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Inscribed and Circumscribed Polygons by Linda Triplett

Inscribed and Circumscribed Polygons by Linda Triplett
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2017-11-01 06:18
CirclePolygonTrigonometryOptimizationGeometric Construction
This example demonstrates the construction of inscribed and circumscribed polygons, showcasing their geometric relationships. Key math concepts include polygons, circles, angles, orthogonal lines, intersections, and circumferences. It utilizes GeoGebra commands like Circle, Point, Rotate, Angle, Polygon, OrthogonalLine, Intersect, Circumference, and PointIn. Suitable for high school mathematics education to understand polygonal properties and optimization problems.

GeoGebra Commands & Parameters

  1. Circle(A, 5) → c
  2. Point(c) → B
  3. Rotate(B, (360 / n)°, A) → B'
  4. Angle(B, A, B') → α
  5. Polygon(B, B', n) → poly1, f, f_1, g_{10}, C, I, K, L, P, Q, R, S, T, g_1, B_1, C_1, D_1, E_1, F_1, L_1, M_1, N_1, O_1, T_1, m_1, U_1, V_1, B_2, D_2, E_2, F_2, J_2, K_2, N_2, O_2, n_1, R_2, S_2, V_2, W_2, B_3, D_3, F_3, G_3, H_3, I_3, p_1, J_3, P_3, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, H_4, q_1, I_4, J_4, K_4, L_4, R_4, S_4, V_4, Z_4, A_5, B_5, r_1, C_5, D_5, E_5, F_5, G_5, H_5, I_5, J_5, K_5, L_5, d_1, M_5, N_5, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, e_1, N_6, O_6, P_6, Q_6, F_7, G_7, J_7, L_7, M_7, N_7, f_2, O_7, P_7, Q_7, R_7, S_7, T_7, U_7, V_7, W_7, g, g_2, l_2, m_2, n_2, s_2, a_2, b_2, c_2, g_3, h_3, h, k_3, l_3, p_3, q_3, t_3, a_3, d_3, f_4, h_4, i_4, m, j_4, k_4, l_4, s_4, t_4, a_4, b_4, c_4, d_4, e_4, q, f_5, p_5, q_5, r_5, s_5, t_5, f_6, g_6, j_6, l_6, r, m_6, n_6, p_6, q_6, r_6, s_6, t_6, a_6, b_6, c_6, a, d_6, e_6, f_7, g_7, d_7, e_7, f_8, g_8, h_8, i_8, b, j_8, k_8, l_8, m_8, n_8, p_8, i_9, j_9, m_9, p_9, e, q_9, r_9, s_9, t_9, a_9, b_9, c_9, d_9, e_9, f_{10}
  6. OrthogonalLine(A, f) → i
  7. Intersect(i, f) → D
  8. Circle(A, D) → d
  9. Intersect(d, h) → E, F
  10. Intersect(d, g) → G, M
  11. Polygon(D, G, n) → poly2, j, k_1, t_{10}, H, J, N, O, U, V, W, Z, A_1, l_1, G_1, H_1, I_1, J_1, K_1, P_1, Q_1, R_1, S_1, W_1, s_1, Z_1, A_2, C_2, G_2, H_2, I_2, L_2, M_2, P_2, Q_2, t_1, T_2, U_2, Z_2, A_3, C_3, E_3, K_3, L_3, M_3, N_3, a_1, O_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, M_4, b_1, N_4, O_4, P_4, Q_4, T_4, U_4, W_4, O_5, P_5, Q_5, c_1, R_5, S_5, T_5, U_5, V_5, W_5, Z_5, A_6, B_6, C_6, h_2, D_6, E_6, R_6, S_6, T_6, U_6, V_6, W_6, Z_6, A_7, i_2, B_7, C_7, D_7, E_7, H_7, I_7, K_7, Z_7, A_8, B_8, j_2, C_8, D_8, E_8, F_8, G_8, H_8, I_8, J_8, K_8, k, k_2, p_2, q_2, r_2, t_2, d_2, e_2, f_3, i_3, j_3, l, m_3, n_3, r_3, s_3, b_3, c_3, e_3, g_4, m_4, n_4, p, p_4, q_4, r_4, g_5, h_5, i_5, j_5, k_5, l_5, m_5, s, n_5, a_5, b_5, c_5, d_5, e_5, h_6, i_6, k_6, h_7, t, i_7, j_7, k_7, l_7, m_7, n_7, p_7, q_7, r_7, s_7, h_1, t_7, a_7, b_7, c_7, q_8, r_8, s_8, t_8, a_8, b_8, i_1, c_8, d_8, e_8, f_9, g_9, h_9, k_9, l_9, n_9, h_{10}, j_1, i_{10}, j_{10}, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, q_{10}, r_{10}, s_{10}
  12. Circumference(d) → circumferenced
  13. PointIn(d) → Pointd