Animated Net of a Square Pyramid by syjang
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This example demonstrates the net of a square pyramid in an animated form. Key mathematical concepts include solid geometry and polyhedron nets. Using GeoGebra commands such as Point, Segment, Line, Polygon, etc., a dynamic net of a square pyramid is constructed. Suitable for middle school and above students learning solid geometry.
GeoGebra Commands & Parameters
Point(Circle[A, w]) → BSegment(A, B) → aLine(A, B) → b_2Circle(B, (3 * w / 4.5)) → cIntersect(c, b_2, 2) → CRotate(C, 30°, B) → C'Line(C', b_2) → dSegment(B, C') → eLine(A, e) → fIntersect(d, f) → DPolygon(A, B, C', D) → poly1, a_1, b_1, c', d_1Segment(A, C') → gSegment(D, B) → h_1Intersect(g, h_1) → EOrthogonalLine(E, a_1) → iCircle(E, h) → kIntersect(k, i, 2) → FSegment(B, F) → jSegment(C', F) → l_5Segment(F, D) → mSegment(F, A) → nSegment(E, F) → pSegment(A, D) → qMidpoint(b_1) → GSegment(G, F) → rAngle(G, E, F) → αSegment(E, G) → tLine(E, G) → c_1Circle(G, F) → f_1Intersect(f_1, c_1, 2) → HIntersect(c_1, d_1) → ICircle(I, F) → g_1Intersect(g_1, c_1, 1) → JVector(F, J) → uPoint(c') → LCircle(L, F) → q_1Vector(F, H) → w_3Midpoint(A, B) → KLine(K, E) → e_1Circle(K, h) → p_1Intersect(e_1, c') → MCircle(M, h) → r_1Intersect(r_1, e_1, 2) → NIntersect(p_1, e_1, 1) → OVector(F, N) → vVector(F, O) → zTranslate(F, Vector[(z * o)]) → F'_1Translate(F, Vector[(u * (o - 1))]) → F'_2Translate(F, Vector[(v * (o - 2))]) → F'_3Translate(F, Vector[(w_3 * (o - 3))]) → F'Segment(F, N) → sLineBisector(s) → a_2Intersect(a_2, c') → PCircleArc(P, N, F) → c_2Ray(P, F'_3) → d_2Intersect(c_2, d_2, 1) → QSegment(F, O) → e_2LineBisector(e_2) → f_2Intersect(f_2, a_1) → RCircleArc(R, F, O) → g_2Ray(R, F'_1) → h_2Intersect(g_2, h_2, 1) → SCircleArc(I, F, J) → k_2CircleArc(G, H, F) → p_2Ray(I, F'_2) → i_2Intersect(k_2, i_2, 1) → TRay(G, F') → j_2Intersect(p_2, j_2, 1) → UCircle(I, E) → s_1OrthogonalLine(I, a_1) → i_1Intersect(s_1, i_1, 2) → VIntersect(s_1, i_1, 1) → WOrthogonalLine(V, i_1) → j_1OrthogonalLine(W, i_1) → k_1OrthogonalLine(G, k_1) → l_1Intersect(j_1, l_1) → ZIntersect(k_1, l_1) → A_1Midpoint(V, Z) → B_1Midpoint(A_1, W) → C_1Circle(B_1, r) → t_1Circle(C_1, r) → q_2OrthogonalLine(B_1, k_1) → m_1Intersect(t_1, m_1, 1) → D_1Intersect(q_2, m_1, 2) → E_1Vector(C', Z) → u_1Vector(B, A_1) → v_1Vector(N, D_1) → w_1Vector(O, E_1) → z_1Translate(N, Vector[(w_1 * (o - 4))]) → N'Translate(O, Vector[(z_1 * (o - 4))]) → O'Translate(B, Vector[(v_1 * (o - 4))]) → B'Translate(A, Vector[(v_1 * (o - 4))]) → A'Translate(C', Vector[(u_1 * (o - 4))]) → C''Translate(D, Vector[(u_1 * (o - 4))]) → D'If(o < 1, S, If[o < 4, O, If[o < 5, O', E_1]]) → F_1If(o < 1, F, If[o < 2, T, J]) → G_1If(o < 3, F, If[o < 4, U, H]) → H_1If(o < 2, F, If[o < 3, Q, If[o < 4, N, If[o < 5, N', D_1]]]) → I_1If(o < 4, A, If[o < 5, A', W]) → J_1If(o < 4, B, If[o < 5, B', A_1]) → K_1If(o < 4, C', If[o < 5, C'', Z]) → L_1If(o < 4, D, If[o < 5, D', V]) → M_1Polygon(F_1, J_1, K_1) → poly2, k_3, f_3, j_3Polygon(L_1, H_1, K_1) → poly3, k_4, l_2, h_3Polygon(L_1, I_1, M_1) → poly4, m_2, l_3, i_3Polygon(M_1, G_1, J_1) → poly5, j_4, m_3, g_3Intersect(m, j_3) → N_1Segment(I_1, N_1) → n_1Intersect(j_3, i_3) → O_1Intersect(c', i_3) → Q_1Intersect(c', i_3) → R_1Intersect(c', i_3) → S_1Intersect(c', i_3) → U_1Intersect(c', i_3) → A_2Intersect(l_2, i_3) → B_2Segment(B_2, O_1) → n_2Segment(B_2, M_1) → r_2Midpoint(M_1, L_1) → C_2Midpoint(L_1, K_1) → D_2Midpoint(K_1, J_1) → E_2Midpoint(J_1, M_1) → F_2Segment(G_1, F_2) → s_2Segment(C_2, I_1) → t_2Segment(D_2, H_1) → a_3Segment(E_2, F_1) → b_3Polygon(J_1, M_1, L_1, K_1) → poly6, j_5, m_4, l_4, k_5Intersect(j_3, d_1) → P_1Segment(P_1, M_1) → c_3Midpoint(p) → V_1OrthogonalLine(V_1, p) → d_3Point(d_3) → W_1Vector(W_1, V_1) → u_2Midpoint(r) → T_1Midpoint(a_3) → Z_1Point(a_2) → G_2Vector(G_2, T_1) → v_2Vector(G_2, Z_1) → w_2Point(Circle[H_2, w]) → I_2Segment(H_2, I_2) → e_3Line(H_2, I_2) → bCircle(I_2, (3 * w / 4.5)) → p_3Intersect(p_3, b, 2) → J_2Rotate(J_2, 30°, I_2) → K_2Segment(I_2, K_2) → n_3Line(K_2, b) → q_3Line(H_2, n_3) → r_3Intersect(q_3, r_3) → L_2Segment(H_2, K_2) → s_3Segment(I_2, L_2) → t_3Intersect(s_3, t_3) → M_2Circle(M_2, h) → c_4OrthogonalLine(M_2, b) → a_4Intersect(c_4, a_4, 2) → N_2Polygon(H_2, N_2, I_2) → poly7, i_4, h_4, n_4Polygon(I_2, N_2, K_2) → poly8, k_6, i_5, n_5Polygon(H_2, L_2, K_2, I_2) → poly9, h_5, l_6, k_7, i_6Polygon(H_2, N_2, L_2) → poly10, l_7, h_6, n_6Polygon(L_2, N_2, K_2) → poly11, k_8, l_8, n_7Midpoint(k_7) → O_2Segment(M_2, O_2) → b_4Segment(M_2, N_2) → d_4Segment(N_2, O_2) → e_4Angle(O_2, M_2, N_2) → βMidpoint(N_2, M_2) → P_2Midpoint(O_2, N_2) → Q_2Line(P_2, Q_2) → f_4Circle(P_2, w) → g_4Intersect(g_4, f_4, 1) → R_2Intersect(g_4, f_4, 2) → S_2Vector(R_2, P_2) → z_2Vector(S_2, Q_2) → u_3Midpoint(b_3) → V_2
AI Drawing Prompt Reference
Draw an animated net of a square pyramid. Start with a circle and a point on it as one vertex of the base square. Connect this point to the center to form a side, then use rotation and intersections to construct the other three vertices of the square. Find the intersection of the square's diagonals, draw a perpendicular line from this center, and use a circle to locate the apex above the base. Connect the apex to each base vertex to form the triangular facescars. Finally, unfold the side triangles onto the plane using translations and vectors, showing the net in motion.
The prompt above was compiled from the original drawing commands and is for reference only.