Gigantotron 几何相似性演示
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所属专题
Transformations
①本范例演示了棱柱体积与表面积的计算及几何相似性原理;②涉及核心数学概念包括面积、体积、方程、算术运算、等腰三角形、梯形及几何变换;③作图要点:使用 Line, OrthogonalLine, Rotate, Circle, Intersect, Polygon, Segment 等命令构建几何图形,并通过对象 A, B, a, b, b', H, W, L, c, d, e, C, D, E, f, g, i, j, k, l, F, G, m, H_1, n, I, poly1, a_1, c_1, f_1, d_1, poly2, d_2, g_1, i_1, f_2, poly3, c_2, f_3, i_2 等对象实现;④适合高中及以上学生及数学教师用于立体几何、相似性及计算教学。
GeoGebra 命令及参数
Line(A, B) → aOrthogonalLine(A, a) → bRotate(b, 30*°, A) → b'Circle(A, H) → cCircle(A, W) → dCircle(A, L) → eIntersect(c, a, 2) → CIntersect(d, b, 1) → DIntersect(e, b', 1) → EOrthogonalLine(C, a) → fOrthogonalLine(D, b) → gOrthogonalLine(E, a) → iLine(D, b') → jLine(E, a) → kLine(C, b') → lIntersect(f, g) → FIntersect(i, j) → GLine(G, a) → mIntersect(k, l) → H_1Line(F, b') → nIntersect(m, n) → IPolygon(A, C, F, D) → poly1, a_1, c_1, f_1, d_1Polygon(D, G, I, F) → poly2, d_2, g_1, i_1, f_2Polygon(C, F, I, H_1) → poly3, c_2, f_3, i_2, h_1Segment(G, E) → pSegment(H_1, E) → qSegment(E, A) → rLine(A, D) → hOrthogonalLine(G, h) → sIntersect(h, s) → JCircle(J, 2) → tIntersect(t, h, 2) → KLine(A, D) → b_1OrthogonalLine(K, b_1) → e_1Line(K, d_2) → j_1Circle(K, scale * H) → k_1Circle(K, scale * W) → p_1Circle(K, scale * L) → q_1Intersect(k_1, e_1, 2) → MIntersect(p_1, b_1, 2) → NIntersect(q_1, j_1, 2) → OLine(N, e_1) → l_1Line(M, b_1) → m_1Line(N, j_1) → n_1Line(O, e_1) → r_1Line(M, j_1) → s_1Intersect(l_1, m_1) → PIntersect(r_1, s_1) → QLine(Q, b_1) → a_2Polygon(K, N, P, M) → poly4, k_2, n_2, p_2, m_2Segment(K, O) → b_2Segment(O, Q) → e_2Line(N, h_1) → t_1Line(O, k_2) → g_2Line(Q, g_2) → h_2Intersect(t_1, g_2) → RLine(R, n_2) → j_2Intersect(h_2, j_2) → SPolygon(N, R, S, P) → poly5, n_3, r_2, s_2, p_3Polygon(S, Q, M, P) → poly6, s_3, q_2, m_3, p_4Segment(O, R) → l_2
AI 绘图提示语参考
绘制一个包含三个相似四边形的立体几何图形。首先,以点A和B为端点画一条线段,然后构造与这条线段垂直的线b,接着旋转b得到b'。通过点A和半径H、W、L分别画三个圆,与线段和圆相交得到C、D、E。构造C、D、E的垂线f、g、i,以及D、E、C的连线j、k、l,然后相交得到F、G、H_1。接着构造四边形ACFD、DGIF、CFIH_1。
以上提示语为根据原始绘图命令整理而来,仅供参考。