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截角立方八面体：顶点平均距离与截角参数的关系

截角立方八面体：顶点平均距离与截角参数的关系
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2020-01-08 20:58
立体几何最值优化参数方程几何作图
①本范例演示截角立方八面体中，顶点平均距离随截角参数变化的规律及极端分布现象；②涉及核心数学概念包括多面体几何、参数化、平均距离计算、优化问题；③作图要点运用了Join, Unique, Length, Sphere, Zip, Ray, UnicodeToLetter, Text, Sum, TableText等GeoGebra命令与对象，通过滑块动态展示参数与距离关系；④适合高中及以上学生及数学爱好者学习多面体性质与参数化几何。

GeoGebra 命令及参数

  1. Join(Zip[lP0(x(a)) + ((lP0(y(a)) - lP0(x(a))) * {t, 1 - t}), a, segN]) → lVV
  2. Unique(lVV) → lP'
  3. Length(lP') → n
  4. Length(lVV(1)) → R2
  5. Sphere(O, R1) → sp1
  6. Sphere(O, R2) → sp2
  7. Zip(Polygon[a], a, v_poly06) → poly06
  8. Zip(Segment[lP0(x(a)), lP0(y(a))], a, segN1) → seg1
  9. Zip(Segment[lP0(x(a)), lP0(y(a))], a, segN2) → seg2
  10. Zip(Polygon[a], a, v_poly04) → poly04
  11. Zip(Polygon[a], a, v_poly08) → poly08
  12. Ray(B, AA) → h
  13. UnicodeToLetter(34) → u34
  14. Text("" + p3) → txt_p
  15. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m1(k), m2(k)], " "], k, 1, 5]]) → txtUm1
  16. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ4) → segΔ4
  17. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ6) → segΔ6
  18. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ8) → segΔ8
  19. TableText(Append["\;\;\; \fgcolor{red}{4-gons}", segΔ4], Append["\;\;\; \fgcolor{#FFBF00}{6-gons}", segΔ6], Append["\;\;\; \fgcolor{#5D8AA8}{8-gons}", segΔ8], "v") → text3a