金字塔的展开图
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①本范例演示金字塔的展开图,即其表面展开后的平面图形;②涉及核心数学概念包括多边形、立体几何、几何作图、旋转与平移;③作图要点提炼自GeoGebra命令:Point, Segment, Line, Circle, Intersect, Rotate, Polygon, OrthogonalLine, Midpoint, Vector, Translate, LineBisector, CircleArc, Ray, If等,用于构建金字塔的各个面和边;④适合高中立体几何教学,帮助学生理解三维图形与二维展开图的关系,培养空间想象能力。
GeoGebra 命令及参数
Point(Circle[A, l]) → BSegment(A, B) → aLine(A, B) → b_2Circle(B, (3 * l / 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(A, D) → qMidpoint(b_1) → GSegment(G, F) → rLine(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) → wMidpoint(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 * (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_2Polygon(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(r) → T_1Point(a_2) → G_2
AI 绘图提示语参考
绘制一个四棱锥的展开图。首先,创建一个圆心为A的圆,从中选取一点B。接着,连接A和B,再创建一条平行于AB的线b2。以B为圆心,创建一个圆c,与b2相交于C点。将C绕B旋转30度得到C',连接B和C',再创建一条平行于BC'的线d。d与AB的交点为D。使用A、B、C'、D作为顶点,绘制一个多边形。继续构造其他边和辅助线,最终形成四棱锥的展开图。
以上提示语为根据原始绘图命令整理而来,仅供参考。