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识别质数：通过图形理解数的性质

识别质数：通过图形理解数的性质
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2022-11-15 05:08
几何作图
这个范例演示了如何通过图形直观地判断一个数是质数、合数还是其他。核心数学概念包括质数定义、因数分解和图形化表示。作图要点包括使用GeoGebra命令如Shuffle、Element、If、Div、Mod等来构建判断逻辑和可视化图形。适合小学四年级到五年级的学生，用于数感培养和因数倍数学习。

GeoGebra 命令及参数

  1. Shuffle(Sequence[2, 100]) → randomList1, {49, 97, 21, 85, 100, 74, 42, 36, 4, 50, 41, 20, 84, 61, 65, 67, 8, 48, 31, 45, 80, 69, 6, 57, 34, 66, 54, 53, 87, 96, 63, 64, 47, 9, 13, 99, 81, 44, 72, 14, 29, 88, 56, 3, 17, 59, 78, 52, 25, 70, 68, 86, 32, 71, 24, 75, 38, 90, 73, 18, 91, 77, 7, 19, 60, 16, 43, 23, 33, 22, 55, 27, 2, 94, 5, 15, 98, 46, 62, 11, 95, 89, 10, 93, 92, 40, 39, 58, 30, 83, 28, 26, 35, 76, 79, 12, 51, 82, 37}
  2. Element(randomList1, Mod[countQuestion, 20] + 1) → number
  3. If(IsPrime[number], 2, 3) → rightAns
  4. Div(number, columnsSolution) → quotientSolution
  5. Element(randomList1, Mod[countQuestion, 20] + 1) → randomNum1
  6. Mod(number, columns) → remainder
  7. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  8. Div(number, columns) → quotient
  9. Distance(Corner[1], Corner[2]) → width
  10. Distance(Corner[4], Corner[1]) → height
  11. Polygon({VisualC1, VisualC2, VisualC3, VisualC4}) → box
  12. Corner(5) → AppSize
  13. Sequence(Circle[O + ((m * horGap), ((-quotient) * vertGap)), radius], m, 0, remainder - 1) → circlesRest
  14. Sequence(Sequence[Circle[O + ((m * horGap), ((-n) * vertGap)), radius], m, 0, columns - 1], n, 0, quotient - 1) → circles, {{(x - 0.048506653438569323)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.16675262359498694)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.2849985937514045)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.40324456390782215)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.5214905340642397)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.6397365042206573)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.757982474377075)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.8762284445334926)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 0.9944744146899102)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.1127203848463278)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.2309663550027454)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.349212325159163)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.4674582953155808)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.5857042654719984)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.703950235628416)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.8221962057848335)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 1.9404421759412511)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.0586881460976687)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.176934116254086)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.295180086410504)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.413426056566921)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.531672026723339)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.6499179968797564)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.768163967036174)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 2.886409937192592)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.0046559073490093)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.122901877505427)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.2411478476618445)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.3593938178182623)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.4776397879746797)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.5958857581310975)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.714131728287515)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.8323776984439326)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 3.9506236686003504)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.068869638756769)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.187115608913186)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.305361579069603)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.423607549226021)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.541853519382439)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.660099489538856)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.778345459695274)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 4.896591429851692)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.014837400008109)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.133083370164527)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.251329340320944)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.369575310477362)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.48782128063378)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.606067250790197)² + (y - 6.601894984084424)² = 0.002237137513317185, (x - 5.724313220946615)² + (y - 6.601894984084424)² = 0.002237137513317185}}
  15. If(rightAns ≟ 2, true, remainder ≟ 0 ∧ columns ≠ 1 ∧ columns ≠ number) → correctVisual
  16. IndexOf({IsPrime[number], correctAnswer}, {{true, true}, {true, false}, {false, false}, {false, true}}) → solutionCase
  17. Element({"YES and PRIME (correct)", "YES and COMPOSITE (incorrect)", "NO and PRIME (incorrect)", "NO and COMPOSITE (correct)"}, solutionCase) → solutionCaseDescription
  18. Mod(number, columnsSolution) → remainderSolution
  19. Sequence(Sequence[Circle[OSolution + ((m * horGapSolution), ((-n) * vertGapSolution)), radiusSolution], m, 0, columnsSolution - 1], n, 0, quotientSolution - 1) → circlesSolution, {{(x - 0.40324456390782215)² + (y - 6.643243796547203)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 6.643243796547203)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 6.643243796547203)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 6.643243796547203)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 6.643243796547203)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 6.643243796547203)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 6.643243796547203)² = 0.03939204768957061}, {(x - 0.40324456390782215)² + (y - 6.147058046993857)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 6.147058046993857)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 6.147058046993857)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 6.147058046993857)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 6.147058046993857)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 6.147058046993857)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 6.147058046993857)² = 0.03939204768957061}, {(x - 0.40324456390782215)² + (y - 5.65087229744051)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 5.65087229744051)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 5.65087229744051)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 5.65087229744051)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 5.65087229744051)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 5.65087229744051)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 5.65087229744051)² = 0.03939204768957061}, {(x - 0.40324456390782215)² + (y - 5.154686547887164)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 5.154686547887164)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 5.154686547887164)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 5.154686547887164)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 5.154686547887164)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 5.154686547887164)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 5.154686547887164)² = 0.03939204768957061}, {(x - 0.40324456390782215)² + (y - 4.658500798333817)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 4.658500798333817)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 4.658500798333817)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 4.658500798333817)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 4.658500798333817)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 4.658500798333817)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 4.658500798333817)² = 0.03939204768957061}, {(x - 0.40324456390782215)² + (y - 4.162315048780471)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 4.162315048780471)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 4.162315048780471)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 4.162315048780471)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 4.162315048780471)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 4.162315048780471)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 4.162315048780471)² = 0.03939204768957061}, {(x - 0.40324456390782215)² + (y - 3.6661292992271246)² = 0.03939204768957061, (x - 1.2309663550027454)² + (y - 3.6661292992271246)² = 0.03939204768957061, (x - 2.0586881460976687)² + (y - 3.6661292992271246)² = 0.03939204768957061, (x - 2.886409937192592)² + (y - 3.6661292992271246)² = 0.03939204768957061, (x - 3.7141317282875153)² + (y - 3.6661292992271246)² = 0.03939204768957061, (x - 4.541853519382439)² + (y - 3.6661292992271246)² = 0.03939204768957061, (x - 5.369575310477362)² + (y - 3.6661292992271246)² = 0.03939204768957061}}
  20. Element(Element[Factors[number], 2], 1) → exampleFactor

AI 绘图提示语参考

画一个包含随机数字的数学可视化图形，展示该数字是否为质数。图形中心是一个边框框，内部有若干圆形代表数字的因子。根据数字是否为质数，左侧区域显示对应数量的圆形，右侧区域根据质数和合数的判断显示不同颜色的圆形。整体布局清晰，便于理解质数和合数的概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。