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Comparing Two Fractions: Geometric Construction and Function Graphs

Comparing Two Fractions: Geometric Construction and Function Graphs
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2019-01-08 09:24
FunctionGeometric Construction
This example demonstrates how to compare two fractions using geometric constructions and function graphs. Key mathematical concepts include fractions, step functions, addition, correlation, standard deviation, and the Pythagorean theorem. Construction involves GeoGebra commands such as Intersect, Point, Segment, Sequence, and Polygon. Suitable for middle or high school mathematics education to understand the relationship between fractions, geometry, and functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → C
  4. Segment(A, B) → f
  5. Segment(B, D) → g
  6. Segment(D, C) → h
  7. Segment(C, A) → i
  8. Sequence(A + ((B - A) * t), t, 0, 1, 1 / penyebut) → L_1
  9. Sequence(C + ((D - C) * t), t, 0, 1, 1 / penyebut) → L_2
  10. Sequence(C + ((D - C) * t), t, 0, 1, 1 / penyebut) → L_3
  11. Sequence(Segment[Element[L_1, k], Element[L_2, k]], k, 1, penyebut) → L_4
  12. Sequence(Segment[Element[L_1, k], Element[L_2, k]], k, 1, penyebut) → L_5
  13. Point(Circle[A, a]) → E
  14. Polygon(A, E, F, C) → q1, a_1, e, f_1, c
  15. Sequence(G + ((H - G) * t), t, 0, 1, 1 / penyebut2) → l1
  16. Sequence(I + ((J - I) * t), t, 0, 1, 1 / penyebut2) → l2
  17. Sequence(Segment[Element[l1, r], Element[l2, r]], r, 1, penyebut2) → l3
  18. Sequence(Segment[Element[l1, r], Element[l2, r]], r, 1, penyebut2) → l4
  19. Polygon(G, X, Y, I) → q2, g_1, x_1, y_1, i_1
  20. Segment(G, H) → j
  21. Segment(H, J) → k
  22. Segment(J, I) → l
  23. Segment(I, G) → m