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Dependence of Average Distance on Truncation Parameter in Truncated Square Antip

Dependence of Average Distance on Truncation Parameter in Truncated Square Antip
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2020-01-13 20:52
PolygonSolid GeometryOptimizationGeometric ConstructionSlider Animation
This example demonstrates how the average distance between vertices of a truncated square antiprism depends on the truncation parameter. By adjusting the truncation parameter, the extreme distribution of vertices can be observed. Commands used include Join, Unique, Length, Text, Sum, Sphere, Ray, Zip, UnicodeToLetter, TableText, etc. Suitable for high school mathematics education, particularly in coordinate geometry and solid geometry.

GeoGebra Commands & Parameters

  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. Text("" + p3) → txt_p
  6. Sum(Flatten[Sequence[Append[Sequence[Element[txt_p, i], i, m1(k), m2(k)], " "], k, 1, 5]]) → txtUm1
  7. Sphere(O, R1) → sp1
  8. Sphere(O, R2) → sp2
  9. Ray(B, AA) → h
  10. Text(text12, C, false, true) → text8
  11. Zip(Polygon[a], a, v_poly08) → poly08
  12. Zip(Segment[lP0(x(a)), lP0(y(a))], a, segN1) → seg1
  13. Zip(Segment[lP0(x(a)), lP0(y(a))], a, segN2) → seg2
  14. Zip(Polygon[a], a, v_poly04) → poly04
  15. Zip(Polygon[a], a, v_poly06) → poly06
  16. UnicodeToLetter(34) → u34
  17. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ4) → segΔ4
  18. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ8) → segΔ8
  19. Zip(Segment[lVV(x(a)), lVV(y(a))], a, segNΔ6) → segΔ6
  20. TableText(Append["\;\;\; \fgcolor{#08E8DE}{4-gons}", segΔ4], Append["\;\;\; \fgcolor{#B5A642}{6-gons}", segΔ4], Append["\;\;\; \fgcolor{#007FFF}{8-gons}", segΔ8], "v") → text3a