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Geometric Mean Demonstration by redean6

Geometric Mean Demonstration by redean6
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2018-04-02 21:53
TrigonometryCoordinate Geometry
This example demonstrates how to construct geometric figures to illustrate the geometric mean of the numbers 5, 12, and 13. It involves core mathematical concepts such as geometric mean, tangent function, standard deviation, inequalities, and integral calculus. The construction uses commands like Point, Segment, Circle, Intersect, Polygon, OrthogonalLine, Rotate, and objects like A, B, f, c, d, etc. It is suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 13]) → B
  2. Segment(A, B) → f
  3. Circle(A, 5) → c
  4. Circle(B, 12) → d
  5. Intersect(c, d, 1) → C
  6. Polygon(A, C, B) → t1, b, a, c_1
  7. OrthogonalLine(C, f) → g
  8. Intersect(g, f) → D
  9. Segment(C, D) → h
  10. Polygon(A, C, D) → t2, d_1, a_1, c_2
  11. Polygon(C, B, D) → t3, d_2, c_3, b_1
  12. Rotate(C, α, B) → C'
  13. Rotate(B, α, B) → B'
  14. Rotate(D, α, B) → D'
  15. Polygon(C', B', D') → t3', d', c', b'
  16. Rotate(A, (-β), A) → A'
  17. Rotate(C, (-β), A) → C'_1
  18. Rotate(D, (-β), A) → D'_1
  19. Polygon(A', C'_1, D'_1) → t2', d'_1, a', c'_1

AI Drawing Prompt Reference

Draw a geometric figure with three circles and their intersection point C, where circle A has a radius of 5, circle B has a radius of 12, and circle C has a radius of 13. Connect points A and B to form line segment f, and point C is the intersection of circles A and B. Construct a triangle ABC with C as the vertex, then draw a perpendicular line from C to line segment f, intersecting at point D, and connect C and D to form line segment h. Next, rotate triangle BCD around point B to form a new triangle B'D'C', and rotate triangle ACD around point A to form a new triangle A'C'D'.
The prompt above was compiled from the original drawing commands and is for reference only.