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3D Dynamic Construction for Centroid Study

3D Dynamic Construction for Centroid Study
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2019-03-27 02:05
VectorCoordinate GeometrySolid GeometryProbability & StatisticsGeometric Construction
This example demonstrates the properties of the centroid in 3D space through dynamic construction. It involves core math concepts like vectors, 3D coordinates, arithmetic mean, centroid, geometric transformations, and probability distributions. Constructed using GeoGebra commands such as Textfield, Sphere, PointIn, Zip, Sum, Segment, and LaTeX, it offers interactive exploration. Suitable for high school students and math enthusiasts studying solid geometry and probability & statistics.

GeoGebra Commands & Parameters

  1. Textfield(n) → InputBox1
  2. Sphere((0, 0, 0), R) → b
  3. UnicodeToLetter(34) → u34
  4. PointIn(b) → P_{1}
  5. PointIn(b) → P_{2}
  6. PointIn(b) → P_{3}
  7. PointIn(b) → P_{4}
  8. PointIn(b) → P_{5}
  9. Zip(Segment[C_m, a], a, lP) → segC_m
  10. Zip(Segment[B, a], a, lP) → segB
  11. Sum(segB^(2)) → SumB_q
  12. Sum(segC_m^(2)) → SumA_q
  13. Segment(C_m, B) → f
  14. LaTeX(text1) → text6