Explanation of Invariance of the Sum of Squares of Distances Using Steiner Theor

Explanation of Invariance of the Sum of Squares of Distances Using Steiner Theor
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2019-05-24 03:22
This example demonstrates the invariance of the sum of squares of distances in a plane using Steiner's theorem. Key mathematical concepts include Steiner's theorem, centroid, distance calculations, and analytical geometry. GeoGebra commands and objects used in the construction are Circle, Point, Flatten, Zip, Length, and RotateText. Suitable for high school students and math enthusiasts to explore geometric invariants and properties of special points, this can be used for educational demonstrations or research.

GeoGebra Commands & Parameters

  1. Circle(O, r) → c
  2. Point(c) → A_6
  3. Point(c) → A_5
  4. Point(c) → A_4
  5. Point(c) → A_3
  6. Point(c) → A_2
  7. Point(c) → A_1
  8. Flatten({l, (-l)}) → l1
  9. Point(c) → D
  10. Zip(Segment[D, a], a, l1) → l2
  11. Length(l2) → n
  12. Zip(Text["A_{" + (k) + "}", b + (0.2, 0.2)], k, Sequence[n], b, l1) → l4
  13. RotateText(txt, 90°) → txt1
  14. Circle(Cm, R) → d
  15. Point(d) → B
  16. Zip(Segment[B, a], a, l1) → l2_B