MathPlotAI Logo MathPlotAI

Area/Variance = Constant Demonstration

Area/Variance = Constant Demonstration
Loading the math board and drawing, please wait…
2016-02-28 06:19
VectorCalculusProbability & StatisticsGeometric Construction
In collections Complex Math
This example demonstrates the geometric phenomenon where the ratio of Area to Variance is constant, involving core math concepts like Area, Variance, Arithmetic Mean, Geometric Transformations, and Piecewise Functions. It is constructed using GeoGebra commands such as Vector, Point, Segment, Integral, and Textfield, with objects like a, u, v, A, B, C, μ, etc. Suitable for high school and above, helping learners understand the connection between statistics and geometry.

GeoGebra Commands & Parameters

  1. Vector(((a * 1.16), 0)) → u
  2. Vector((0, (a * 1.16))) → v
  3. Point(v) → B
  4. Point(u) → C
  5. Segment(A, B) → b
  6. Segment(A, C) → c
  7. Point(b) → D
  8. Point(c) → E
  9. Segment(E, D) → m
  10. Integral(p, -200, 200) → Deviation_a
  11. Integral(p(x) / a, 0, 0.851) → probabilities
  12. Textfield(a) → InputBox1
  13. Segment(F, G) → e
  14. Segment(H, I) → q