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Largest Possibility? by Tim Brzezinski

Largest Possibility? by Tim Brzezinski
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2021-12-13 00:58
FunctionCoordinate GeometryProbability & StatisticsOptimizationGeometric Construction
In collections Open Middle: Distance in the Coordinate Plane
This example demonstrates the geometric construction of a quadrilateral inscribed in a parabola, analyzing the maximum possibilities involved. It involves logarithmic functions, geometric distribution, and percentages. Key GeoGebra commands/objects used include PointIn, Segment, SurdText, Textfield, Point, If, Mode, Intersect, Polygon, Angle for dynamic constructions and conditional logic. Suitable for high school and above students exploring the intersection of analytical geometry and probability & statistics.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(e) → B
  3. Segment(A, B) → f
  4. SurdText(f) → text1
  5. Textfield(j) → InputBox1
  6. Textfield(k) → InputBox2
  7. Point(Circle[A, sqrt((10 * j) + k)]) → C
  8. Segment(A, C) → l
  9. If(m < i, "Too short!", m > i, "Too long!", "This value is correct!") → text7
  10. Mode(l1) → l2
  11. If(Length[l2] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text8
  12. Intersect(eq1, p) → D
  13. Polygon(A, D, B) → t1, b_1, a_1, d_1
  14. Segment(A, D) → q
  15. Segment(D, B) → r
  16. Angle(B, D, A) → α

AI Drawing Prompt Reference

Draw two points on a parabola, connect them to form a line segment, and calculate and draw a circle based on input values. The circle intersects the parabola to get a third point, forming a quadrilateral with the three points. Display different text prompts based on the length of the line segment, and analyze whether the digits of the segment length repeat.
The prompt above was compiled from the original drawing commands and is for reference only.