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分数比较的可视化演示（D Mentrard）

分数比较的可视化演示（D Mentrard）
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2020-03-07 07:35
圆数列不等式几何作图
① This example visually compares two fractions using circular sectors and bar representations, making the relative size of fractions intuitive. ② Core math concepts include fraction equivalence, common denominators via LCM, inequalities, and representing fractions as areas or lengths. ③ Construction highlights: uses GeoGebra commands such as Circle, CircleSector, Segment, Zip, Sequence, Append, LCM, Translate, Rotate, Mirror, Vector, Text, and Midpoint to build fraction models, arrange them with transformations, and annotate comparisons. ④ Suitable for upper elementary to middle school students learning fraction comparison, common denominators, and inequality concepts, as well as for teachers creating interactive demonstrations.

GeoGebra 命令及参数

  1. Circle(A, Size) → c_1
  2. Point(c_1) → B
  3. Segment(A, B) → a_1
  4. Append(Sequence[Rotate[B, i, A], i, (360 / b)°, 359.9°, (360 / b)°], Rotate[B, 359.99°, A]) → ListP
  5. CircleSector(A, B, Element[ListP, a]) → Shade
  6. Circle(C, Size) → d_1
  7. Point(d_1) → D
  8. Append(Sequence[Rotate[D, s, C], s, (360 / d)°, 359.9°, (360 / d)°], Rotate[D, 359.99°, C]) → ListP2
  9. CircleSector(C, D, Element[ListP2, c]) → Shade2
  10. Segment(C, D) → b_1
  11. Zip(Segment[C, W], W, ListP2) → ListS2
  12. Zip(Segment[A, Z], Z, ListP) → ListS
  13. LCM(b, d) → mm
  14. Sequence(Rotate[F, i, E], i, 0, 6.283185307179586, (2 * π / mm)) → liste1
  15. Circle(E, F) → e
  16. Vector(A, E) → u
  17. Vector(E, G) → v
  18. Sequence(Segment[E, Element[liste1, i]], i, 1, Length[liste1]) → liste2
  19. Vector(C, G) → w
  20. Translate(e, v) → e'
  21. Translate(liste2, v) → liste2'
  22. Rotate(F, ((aa * 2) * π / mm), E) → AA
  23. CircleSector(E, F, AA) → f
  24. Translate(F, v) → F'
  25. Rotate(F', ((bb * 2) * π / mm), G) → BB
  26. CircleSector(G, F', BB) → g
  27. Mirror(D, C) → D'
  28. Mirror(F', G) → F''
  29. Text(If[aa ≟ bb, "=", If[aa > bb, ">", "<"]]) → texte6
  30. Text(If[aa ≟ bb, "=", If[aa > bb, ">", "<"]]) → texte7
  31. Midpoint(A, C) → H
  32. Midpoint(E, G) → I
  33. Text(If[aa ≟ bb, "=", If[aa > bb, ">", "<"]]) → texte9