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计算多边形周长：用几何工具探索图形

计算多边形周长：用几何工具探索图形
几何画板及绘图内容加载中，请稍等……
2023-06-15 22:07
多边形几何作图滑块动画
本活动演示如何使用GeoGebra计算不同多边形的周长。核心数学概念包括周长定义、测量方法以及几何作图技巧。作图要点涉及使用Polygon、Segment、Semicircle等命令构建图形，并计算各边长度之和。适合小学高年级学生用于数学实践和课堂练习。

GeoGebra 命令及参数

  1. Shuffle(Sequence[t, t, 4, 9, 0.5]) → allSides, {4.5, 6, 7, 8, 5, 8.5, 9, 7.5, 4, 5.5, 6.5}
  2. Element(allSides, Mod[countQuestion, Length[allSides]] + 1) → sideLen
  3. Shuffle(Sequence[t, t, 1, 3.5, 0.5]) → allSidesRec, {2, 1, 3, 2.5, 1.5, 3.5}
  4. Element(allSidesRec, Mod[countQuestion, Length[allSidesRec]] + 1) → sideRecLen
  5. Shuffle({{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}}) → allTriSides, {{5, 12, 13}, {3, 4, 5}, {8, 15, 17}, {7, 24, 25}}
  6. Element(allTriSides, Mod[countQuestion, Length[allTriSides]] + 1) → triSides
  7. Shuffle(Sequence[t, t, 1, 7, 1]) → allCases, {3, 1, 5, 7, 4, 2, 6}
  8. Element(allCases, Mod[countQuestion, Length[allCases]] + 1) → caseNum
  9. Polygon(F, GP, 8) → octa, e, P, Q, R, S, T, f_1, g_1, h_1, i_1, j_1, k_1, l_1, O
  10. Polygon(F, G, 5) → pent, m, n, p, q, r, H, I, J
  11. Polygon(F, G, 6) → hex, s, N, t, a, b, c, d, K, L, M
  12. Polygon(A, B, 3) → regTri, f, g, h, C
  13. Polygon(A, B, 4) → squa, i, j, k, l, D, E
  14. Circle(V, rag) → d_1
  15. Polygon(U, V, V1, U1) → rect, u_1, v_1, v1, u1
  16. Semicircle(U, V) → c_1
  17. Intersect(c_1, d_1) → VV, , ,
  18. Polygon(U, V, VV) → tri, vv, u, v
  19. Point(allPoly(caseNum)) → ANIP
  20. PathParameter(ANIP) → pathPar
  21. Sequence(Random[0, 99] / 100, A, 1, 200) → allRandomSeeds, {0.43, 0.26, 0.38, 0.39, 0.32, 0.46, 0.81, 0.53, 0.25, 0.11, 0.64, 0.96, 0.8, 0.14, 0.48, 0.17, 0.93, 0.13, 0.09, 0.28, 0.74, 0.39, 0.84, 0.41, 0.62, 0.18, 0.74, 0.37, 0.01, 0.62, 0.24, 0.96, 0.56, 0.31, 0.64, 0.29, 0.52, 0.31, 0.59, 0.64, 0.62, 0.62, 0.77, 0.78, 0.06, 0.07, 0.73, 0.2, 0.49, 0.48, 0.92, 0, 0.74, 0.39, 0.25, 0.36, 0.63, 0.35, 0.99, 0.61, 0.02, 0.66, 0.95, 0.42, 0.26, 0.84, 0.92, 0.67, 0.33, 0.22, 0.81, 0.55, 0.61, 0.46, 0.54, 0.9, 0.82, 0.59, 0.15, 0.28, 0.4, 0.49, 0.31, 0.65, 0.16, 0.21, 0.88, 0.61, 0.49, 0.64, 0.29, 0.93, 0.98, 0.38, 0.93, 0.25, 0.47, 0.3, 0.86, 0.45, 0.01, 0.78, 0.99, 0.63, 0.15, 0.92, 0.34, 0.82, 0.47, 0.96, 0.07, 0.53, 0.86, 0.93, 0.29, 0.28, 0.36, 0.63, 0.26, 0.16, 0.08, 0.84, 0, 0.87, 0.36, 0.38, 0.59, 0.58, 0.45, 0.81, 0.18, 0.19, 0.78, 0.42, 0.65, 0.62, 0.99, 0.91, 0.36, 0.88, 0.37, 0.96, 0.51, 0.92, 0.09, 0.55, 0.2, 0.53, 0.1, 0.44, 0.79, 0.02, 0.07, 0.88, 0.03, 0.84, 0.47, 0.1, 0.96, 0.55, 0.4, 0.4, 0.72, 0.24, 0.95, 0.6, 0.44, 0.07, 0.1, 0.84, 0.7, 0.3, 0.48, 0.22, 0.62, 0.19, 0.55, 0.72, 0.54, 0.56, 0.99, 0.28, 0.09, 0.53, 0.55, 0.31, 0.04, 0.4, 0.08, 0.14, 0, 0.51, 0.7, 0.64, 0.68, 0.73, 0.64, 0.59, 0, 0.39}
  22. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  23. Textfield(input1) → InputBox1
  24. Textfield(input2) → InputBox2
  25. If(pathPar < 1 / 3, PolyLine[{U, ANIP}], 1 / 3 ≤ pathPar < 2 / 3, PolyLine[{U, V, ANIP}], PolyLine[{U, V, VV, ANIP}]) → fullPath1
  26. If(pathPar < 1 / 3, PolyLine[{A, ANIP}], 1 / 3 ≤ pathPar < 2 / 3, PolyLine[{A, B, ANIP}], PolyLine[{A, B, C, ANIP}]) → fullPath2
  27. If(pathPar < 1 / 4, PolyLine[{A, ANIP}], 1 / 4 ≤ pathPar < 2 / 4, PolyLine[{A, B, ANIP}], 2 / 4 ≤ pathPar < 3 / 4, PolyLine[{A, B, D, ANIP}], PolyLine[{A, B, D, E, ANIP}]) → fullPath3
  28. If(pathPar < 0.25, PolyLine[{U, ANIP}], 0.25 ≤ pathPar < 0.5, PolyLine[{U, V, ANIP}], 0.5 ≤ pathPar < 0.75, PolyLine[{U, V, V1, ANIP}], PolyLine[{U, V, V1, U1, ANIP}]) → fullPath4
  29. If(pathPar < 1 / 5, PolyLine[{F, ANIP}], 1 / 5 ≤ pathPar < 2 / 5, PolyLine[{F, G, ANIP}], 2 / 5 ≤ pathPar < 3 / 5, PolyLine[{F, G, H, ANIP}], 3 / 5 ≤ pathPar < 4 / 5, PolyLine[{F, G, H, I, ANIP}], PolyLine[{F, G, H, I, J, ANIP}]) → fullPath5
  30. If(pathPar < 1 / 6, PolyLine[{F, ANIP}], PolyLine[{F, G, K, L, M, N, ANIP}], 1 / 6 ≤ pathPar < 2 / 6, PolyLine[{F, G, ANIP}], 2 / 6 ≤ pathPar < 3 / 6, PolyLine[{F, G, K, ANIP}], 3 / 6 ≤ pathPar < 4 / 6, PolyLine[{F, G, K, L, ANIP}], 4 / 6 ≤ pathPar < 5 / 6, PolyLine[{F, G, K, L, M, ANIP}]) → fullPath6
  31. If(pathPar < 1 / 8, PolyLine[{F, ANIP}], 5 / 8 ≤ pathPar < 6 / 8, PolyLine[{F, GP, O, P, Q, R, ANIP}], 6 / 8 ≤ pathPar < 7 / 8, PolyLine[{F, GP, O, P, Q, R, S, ANIP}], PolyLine[{F, GP, O, P, Q, R, S, T, ANIP}], 1 / 8 ≤ pathPar < 2 / 8, PolyLine[{F, GP, ANIP}], 2 / 8 ≤ pathPar < 3 / 8, PolyLine[{F, GP, O, ANIP}], 3 / 8 ≤ pathPar < 4 / 8, PolyLine[{F, GP, O, P, ANIP}], 4 / 8 ≤ pathPar < 5 / 8, PolyLine[{F, GP, O, P, Q, ANIP}]) → fullPath7
  32. Zip(A / B, A, allPaths, B, allFacts) → allStudPaths
  33. Corner(5) → layoutAppSize
  34. Segment(PMoveA, PMoveB) → displaySegment
  35. expandSegment(PMoveA, PMoveB, (pulsing * 7), Corner[1], Corner[3], Corner[5]) → pulsingObject
  36. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  37. Segment(U, V) → m_1
  38. PolyLine({U, V, VV, U}) → fakePath1
  39. PolyLine({A, B, C, A}) → fakePath2
  40. PolyLine({A, B, D, E, A}) → fakePath3
  41. PolyLine({U, V, V1, U1, U}) → fakePath4
  42. PolyLine({F, G, H, I, J, F}) → fakePath5
  43. PolyLine({F, G, K, L, M, N, F}) → fakePath6
  44. PolyLine({F, GP, O, P, Q, R, S, T, F}) → fakePath7

AI 绘图提示语参考

绘制一个包含多种多边形和圆形的组合图形，包括正三角形、正方形、正五边形、正六边形、正八边形、矩形、半圆和圆。所有图形共享部分顶点，并围绕一个中心点排列。每个多边形内部有一条从起点沿边到终点的路径，路径长度随滑块变化。图形旁有输入框用于输入周长答案，并显示动态的路径动画。整体布局清晰，适合教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。