 05:50
最值优化几何作图滑块动画
这个范例通过GeoGebra动态演示如何寻找两位数乘积最接近目标值的数对。核心数学概念是估算与最值优化。作图要点包括使用Sequence、Shuffle、Min、Max等命令生成随机数对，并通过distanceProducts计算乘积距离。适合小学四年级至五年级学生，用于理解估算策略和几何直观。

GeoGebra 命令及参数

  1. Sequence((allSelections(A, 1) * allSelections(A, 2)), A, 1, Length[allSelections]) → allSelectedProducts, {}
  2. Shuffle(Remove[Sequence[2, 99], {10, 20, 30, 40, 50, 60, 70, 80, 90}]) → possibleNumbers, {99, 69, 56, 88, 93, 91, 2, 4, 24, 82, 31, 5, 61, 53, 76, 58, 86, 85, 81, 21, 48, 94, 23, 75, 95, 16, 51, 66, 32, 59, 6, 72, 39, 18, 98, 52, 11, 77, 3, 67, 37, 8, 14, 84, 25, 45, 83, 54, 22, 28, 9, 36, 15, 13, 68, 62, 96, 17, 7, 63, 35, 46, 43, 64, 71, 55, 42, 78, 73, 49, 92, 33, 57, 44, 47, 34, 38, 41, 26, 87, 27, 65, 19, 74, 12, 97, 89, 79, 29}
  3. Sequence(Element[possibleNumbers, Mod[randomIndex + A, Length[possibleNumbers]] + 1], A, 1, 7) → currentNumbers
  4. RemoveUndefined(Flatten[Sequence[Sequence[If[i < j, (allNums(i) * allNums(j))], i, 1, 7], j, 1, 7]]) → possibleProducts
  5. Min(possibleProducts) → productLowest
  6. Max(possibleProducts) → productHighest
  7. Max(expectedProduct - productLowest, productHighest - expectedProduct) → displayRange
  8. Zip(If[abs((expectedProduct - A) / displayRange) > 0.75, 1, If[abs((expectedProduct - A) / displayRange) > 0.35, 2, 3]], A, allSelectedProducts) → colorIndex
  9. Zip(abs(expectedProduct - A), A, possibleProducts) → distanceProducts
  10. Element(possibleProducts, IndexOf[Min[distanceProducts], distanceProducts]) → closestProduct
  11. Shuffle(Sequence[1, 7]) → randomIndex2, {6, 1, 3, 4, 2, 7, 5}
  12. Element(randomIndex2, Mod[countQuestion, Length[randomIndex2]] + 1) → index2Tmp
  13. Shuffle(Sequence[1, 7]) → randomIndex1, {5, 3, 4, 7, 1, 6, 2}
  14. Element(randomIndex1, Mod[countQuestion, Length[randomIndex1]] + 1) → index1
  15. If(index1 ≟ index2Tmp, Mod[index1 + 1, Length[randomIndex2]] + 1, index2Tmp) → index2
  16. Zip(If[abs((expectedProduct - A) / displayRange) > 0.75, colorSpectrum(1), If[abs((expectedProduct - A) / displayRange) > 0.35, colorSpectrum(2), colorSpectrum(3)]], A, allSelectedProducts) → allColors
  17. Sequence((((((If[highlightRow ≟ A, (("\textcolor{" * colorSpectrum(colorIndex(A))) * "}\fbox"), "\fbox\textcolor{#252525}"] * "{") * allSelections(A, 1)) * "\times") * allSelections(A, 2)) * "}"), A, 1, Length[allSelections]) → coloredData
  18. Shuffle({1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2}) → randomIndices, {1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2}
  19. Element(randomIndices, Mod[countQuestion + 2, Length[randomIndices]] + 1) → opIndex3
  20. Element(randomIndices, Mod[countQuestion + 1, Length[randomIndices]] + 1) → opIndex2
  21. Element(randomIndices, Mod[countQuestion, Length[randomIndices]] + 1) → opIndex1
  22. makeBox(Anchor2 + (((-1.2 * boxWidth)) / 2, boxHeight / 2), (1.2 * boxWidth), boxHeight) → region2
  23. Zip(IsInRegion[A, region2], A, allPoints) → countRegion2
  24. makeBox(Anchor1 + (((-1.2 * boxWidth)) / 2, boxHeight / 2), (1.2 * boxWidth), boxHeight) → region1
  25. Zip(IsInRegion[A, region1], A, allPoints) → countRegion1
  26. Shuffle(Sequence[1, 9]) → randomDigits5, {7, 8, 5, 4, 1, 3, 9, 6, 2}
  27. Shuffle(Sequence[1, 9]) → randomDigits4, {1, 6, 8, 5, 4, 3, 7, 9, 2}
  28. Shuffle(Sequence[1, 9]) → randomDigits3, {3, 9, 5, 1, 7, 6, 2, 4, 8}
  29. Shuffle(Sequence[1, 9]) → randomDigits2, {1, 3, 2, 8, 9, 7, 5, 4, 6}
  30. Shuffle(Sequence[1, 9]) → randomDigits1, {6, 9, 3, 2, 7, 4, 5, 8, 1}
  31. Zip(Join[{A, A}], A, {randomDigits1, randomDigits2, randomDigits3, randomDigits4, randomDigits5}) → allRandom
  32. Take(Element[allRandom, randomIndex], startIndex, startIndex + 4) → currentRandoms
  33. makeBox(P5, boxWidth, boxHeight) → box5
  34. makeBox(P3, boxWidth, boxHeight) → box3
  35. makeBox(P2, boxWidth, boxHeight) → box2
  36. makeBox(P1, boxWidth, boxHeight) → box1
  37. Corner(5) → Dims
  38. makeBox(Anchor2, boxWidth, boxHeight) → boxB
  39. makeBox(Anchor1, boxWidth, boxHeight) → boxA
  40. Midpoint(Corner[2], Corner[1]) → PCenter
  41. makeBox(P7, boxWidth, boxHeight) → box7
  42. Zip(Text[("" * A), B + (boxHeight / 2 + 0.2, ((-boxWidth)) / 2), true, true, 0, 0], A, {num1, num2, num3, num4, num5, num6, num7}, B, {P1, P2, P3, P4, P5, P6, P7}) → digitText
  43. Sequence(HomeAnchor + (((A * 1.5) * boxWidth), 0), A, 0, 6) → homePoints
  44. Sequence(If[countRegion1(A) ∧ (countEntries(1) ≟ 1 ∨ movedBox ≟ A), Anchor1, If[countRegion2(A) ∧ (countEntries(2) ≟ 1 ∨ movedBox ≟ A), Anchor2, homePoints(A)]], A, 1, 7) → allLocations
  45. Segment(AnchorLine, AnchorLineEnd) → numberLine
  46. Min(possibleProducts) → minProduct
  47. Max(possibleProducts) → maxProduct
  48. Sequence((((allSelectedProducts(A) - expectedProduct) / displayRange * lineLength / 2), 0), A, 1, Length[allSelectedProducts]) → allDisplayPoints
  49. Vector((0, -5), (0, -1)) → vCorrect
  50. Sequence(If[allSelectedProducts(A) ≟ closestProduct, (("\textcolor{" * colorTealSuccess) * "}{✓ }"), ""], A, 1, Length[allSelectedProducts]) → checks
  51. Length(allSelections) → numTries
  52. Text(("" * expectedProduct), PointN + (0, -7), false, true, 0, 0) → lblExpected
  53. Zip(abs(A - expectedProduct), A, allSelectedProducts) → allDistances
  54. Translate(Vector[(0, 5), (0, 0)], CurrentDisplayPoint + (0, 6)) → arrowCurrent
  55. makeBox(P4, boxWidth, boxHeight) → box4
  56. makeBox(P6, boxWidth, boxHeight) → box6
  57. Flatten(Sequence[Sequence[AnchorFactors + ((i * 11.2), (j * (-5.3))), i, 0, 7], j, 0, 2]) → allFactorPoints
  58. Zip(Text[("" * A), B, true, true, 1, 0], A, coloredData, B, allFactorPoints) → displayData

AI 绘图提示语参考

绘制一个数学可视化图形，展示如何找到两个两位数相乘最接近目标值的数对。图形包含一个滑动条控制目标值，随机生成多个两位数，并通过计算所有可能乘积来找到最接近目标值的乘积。用不同颜色标记最接近和最远的乘积，并用几何方式展示每个乘积与目标值的距离。最终图形应直观展示优化过程和几何直觉。
以上提示语为根据原始绘图命令整理而来，仅供参考。