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Concept of Ratios(2)

Concept of Ratios(2)
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2017-07-01 23:18
FunctionSequenceGeometric Construction
This example illustrates the concept of ratios and their applications. By constructing geometric representations of ratios, students can intuitively understand the meaning of ratios. Commands used include point, GCD, sequence, and division. Suitable for middle school and above students to learn about proportional relationships.

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

Draw a ratio concept diagram, including two numbers a and b represented by points A and B on the x-axis and y-axis respectively, with the distance between A and B being the least common multiple of a and b. Use a and b to create a grid with row and column counts of a and b respectively. Based on the ratio of a and b, draw a series of rectangles with widths and heights as multiples of a and b. Finally, add input boxes for a and b values and draw a line segment from the origin to a distance of a+b+1.
The prompt above was compiled from the original drawing commands and is for reference only.