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Part-Whole Rectangles

Part-Whole Rectangles
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2015-09-15 23:24
Coordinate GeometryDerivativeParametric EquationGeometric Construction
This example demonstrates part-whole relationships through rectangle segmentation and comparison. It involves core math concepts like coordinate geometry, parametric equations, derivatives, and geometric transformations. Construction uses commands such as Segment, Sequence, Point, Intersect, Polygon, If, Midpoint, OrthogonalLine, and Textfield. Suitable for high school mathematics teaching, illustrating function, geometric construction, and parametric equation applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Sequence(Point[{((x(B) - x(A)) / 8 * i) + x(A), ((y(B) - y(A)) / 9 * i) + y(A)}], i, 0, 8, 1) → list1
  3. Point(list1) → bound1
  4. Point(list1) → bound2
  5. Intersect(xAxis, yAxis) → C
  6. Point(xAxis) → D
  7. Polygon(C, D, E, F) → poly1, c_1, d, e, f_1
  8. If(x(bound1) ≟ x(Element[list1, 1]), 10, If[x(bound1) ≟ x(Element[list1, 2]), 20, If[x(bound1) ≟ x(Element[list1, 3]), 50, If[x(bound1) ≟ x(Element[list1, 4]), 100, If[x(bound1) ≟ x(Element[list1, 5]), 200, If[x(bound1) ≟ x(Element[list1, 6]), 500, If[x(bound1) ≟ x(Element[list1, 7]), 1000, If[x(bound1) ≟ x(Element[list1, 8]), 5000, 10000]]]]]]]) → B1
  9. If(x(bound2) ≟ x(Element[list1, 1]), 10, If[x(bound2) ≟ x(Element[list1, 2]), 20, If[x(bound2) ≟ x(Element[list1, 3]), 50, If[x(bound2) ≟ x(Element[list1, 4]), 100, If[x(bound2) ≟ x(Element[list1, 5]), 200, If[x(bound2) ≟ x(Element[list1, 6]), 500, If[x(bound2) ≟ x(Element[list1, 7]), 1000, If[x(bound2) ≟ x(Element[list1, 8]), 5000, 10000]]]]]]]) → B2
  10. Midpoint(C, F) → G
  11. Midpoint(E, D) → H
  12. Point(Segment[G, H]) → I
  13. OrthogonalLine(I, e) → h
  14. Intersect(h, e) → J
  15. Intersect(h, c_1) → K
  16. Polygon(F, J, K, C) → poly2, f_2, j, k, c_2
  17. Midpoint(I, G) → textpoint
  18. Point(yAxis) → L
  19. Point(yAxis) → M
  20. Polygon(L, M, N, O) → poly3, l, m, n_2, o
  21. Point(yAxis) → P
  22. Point(yAxis) → Q
  23. Point(yAxis) → U
  24. Segment(P, Q) → i
  25. Segment(U, T) → p
  26. Segment(R, S) → q
  27. Polygon(L, (answerx, (-2)), (answerx, (-4)), M) → poly4, l_1, r, s, m_1
  28. Midpoint(Midpoint[L, M], (answerx, (-3))) → textpoint2
  29. Textfield(inTxt) → InputBox1
  30. Textfield(inTxt_3) → InputBox2