Fraction Number with Geometric Construction

Fraction Number with Geometric Construction
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2020-04-29 12:34
① This GeoGebra example demonstrates a fraction number represented on a number line, enriched with geometric elements such as circles, rotations, segments, and sectors, making the abstract concept of fractions visually tangible. ② Core mathematical concepts include the numerical value of fractions, proportional segments on a number line, equilateral triangles, linear regression, roots, and indefinite integrals, highlighting the interconnection between fractions, geometry, and algebra. ③ Construction details: Based on the summary, the example uses GeoGebra commands like Circle, Rotate, Angle, Segment, and CircleSector, with multiple points (A, B, C, D, E, etc.) and angle parameters (α, β, γ, etc.). Rotations and circular sectors are employed to illustrate part-whole relationships, while equilateral triangles and linear regression add further geometric insight. ④ Suitable for middle and high school mathematics (e.g., fraction concepts in middle school, geometry-function integration in high school), this example serves as an interactive teaching tool for teachers to help students understand fraction positioning on a number line and its geometric interpretation.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Rotate(B, (360°) / Dinometer, A) → B'
  3. Angle(B, A, B') → α
  4. Rotate(B', (360°) / Dinometer, A) → B''
  5. Angle(B', A, B'') → β
  6. Rotate(B'', (360°) / Dinometer, A) → B'''
  7. Angle(B'', A, B''') → γ
  8. Rotate(B''', (360°) / Dinometer, A) → C
  9. Angle(B''', A, C) → δ
  10. Rotate(C, (360°) / Dinometer, A) → C'
  11. Angle(C, A, C') → ε
  12. Rotate(C', (360°) / Dinometer, A) → C''
  13. Angle(C', A, C'') → ζ
  14. Rotate(C'', (360°) / Dinometer, A) → C'''
  15. Angle(C'', A, C''') → η
  16. Rotate(C''', (360°) / Dinometer, A) → D
  17. Angle(C''', A, D) → θ
  18. Rotate(D, (360°) / Dinometer, A) → D'
  19. Angle(D, A, D') → ι
  20. Rotate(D', (360°) / Dinometer, A) → D''
  21. Angle(D', A, D'') → κ
  22. Rotate(D'', (360°) / Dinometer, A) → D'''
  23. Angle(D'', A, D''') → λ
  24. Segment(A, B) → f
  25. Segment(A, B') → g
  26. Segment(A, B'') → h
  27. Segment(A, B''') → i
  28. Segment(A, C) → j
  29. Segment(A, C') → k
  30. Segment(A, C'') → l
  31. Segment(A, C''') → m
  32. Segment(A, D) → n
  33. Segment(A, D') → p
  34. Segment(A, D'') → q
  35. Segment(A, D''') → r
  36. Rotate(B, (360° * Numaritar / Dinometer), A) → B'_1
  37. Angle(B, A, B'_1) → μ
  38. CircleSector(A, B, B'_1) → d