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Understanding Percentages in Geometry and Algebra

Understanding Percentages in Geometry and Algebra
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2023-12-21 01:20
FunctionSequenceGeometric Construction
In collections The Fractions book
This example demonstrates the application of percentages through geometric and algebraic operations. Key mathematical concepts include ratios, fractions, and geometric transformations. Construction involves GeoGebra commands like Sequence, Polygon, Circle, and Translate. Suitable for middle school or high school students learning the integration of geometry and algebra.

GeoGebra Commands & Parameters

  1. Sequence((k, y(E)), k, x(E), x(F), Distance[E, F] / 100) → ptGrid
  2. Polygon(A, B, 4) → poly1remplil, j, m, n, p, M, N
  3. Polygon(A, B, 4) → poly1tour, f, g, h, i, C, D
  4. Mirror(P1, yAxis) → P1'
  5. Mirror(P1', xAxis) → P1''
  6. Mirror(P1'', yAxis) → P1'''
  7. Polygon(P1, P1', P1'', P1''') → blanc, p1, p1', p1'', p1'''
  8. Segment(E, F) → segmPerc
  9. Sequence(Segment[(t, y(E) - 0.8), (t, y(E) + 0.8)], t, x(E), x(F), Distance[E, F] / 10) → longgrad1
  10. Sequence(Segment[(t, y(E) - 0.9), (t, y(E) + 0.9)], t, x(E), x(F), Distance[E, F] / 20) → intergrad1
  11. Sequence(Segment[(t, y(E) - 0.2), (t, y(E) + 0.2)], t, x(E), x(F), Distance[E, F] / 100) → petitgrad1
  12. Sequence(E + (k / 100 * (F - E)), k, 0, 100) → segmGrid
  13. Zip({Segment[(k, 0), (k, 10)], Segment[(0, k), (10, k)]}, k, 1…10) → carre
  14. Segment(G, H) → segmNum
  15. Vector(E, G) → u
  16. Translate(longgrad1, u) → longgrad2
  17. Translate(petitgrad1, u) → petitgrad2
  18. If(x(P) ≠ x(F), Polygon[A, L, Pointfin, I, K, D], poly1remplil) → poly2
  19. Vector(O, R) → v
  20. Vector(A, S) → w
  21. Translate(carre, w) → Divcarre'
  22. Translate(poly2, w) → poly2'
  23. Translate(A, w) → A'
  24. Translate(B, w) → B'
  25. Segment(A', B') → f'
  26. Segment(S, S + (0, 10)) → k
  27. Polygon(E + (0, 0.9), F + (0, 0.9), F + (0, -0.9), E + (0, -0.9)) → q1, l, q, r, s
  28. Polygon(E + (0, 0.9), P + (0, 0.9), P + (0, -0.9), E - (0, 0.9)) → q2, t, c, d, e
  29. Segment(G, Q) → f_1
  30. Translate(Pointfin, w) → pointfin'
  31. Sequence((t, y(E) + 0.9), t, x(E), x(F), Distance[E, F] / 10) → l1
  32. Circle(U, 5) → c_1
  33. Sequence(Rotate[V, i, U], i, 0, (2 * pi), (2 * pi / 20)) → l3
  34. Rotate(V, ((a / 100 * 2) * pi), U) → V'
  35. CircleSector(U, V, V') → d_1
  36. Sequence((t, y(G) + 0.9), t, x(E), x(F), Distance[E, F] / 10) → l6
  37. Sequence(Text[(10 * i), Element[l1, i] + (2.2, 0.2)], i, 0, Length[l1] - 1, 1) → l2
  38. Sequence(Segment[Element[l3, i], U], i, 1, Length[l3], 1) → l4
  39. GCD(a, 100) → aa
  40. Circle(W, 5) → e_1
  41. Sequence(Rotate[Z, i, W], i, 0, (2 * pi), (2 * pi / (100 / aa))) → l8
  42. Rotate(Z, ((a / aa * 2) * pi / (100 / aa)), W) → Z'
  43. CircleSector(W, Z, Z') → g_1
  44. Sequence(Segment[W, Element[l8, i]], i, 1, Length[l8]) → l9
  45. Mirror(B_1, A_1) → C_1
  46. Ellipse(C_1, B_1, D_1) → h_1
  47. Midpoint(E_1, F_1) → G_1
  48. Segment(E_1, B_1) → i_1
  49. Segment(F_1, C_1) → j_1
  50. Vector(A_1, G_1) → u_1
  51. Sequence(Translate[h_1, Vector[(i * u_1)]], i, 0, 1, 0.1) → l10
  52. Translate(h_1, Vector[(valDec * u_1)]) → k_1
  53. Translate(B_1, Vector[(valDec * u_1)]) → H_1
  54. Translate(C_1, Vector[(valDec * u_1)]) → I_1
  55. Polygon(H_1, B_1, C_1, I_1) → q3, l_1, b_1, m_1, n_1
  56. Ellipse(C_1, B_1, D_1) → p_1
  57. Sequence(Text[(10 * i / 2) + "%", (1.15 * Element[l3, i + 1]) + (-3.2, -1.5)], i, 0, Length[l3] - 2, 1) → l5
  58. Sequence(Translate[C_1, Vector[(i * u_1)]], i, 0, 1, 0.1) → l11
  59. Sequence(Text[(0.1 * i) + "L", Element[l11, i] + (0.2, 0.5)], i, 0, Length[l11] - 1, 1) → l12
  60. Translate(h_1, Vector[(valDec * u_1)]) → q_1
  61. Vector(J_1, K_1) → v_1
  62. Vector(L_1, M_1) → w_1
  63. Vector(N_1, O_1) → a_1
  64. Vector(P_1, Q_1) → r_1
  65. Sequence(Segment[(t, y(G) - 0.4), (t, y(G) + 0.4)], t, x(G), x(H), Distance[G, H] / 20) → intergrad2
  66. Sequence(Text[i / 10, Element[l6, i] + (2.25, 0.2)], i, 0, Length[l1] - 1, 1) → l7

AI Drawing Prompt Reference

Draw a comprehensive geometric and algebraic diagram demonstrating percentages. Start with a square, subdivided into a grid with tick marks. Above the square, draw a horizontal number line from 0 to 100 with labeled ticks. Below the number line, place a rectangle divided into 100 vertical strips, with a portion shaded to represent a percentage. Next to it, draw a circle with a sector highlighted to show the same percentage, and label the angle. Also include an ellipse to illustrate the relationship between percentages and geometric shapes. Finally, add arrows and labels to explain the connections between the parts.
The prompt above was compiled from the original drawing commands and is for reference only.