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Fraction Quantity Comparison

Fraction Quantity Comparison
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2019-03-24 13:12
TriangleSolid GeometryGeometric Construction
This example dynamically demonstrates the comparison of fractions, visually showcasing the quantitative relationships in different geometric shapes. It involves core mathematical concepts such as fractions, geometric constructions, equilateral triangles, orthocenter, solid geometry, and Pythagorean theorem. GeoGebra commands and objects like Point, GCD, Polygon, Sequence, PolyLine, Mirror, Segment, If, Div, and Mod are used in the construction process. It is suitable for high school mathematics teaching, helping students understand the application of fractions in geometry.

GeoGebra Commands & Parameters

  1. Point(Sequence[A + (i, 0), i, 1, 24]) → P
  2. Point(Sequence[B + (i, 0), i, 1, 24]) → Q
  3. GCD(num1 - num2, If[a, num2, num1]) → hcf
  4. Polygon({A, P, P + (0, 1), A + (0, 1)}) → q1
  5. Polygon({B, Q, Q + (0, 1), B + (0, 1)}) → q2
  6. Sequence(Translate[pic1, Vector[A + (i - 1, 0)]], i, 1, num1) → l1
  7. Sequence(Translate[pic2, Vector[B + (i - 1, 0)]], i, 1, num2) → l2
  8. Polygon({P, (x(Q), y(P)), (x(Q), y(P) + 1), P + (0, 1)}) → q3
  9. Polygon({Q, Q + (x(P) - x(Q), 0), Q + (x(P) - x(Q), 1), Q + (0, 1)}) → q4
  10. PolyLine(C + (0, 0.5), C + (0, 0.7), ((x(C) + x(D)) / 2, y(C) + 0.7), ((x(C) + x(D)) / 2, y(C) + 0.9), ((x(C) + x(D)) / 2, y(C) + 0.7), D + (0, 0.7), D + (0, 0.5)) → f
  11. Mirror(f, y = y(A) + 0.5) → f'
  12. Segment(Q + (0, 1), If[x(P) < x(Q), D - (0, 1), C - (0, 1)]) → g
  13. PolyLine(B - (0, 0.5), B - (0, 0.7), ((x(B) + x(Q)) / 2, y(Q) - 0.7), ((x(B) + x(Q)) / 2, y(B) - 0.9), ((x(B) + x(Q)) / 2, y(B) - 0.7), Q - (0, 0.7), Q - (0, 0.5)) → h
  14. PolyLine(E + (0, 0.5), E + (0, 0.7), ((x(E) + x(F)) / 2, y(E) + 0.7), ((x(E) + x(F)) / 2, y(E) + 0.9), ((x(E) + x(F)) / 2, y(E) + 0.7), F + (0, 0.7), F + (0, 0.5)) → i
  15. Mirror(i, y = y(B) + 0.5) → i'
  16. PolyLine(A - (0, 0.5), A - (0, 0.7), ((x(A) + x(P)) / 2, y(P) - 0.7), ((x(A) + x(P)) / 2, y(A) - 0.9), ((x(A) + x(P)) / 2, y(A) - 0.7), P - (0, 0.7), P - (0, 0.5)) → j
  17. If(hcf > 1 ∨ abs(num1 - num2) ≥ If[a, num2, num1], true, false) → simplify
  18. Div(abs(num1 - num2), If[a, num2, num1]) → ainteger_1
  19. Mod(abs(num1 - num2) / hcf, If[a, num2, num1] / hcf) → anumerator