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费马问题相关最大值任务动态构造

费马问题相关最大值任务动态构造
几何画板及绘图内容加载中，请稍等……
2019-02-28 23:15
测试改名0解析几何微积分最值优化几何作图
①本范例演示了与费马问题相关的最大值任务，通过动态构造展示几何图形的变换与优化；②涉及核心数学概念包括面积、微积分、质心、外接圆、几何作图、等腰三角形、特殊点、三角形、多项式函数、平移、函数、乘法、对数函数；③构造要点提炼自GeoGebra命令：Zip, Sequence, UnicodeToLetter, Polygon, Sum, If, Ray, Rotate, Point, Intersect, Segment，对象包括P_{3}, P_{2}, P_{1}, lAngle, lP', P_{1}'}, lP, lr, lP_p, lM, M_{3}, bue, M_{2}, M_{1}, button1, u34, t1, lLog, br, lPoly, lCircle, Oi, F, P_{2}', P_{3}', Cm, M1, M2, M3, polyMax, m_{3}, m_{1}, m_{2}, lh, h_1, h_2, h_3, lAngle3, r_1, r_2；④适合高中及以上数学学习者，用于理解几何优化问题与动态几何软件的应用。

GeoGebra 命令及参数

  1. Zip(Rotate[a1, If[b < 180°, (-(60°)), 60°], a2], a1, {P_{2}, P_{1}, P_{1}}, a2, {P_{3}, P_{3}, P_{2}}, b, {lAngle(3), lAngle(1), lAngle(2)}) → lP'
  2. Sequence(Segment[Element[lP', i], Element[lP, i]], i, 1, 3) → lr
  3. Zip(OrthogonalLine[P, r], P, lP, r, lr) → lP_p
  4. Zip(Intersect[a, b], a, {lP_p(1), lP_p(1), lP_p(2)}, b, {lP_p(2), lP_p(3), lP_p(3)}) → lM
  5. UnicodeToLetter(34) → u34
  6. Polygon(lP) → t1
  7. Zip(120° ≤ t ≤ 240°, t, lAngle) → lLog
  8. Sum(lLog) → br
  9. Zip(Center[c], c, lCircle) → Oi
  10. If(lLog(2), P_{2}, lLog(3), P_{3}, lLog(1), P_{1}, Intersect[lr(2), lr(1)]) → F
  11. Polygon(M_{1}, M_{2}, M_{3}) → polyMax, m_{3}, m_{1}, m_{2}
  12. Zip(Segment[F, a], a, lP) → lh
  13. Zip(Angle[a, b, c], a, lP', b, lP, c, If[bue, {M_{3}, M_{1}, M_{2}}, {M_{2}, M_{3}, M_{1}}]) → lAngle3
  14. Ray(M1', P_{2}) → e2
  15. Rotate(P_{2}, (-(60°)), M1') → M11'
  16. Ray(M1', M11') → e1
  17. Point(e2) → M3'
  18. Rotate(P_{2}, 60°, M3') → M22'
  19. Ray(M3', M22') → e3
  20. Intersect(e1, e3) → M2'
  21. Polygon(M1', M2', M3') → poly, m_3', m_1', m_2'
  22. Intersect(OrthogonalLine[M_{1}, lP_p(1)], lP_p(1)) → H
  23. Segment(M_{1}, H) → hh