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直角三角形、棱柱与勾股定理的探索

直角三角形、棱柱与勾股定理的探索
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2014-06-15 17:54
测试改名0立体几何几何作图
①本范例演示直角三角形、其两直角边上的正方形以及具有相同高度的棱柱之间的关系；②涉及的核心数学概念包括勾股定理、直角三角形、正方形、棱柱、相似变换等；③作图要点——从下方『构造摘要』提炼用到了 Semicircle（半圆）、Point（点）、Polygon（多边形）、Prism（棱柱）、Angle（角度）等 GeoGebra 命令/对象；④适合高中数学学生用于理解空间几何与平面几何的联系，以及勾股定理的立体应用。

GeoGebra 命令及参数

  1. Semicircle(A, B) → c
  2. Point(c) → C
  3. Polygon(A, B, C) → poli1, c_1, a, b
  4. Polygon(C, B, 4) → poli2, d, e, f, g, D, E
  5. Polygon(A, C, 4) → poli3, h_1, i, j, k, F, G
  6. Polygon(B, A, 4) → poli4, l, m, n, p, H, I
  7. Prism(poli4, h) → o, J, spigoloBJ, spigoloAK, spigoloHL, spigoloIM, spigoloJK, spigoloKL, spigoloLM, spigoloJM, K, L, M, facciaABJK, facciaAHLK, facciaHIML, facciaBIMJ, facciaJKLM
  8. Prism(poli3, h) → q, N, spigoloAN, spigoloCO, spigoloFP, spigoloGQ, spigoloNO, spigoloOP, spigoloPQ, spigoloNQ, O, P, Q, facciaACON, facciaCFPO, facciaFGQP, facciaAGQN, facciaNOPQ
  9. Prism(poli2, h) → r, R, spigoloCR, spigoloBS, spigoloDT, spigoloEU, spigoloRS, spigoloST, spigoloTU, spigoloRU, S, T, U, facciaBCRS, facciaBDTS, facciaDEUT, facciaCEUR, facciaRSTU
  10. Angle(A, C, B) → α