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Concept of Ratios-2: Dynamic Visualization and Geometric Construction

Concept of Ratios-2: Dynamic Visualization and Geometric Construction
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2020-07-25 09:37
CircleVectorGeometric ConstructionSlider Animation
① This interactive GeoGebra example dynamically demonstrates the concept of ratios (or proportions) between two numbers, allowing users to adjust values via sliders and input boxes to see how the ratio changes and its geometric interpretation. ② Core mathematical concepts include ratio, greatest common divisor (GCD), simplification of ratios, and the manifestation of ratios in geometric figures such as triangles, circles, conic sections, along with introductory ideas of vectors and differential calculus. ③ Construction highlights: using GeoGebra commands such as Point, GCD, Sequence, Div, Min, Textfield, and Segment, the example builds objects including points A, B, C, D, E, segments a and b, computes the GCD (hcf) to simplify the ratio into a' and b', and employs input boxes and buttons for interactivity; it also constructs circles, lines, and conic sections to link ratios with geometry. ④ Suitable for middle school to high school students learning ratio concepts, and also useful for pre-calculus and vector geometry instruction at the college level as a dynamic teaching tool.

GeoGebra Commands & Parameters

  1. Point(Segment[((2 * d), -1), ((35 * d), -1)]) → B
  2. Point(Segment[((2 * d), 0), ((35 * d), 0)]) → A
  3. GCD(a, b) → hcf
  4. Sequence(((i * d), 0), i, 0, a - 1) → list1
  5. Sequence(((i * d), -1), i, 0, b - 1) → list2
  6. Div(a, int1) → q1
  7. Div(b, int2) → q2
  8. Min(q1, q2) → q
  9. Sequence(Sequence[C + (((i - 1) * d), 0) + ((j - 1) * ((d * (int1 + int2)), 0)), i, 1, int1], j, 1, q) → list3a
  10. Sequence(Sequence[C + (((int1 - 1) * d) + (i * d), 0) + ((((j - 1) * d) * (int1 + int2)), 0), i, 1, int2], j, 1, q) → list3b
  11. Sequence(D + (((i - 1) * d), 0), i, 1, r1) → list3c
  12. Sequence(E + (((i - 1) * d), 0), i, 1, r2) → list3d
  13. Sequence(Polygon[C + (((j * d) * (int1 + int2)) - (0.5 * d), (-d)), C + (((j * d) * (int1 + int2)) - (0.5 * d), d), C + ((((j + 1) * d) * (int1 + int2)) - (0.5 * d), d), C + ((((j + 1) * d) * (int1 + int2)) - (0.5 * d), (-d))], j, 0, q - 1) → listPoly
  14. Textfield(int1) → InputBox1
  15. Textfield(int2) → InputBox2
  16. Segment(C - (d, 0), C + (((a + b + 1) * d), 0)) → f

AI Drawing Prompt Reference

Create a dynamic visualization of the concept of ratios, including two adjustable points A and B, whose positions can be changed via input boxes. Calculate the greatest common divisor of the distances between A and B to simplify the ratio. Use geometric objects like points, segments, circles, and polygons to demonstrate the application of ratios in geometric figures such as triangles, circles, and conic sections. Implement interactivity through buttons and input boxes to observe how changes in the ratio affect the geometric figures.
The prompt above was compiled from the original drawing commands and is for reference only.