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Coin Counting

Coin Counting
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2020-07-06 10:16
FunctionTrigonometryCoordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates using GeoGebra to draw and count different denominations of coins, such as pennies and dimes. It involves core mathematical concepts like addition, arithmetic, coordinate geometry, geometric construction, and probability & statistics. Key GeoGebra commands and objects used include Point, Ellipse, Tangent, Intersect, Segment, pennycenter, Polygon, Mirror, Shuffle, Take, and If. Suitable for middle school and above, it serves as a practical tool for teaching currency calculation, geometric drawing, and basic probability & statistics concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → D
  3. Ellipse(K - (2, 5), K - (0 - 2, 5), 3.5) → p
  4. Ellipse(L - (2, 5), L - (0 - 2, 5), 3.5) → q
  5. Tangent(K, p) → n, r
  6. Tangent(L, q) → s, t
  7. Intersect(p, n) → N
  8. Intersect(p, r) → O
  9. Intersect(q, s) → P
  10. Intersect(q, t) → Q
  11. Segment(K, N) → a_1
  12. Segment(O, K) → b_1
  13. pennycenter(R_{11}, pennysize) → T
  14. pennycenter(R_{13}, pennysize) → U
  15. pennycenter(R_{14}, pennysize) → V
  16. pennycenter(R_{15}, pennysize) → W
  17. pennycenter(R_{16}, pennysize) → Z
  18. pennycenter(R_{10}, pennysize) → A_1
  19. pennycenter(R_{17}, pennysize) → B_1
  20. pennycenter(R_{18}, pennysize) → C_1
  21. pennycenter(R_{19}, pennysize) → D_1
  22. pennycenter(R_1, pennysize) → E_1
  23. pennycenter(R_2, pennysize) → F_1
  24. pennycenter(R_3, pennysize) → G_1
  25. pennycenter(R_4, pennysize) → H_1
  26. pennycenter(R_5, pennysize) → I_1
  27. pennycenter(R_6, pennysize) → J_1
  28. pennycenter(R_7, pennysize) → K_1
  29. pennycenter(R_8, pennysize) → L_1
  30. pennycenter(R_9, pennysize) → M_1
  31. pennycenter(R_{12}, pennysize) → N_1
  32. pennycenter(O_1, nickelsize) → Q_1
  33. pennycenter(O_2, nickelsize) → T_1
  34. pennycenter(O_3, nickelsize) → U_1
  35. pennycenter(O_4, nickelsize) → V_1
  36. pennycenter(O_5, nickelsize) → W_1
  37. pennycenter(O_6, nickelsize) → Z_1
  38. pennycenter(O_7, nickelsize) → A_2
  39. pennycenter(O_8, nickelsize) → B_2
  40. pennycenter(O_9, nickelsize) → C_2
  41. pennycenter(O_{10}, nickelsize) → D_2
  42. pennycenter(O_{11}, nickelsize) → E_2
  43. pennycenter(O_{12}, nickelsize) → F_2
  44. pennycenter(O_{13}, nickelsize) → G_2
  45. pennycenter(O_{14}, nickelsize) → H_2
  46. pennycenter(O_{15}, nickelsize) → I_2
  47. pennycenter(O_{16}, nickelsize) → J_2
  48. pennycenter(O_{17}, nickelsize) → K_2
  49. pennycenter(O_{18}, nickelsize) → L_2
  50. pennycenter(O_{19}, nickelsize) → M_2
  51. pennycenter(O_{20}, nickelsize) → N_2
  52. Point(xAxis) → C_4
  53. Polygon(U_2, V_2, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, U_3, V_3, W_2, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4, Z_2, I_4, J_4, A_3, B_3, C_3, D_3, E_3, F_3) → poly4, u_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, n_3, u_3, v_2, v_3, w_3, z_3, a_4, b_4, c_4, d_4, e_4, f_4, g_4, w_2, h_4, i_4, j_4, z_2, a_3, b_3, c_3, d_3, e_3
  54. Mirror(Rpig, x = -15) → Lpig
  55. Mirror(U_2, x = -15) → K_4
  56. Mirror(V_2, x = -15) → L_4
  57. Mirror(W_2, x = -15) → M_4
  58. Mirror(Z_2, x = -15) → N_4
  59. Mirror(A_3, x = -15) → Q_4
  60. Mirror(B_3, x = -15) → T_4
  61. Mirror(C_3, x = -15) → U_4
  62. Mirror(D_3, x = -15) → V_4
  63. Mirror(E_3, x = -15) → W_4
  64. Mirror(F_3, x = -15) → Z_4
  65. Mirror(G_3, x = -15) → A_5
  66. Mirror(H_3, x = -15) → B_5
  67. Mirror(I_3, x = -15) → C_5
  68. Mirror(J_3, x = -15) → D_5
  69. Mirror(K_3, x = -15) → E_5
  70. Mirror(L_3, x = -15) → F_5
  71. Mirror(M_3, x = -15) → G_5
  72. Mirror(N_3, x = -15) → H_5
  73. Mirror(U_3, x = -15) → I_5
  74. Mirror(V_3, x = -15) → J_5
  75. Mirror(W_3, x = -15) → K_5
  76. Mirror(Z_3, x = -15) → L_5
  77. Mirror(A_4, x = -15) → M_5
  78. Mirror(B_4, x = -15) → N_5
  79. Mirror(C_4, x = -15) → Q_5
  80. Mirror(D_4, x = -15) → T_5
  81. Mirror(E_4, x = -15) → U_5
  82. Mirror(F_4, x = -15) → V_5
  83. Mirror(G_4, x = -15) → W_5
  84. Mirror(H_4, x = -15) → Z_5
  85. Mirror(I_4, x = -15) → A_6
  86. Mirror(J_4, x = -15) → B_6
  87. Polygon(K_4, L_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, M_4, K_5, L_5, M_5, N_5, Q_5, T_5, U_5, V_5, W_5, Z_5, N_4, A_6, B_6, Q_4, T_4, U_4, V_4, W_4, Z_4) → poly4', k_4, z_4, a_5, b_5, c_5, d_5, e_5, f_5, g_5, h_5, i_5, l_4, j_5, k_5, l_5, m_5, n_5, q_5, t_5, u_5, v_5, w_5, m_4, z_5, a_6, b_6, n_4, q_4, t_4, u_4, v_4, w_4
  88. pennycenter(E_6, dimesize) → D_6
  89. pennycenter(E_7, dimesize) → F_6
  90. pennycenter(E_8, dimesize) → G_6
  91. pennycenter(E_9, dimesize) → H_6
  92. pennycenter(E_{10}, dimesize) → I_6
  93. pennycenter(E_{11}, dimesize) → J_6
  94. pennycenter(E_{12}, dimesize) → K_6
  95. pennycenter(E_{13}, dimesize) → L_6
  96. pennycenter(E_{14}, dimesize) → M_6
  97. pennycenter(E_{15}, dimesize) → N_6
  98. pennycenter(E_{16}, dimesize) → Q_6
  99. pennycenter(E_{17}, dimesize) → T_6
  100. pennycenter(E_{18}, dimesize) → U_6
  101. pennycenter(E_{19}, dimesize) → V_6
  102. pennycenter(E_{21}, dimesize) → W_6
  103. pennycenter(E_{22}, dimesize) → Z_6
  104. pennycenter(E_{23}, dimesize) → A_7
  105. pennycenter(E_{24}, dimesize) → B_7
  106. pennycenter(E, dimesize) → D_7
  107. pennycenter(E_{20}, dimesize) → F_7
  108. pennycenter(G_7, quartersize) → I_7
  109. pennycenter(G_{10}, quartersize) → J_7
  110. pennycenter(G_9, quartersize) → K_7
  111. pennycenter(G_8, quartersize) → L_7
  112. pennycenter(G_{14}, quartersize) → M_7
  113. pennycenter(G_{13}, quartersize) → N_7
  114. pennycenter(G_{12}, quartersize) → Q_7
  115. pennycenter(G_{11}, quartersize) → T_7
  116. pennycenter(G_{18}, quartersize) → U_7
  117. pennycenter(G_{17}, quartersize) → V_7
  118. pennycenter(G_{16}, quartersize) → W_7
  119. pennycenter(G_{15}, quartersize) → Z_7
  120. pennycenter(G_{19}, quartersize) → A_8
  121. pennycenter(G_{20}, quartersize) → B_8
  122. pennycenter(G_{21}, quartersize) → D_8
  123. pennycenter(G_{22}, quartersize) → F_8
  124. pennycenter(G_{23}, quartersize) → I_8
  125. pennycenter(G_{24}, quartersize) → J_8
  126. pennycenter(G_{25}, quartersize) → K_8
  127. pennycenter(G_{26}, quartersize) → L_8
  128. Shuffle(Remove[Flatten[Sequence[Sequence[Point[{i, j}], i, -32, -22, 3], j, 8, 0, -3]], {(-32, 8), (-23, 2)}]) → leftbanklist, {(-29, 8), (-26, 2), (-32, 2), (-23, 5), (-26, 8), (-23, 8), (-29, 5), (-32, 5), (-26, 5), (-29, 2)}
  129. Shuffle(Remove[Flatten[Sequence[Sequence[Point[{i, j}], i, -9, 0, 3], j, 8, 0, -3]], {(0, 2), (0, 8)}]) → rightbanklist, {(-6, 2), (-9, 2), (-3, 8), (-6, 5), (-3, 5), (0, 5), (-6, 8), (-9, 5), (-3, 2), (-9, 8)}
  130. Take(Shuffle[Flatten[Sequence[Remove[Unique[{If[d, "P"], If[e, "N"], If[f, "D"], If[g, "Q"]}], {""}], i, 1, 10]]], 1, Random[3, 10]) → bank1
  131. Take(Shuffle[Flatten[Sequence[Remove[Unique[{If[d, "P"], If[e, "N"], If[f, "D"], If[g, "Q"]}], {""}], i, 1, 10]]], 1, Random[3, 10]) → bank2
  132. If(Rtotal ≟ 0, "0¢", If[Rtotal < 100, Rtotal + "¢", "$" + Rhundreds + "." + Rtens + Rones]) → text2
  133. If(Ltotal ≟ 0, "0¢", If[Ltotal < 100, Ltotal + "¢", "$" + Lhundreds + "." + Ltens + Lones]) → text1