Octagon Medians Construction

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2019-12-31 16:42

This example demonstrates the geometric construction and properties of medians in an octagon. It involves core mathematical concepts such as symmetry, polygon construction, midpoint calculation, and vector operations. The construction utilizes GeoGebra commands and objects like Intersect, ConstructionStep, Point, Polygon, Midpoint, Segment, PolyLine, Vector, and Sequence. It is suitable for high school mathematics education, helping students understand geometric constructions and spatial relationships.

GeoGebra Commands & Parameters

Intersect(xAxis, yAxis) → A
ConstructionStep() → stap
Point(xAxis) → B
Polygon(A, B, 8) → veelhoek1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
Polygon(D, C, 8) → veelhoek2, n, J, K, L, M, N, p, q, r, s, t, a, b, I
Polygon(L, K, 8) → veelhoek3, c, P, Q, R, S, T, d, e, f_1, g_1, h_1, i_1, j_1, O
Polygon(R, Q, 8) → veelhoek4, k_1, V, W, Z, A_1, B_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, U
Polygon(B, A, 8) → veelhoek5, t_1, D_1, E_1, F_1, G_1, H_1, a_1, b_1, c_1, d_1, e_1, f_2, g_2, C_1
Polygon(J, I, 8) → veelhoek6, h_2, J_1, K_1, L_1, M_1, N_1, i_2, j_2, k_2, l_2, m_2, n_2, p_2, I_1
Polygon(P, O, 8) → veelhoek7, q_2, P_1, Q_1, R_1, S_1, T_1, r_2, s_2, t_2, a_2, b_2, c_2, d_2, O_1
Polygon(V, U, 8) → veelhoek8, e_2, V_1, W_1, Z_1, A_2, B_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, U_1
Polygon(F, E, 8) → veelhoek9, m_3, D_2, E_2, F_2, G_2, H_2, n_3, p_3, q_3, r_3, s_3, t_3, a_3, C_2
Polygon(N, M, 8) → veelhoek10, b_3, J_2, K_2, L_2, M_2, N_2, c_3, d_3, e_3, f_4, g_4, h_4, i_4, I_2
Polygon(T, S, 8) → veelhoek11, j_4, P_2, Q_2, R_2, S_2, T_2, k_4, l_4, m_4, n_4, p_4, q_4, r_4, O_2
Polygon(B_1, A_1, 8) → veelhoek12, s_4, V_2, W_2, Z_2, A_3, B_3, t_4, a_4, b_4, c_4, d_4, e_4, f_5, U_2
Midpoint(f) → C_3
Midpoint(g) → D_3
Midpoint(h) → E_3
Midpoint(i) → F_3
Midpoint(j) → G_3
Midpoint(k) → H_3
Midpoint(l) → I_3
Midpoint(m) → J_3
Segment(C_3, E_3) → g_5
Segment(D_3, F_3) → h_5
Segment(E_3, G_3) → i_5
Segment(F_3, H_3) → j_5
Segment(G_3, I_3) → k_5
Segment(H_3, J_3) → l_5
Segment(I_3, C_3) → m_5
Segment(J_3, D_3) → n_5
Intersect(i_5, j_5) → K_3
Intersect(j_5, k_5) → L_3
Intersect(k_5, l_5) → M_3
Intersect(l_5, m_5) → N_3
Segment(C_3, E_3) → p_5
Intersect(m_5, n_5) → O_3
Intersect(n_5, p_5) → P_3
Intersect(h_5, p_5) → Q_3
Intersect(h_5, i_5) → R_3
PolyLine(G_3, L_3, D_3, Q_3, E_3, R_3, F_3, K_3, G_3, H_3, M_3, I_3, N_3, J_3, O_3, C_3, P_3) → q_5
Vector(A, I) → hor
Vector(A, F) → vert
Sequence(Translate[Sequence[PolyLine[Translate[G_3, Vector[(nn * hor)]], Translate[L_3, Vector[(nn * hor)]], Translate[H_3, Vector[(nn * hor)]], Translate[M_3, Vector[(nn * hor)]], Translate[I_3, Vector[(nn * hor)]], Translate[N_3, Vector[(nn * hor)]], Translate[J_3, Vector[(nn * hor)]], Translate[O_3, Vector[(nn * hor)]], Translate[C_3, Vector[(nn * hor)]], Translate[P_3, Vector[(nn * hor)]], Translate[D_3, Vector[(nn * hor)]], Translate[Q_3, Vector[(nn * hor)]], Translate[E_3, Vector[(nn * hor)]], Translate[R_3, Vector[(nn * hor)]], Translate[F_3, Vector[(nn * hor)]], Translate[K_3, Vector[(nn * hor)]], Translate[G_3, Vector[(nn * hor)]]], nn, 0, 3], Vector[(mm * vert)]], mm, -1, 1) → l1
Polygon(B, H_1, I, C) → vierhoek1, b_5, r_5, i_6, c_5
Sequence(Translate[Sequence[Polygon[Translate[B, Vector[(nn * hor)]], Translate[H_1, Vector[(nn * hor)]], Translate[I, Vector[(nn * hor)]], Translate[C, Vector[(nn * hor)]]], nn, 0, 2], Vector[(mm * vert)]], mm, 0, 1) → l2

AI Drawing Prompt Reference

Draw a regular octagon and construct the midpoints of its diagonals to form a new octagon. Then, construct a series of parallelograms with the sides of the original octagon as bases, resulting in a centrally symmetric figure.

The prompt above was compiled from the original drawing commands and is for reference only.