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Euclid's Extreme and Mean Proportion Constructions

Euclid's Extreme and Mean Proportion Constructions
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2015-04-12 03:40
CirclePolygonGeometric Construction
This example demonstrates geometric constructions to find extreme and mean proportions, involving core concepts like geometric mean and construction techniques. It uses GeoGebra commands such as Circle, Line, Point, OrthogonalLine, Intersect, Segment, Polygon, and Midpoint. Suitable for high school and above, focusing on geometric construction and proportionality.

GeoGebra Commands & Parameters

  1. Circle(A_1, A) → c_1
  2. Line(A_1, C_1) → a_1
  3. Point(c_1) → D
  4. OrthogonalLine(D, a_1) → b_1
  5. Intersect(c_1, a_1, 1) → E_1
  6. Intersect(a_1, b_1) → C
  7. Segment(E_1, C) → a
  8. Segment(D, C) → b
  9. Intersect(c_1, a_1, 2) → B
  10. Segment(C, B) → c
  11. Polygon(B, E_1, 4) → poly1, e, f, g, h, H_1, G
  12. Midpoint(E_1, H_1) → E
  13. Segment(E, B) → i
  14. Circle(E, B) → k
  15. OrthogonalLine(E_1, a) → j
  16. Intersect(k, j, 2) → F
  17. Polygon(F, E_1, 4) → poly2, l, m, n, p, M, H
  18. Segment(A, D) → d
  19. Segment(D, B) → q

AI Drawing Prompt Reference

Draw a geometric figure with a circle c, a line a passing through its center, the intersection point D of the circle and the line, a line b perpendicular to line a and passing through point D, the intersection point E1 of line a and the circle, another intersection point C of line a and the circle, line segments EC and DC, line segment CB, a polygon F, E1, 4, line segment EB, a circle k with center E and radius EB, a line j perpendicular to line a and passing through point E1, and the intersection point F of circle k and line j, and a polygon F, E1, 4, line segments AD and DB.
The prompt above was compiled from the original drawing commands and is for reference only.