Cash Register: Random Coin Stacking and Geometric Simulation
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Elementary School Applets
① This GeoGebra example simulates a cash register scenario where random coins are generated and stacked within a rectangular area, illustrating the interplay between randomness and geometric shapes. ② Core mathematical concepts include hypergeometric distribution (modeling draws from a finite coin set), random number generation, polygon construction, and volume (via stack height) along with rectangle area. ③ Construction details: uses Point to define coin centers, Polygon to build coin shapes, Shuffle and RandomElement for random selection, Random for stochastic parameters, Intersect for collision detection, and Element/If for conditional logic; objects include numerous points (A, B_4, C_4, etc.) and variables (pennysize, R, S) driven by sliders or random commands. ④ Suitable for middle/high school math or probability/statistics classes, demonstrating random simulation, geometric construction, and distribution concepts, and serving as an introductory example for computational math modeling.
GeoGebra Commands & Parameters
Point(xAxis) → C_4pennycenter(R_{11}, pennysize) → Tpennycenter(R_{13}, pennysize) → Upennycenter(R_{14}, pennysize) → Vpennycenter(R_{15}, pennysize) → Wpennycenter(R_{16}, pennysize) → Zpennycenter(R_{10}, pennysize) → A_1pennycenter(R_{17}, pennysize) → B_1pennycenter(R_{18}, pennysize) → C_1pennycenter(R_{19}, pennysize) → D_1pennycenter(R_1, pennysize) → E_1pennycenter(R_2, pennysize) → F_1pennycenter(R_3, pennysize) → G_1pennycenter(R_4, pennysize) → H_1pennycenter(R_5, pennysize) → I_1pennycenter(R_6, pennysize) → J_1pennycenter(R_7, pennysize) → K_1pennycenter(R_8, pennysize) → L_1pennycenter(R_9, pennysize) → M_1pennycenter(R_{12}, pennysize) → N_1pennycenter(O_1, nickelsize) → Q_1pennycenter(O_2, nickelsize) → T_1pennycenter(O_3, nickelsize) → U_1pennycenter(O_4, nickelsize) → V_1pennycenter(O_5, nickelsize) → W_1pennycenter(O_6, nickelsize) → Z_1pennycenter(O_7, nickelsize) → A_2pennycenter(O_8, nickelsize) → B_2pennycenter(O_9, nickelsize) → C_2pennycenter(O_{10}, nickelsize) → D_2pennycenter(O_{11}, nickelsize) → E_2pennycenter(O_{12}, nickelsize) → F_2pennycenter(O_{13}, nickelsize) → G_2pennycenter(O_{14}, nickelsize) → H_2pennycenter(O_{15}, nickelsize) → I_2pennycenter(O_{16}, nickelsize) → J_2pennycenter(O_{17}, nickelsize) → K_2pennycenter(O_{18}, nickelsize) → L_2pennycenter(O_{19}, nickelsize) → M_2pennycenter(O_{20}, nickelsize) → N_2Polygon(J_3, K_3, C_4, D_4, E_4, F_4, G_4, I_3, L_3, M_3, A, V_3, W_3, Z_3, A_4, B_4) → poly4, h, r, s, t, f_1, g_1, h_1, i_1, i, j, k, l, m, n, p, qpennycenter(E_6, dimesize) → D_6pennycenter(E_7, dimesize) → F_6pennycenter(E_8, dimesize) → G_6pennycenter(E_9, dimesize) → H_6pennycenter(E_{10}, dimesize) → I_6pennycenter(E_{11}, dimesize) → J_6pennycenter(E_{12}, dimesize) → K_6pennycenter(E_{13}, dimesize) → L_6pennycenter(E_{14}, dimesize) → M_6pennycenter(E_{15}, dimesize) → N_6pennycenter(E_{16}, dimesize) → Q_6pennycenter(E_{17}, dimesize) → T_6pennycenter(E_{18}, dimesize) → U_6pennycenter(E_{19}, dimesize) → V_6pennycenter(E_{21}, dimesize) → W_6pennycenter(E_{22}, dimesize) → Z_6pennycenter(E_{23}, dimesize) → A_7pennycenter(E_{24}, dimesize) → B_7pennycenter(E, dimesize) → D_7pennycenter(E_{20}, dimesize) → F_7pennycenter(G_7, quartersize) → I_7pennycenter(G_{10}, quartersize) → J_7pennycenter(G_9, quartersize) → K_7pennycenter(G_8, quartersize) → L_7pennycenter(G_{14}, quartersize) → M_7pennycenter(G_{13}, quartersize) → N_7pennycenter(G_{12}, quartersize) → Q_7pennycenter(G_{11}, quartersize) → T_7pennycenter(G_{18}, quartersize) → U_7pennycenter(G_{17}, quartersize) → V_7pennycenter(G_{16}, quartersize) → W_7pennycenter(G_{15}, quartersize) → Z_7pennycenter(G_{19}, quartersize) → A_8pennycenter(G_{20}, quartersize) → B_8pennycenter(G_{21}, quartersize) → D_8pennycenter(G_{22}, quartersize) → F_8pennycenter(G_{23}, quartersize) → I_8pennycenter(G_{24}, quartersize) → J_8pennycenter(G_{25}, quartersize) → K_8pennycenter(G_{26}, quartersize) → L_8Shuffle(Remove[Flatten[Sequence[Sequence[Point[{i, j}], i, -32, -22, 3], j, 8, 0, -3]], {(-32, 8), (-23, 2)}]) → leftbanklistPolygon(C_4, B_4, A_4, Z_3, E_4, D_4) → poly1, c_4, b_4, a_4, z_3, e_4, d_4Polygon(B, C, D, F) → poly2, b_1, c_1, d_1, f_2Intersect(z_3, e_4) → JPolygon(J, F_4, W_3, Z_3) → poly3, j_2, f_4, w_3, z_1Polygon(F_4, G_4, V_3, W_3) → poly5, f_3, g_4, v_3, w_1Polygon(G_4, I_3, A, V_3) → poly6, g_2, i_3, a_1, v_1Polygon(H_4, I_4, N_3, U_3) → poly7, h_4, i_4, n_3, u_3Polygon(J_3, K_3, L_3, M_3) → poly8, j_3, k_3, l_3, m_3Polygon(K, L, M, N) → poly9, k_2, l_2, m_2, n_1Polygon(O, P, Q, Q_2) → poly10, o, p_1, q_1, q_2RandomElement({"gum", "yo-yo", "bottle of bubbles", "top", "candy", "lollipop", "pencil"}) → buyingElement({"1¢", "10¢", "20¢", "50¢", "$1.00"}, u) → maxTextRandom(Element[{1, 10, 20, 50, 100}, u - 1], Element[{1, 10, 20, 50, 100}, u]) → costIf(cost ≟ 100, "$1.00", Text[cost] + "¢") → costTextIf(Rtotal ≟ 0, "0¢", If[Rtotal < 100, Rtotal + "¢", "$" + Rhundreds + "." + Rtens + Rones]) → text2If(cost ≟ Rtotal, "You bought it!", If[cost > Rtotal, "You haven't paid enough.", "You paid too much."]) → checkText
AI Drawing Prompt Reference
Simulate a cash register scenario with randomly generated and stacked coins of varying sizes within a rectangular area to illustrate the interplay between randomness and geometry. Use random numbers to determine coin positions and sizes, construct coin shapes with polygons, and detect collisions to prevent overlaps. Display stacks of different types of coins (like pennies, nickels, dimes) controlled by sliders for size and quantity, demonstrating probability distributions and geometric construction concepts.
The prompt above was compiled from the original drawing commands and is for reference only.