模块化截面3:三角形
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本范例展示了立方体的模块化截面,重点在于三角形的几何性质。涉及的核心数学概念包括三角形、立方体几何和三角函数。通过使用GeoGebra命令如Circle、Point、Rotate、Cube等,可以构造出立方体的各个面和三角形。适合初中及以上学生或教师使用,用于几何作图和立体几何教学。
GeoGebra 命令及参数
Circle(O, r, xOyPlane) → cPoint(c) → A1Rotate(A1, π / 2, O) → A2Cube(A1, A2, zAxis) → a, A3, caraBCGF, caraCDHG, caraEFGH, aristaAD_1, aristaAB, aristaBC_1, aristaCD, aristaAE_1, aristaDH, arista, A4, aristaEF, aristaBF, aristaFG_1, aristaCG_1, aristaGH_1, A5, A6, A7, A8, caraABCD, caraADHE, caraABFEMidpoint(A1, A7) → centroSequence(Max[0, Min[1, t - s]], s, 0, 6) → slMidpoint(A4, A8) → B4Midpoint(A6, A2) → B2Line(A5, A3) → kSegment(A7, A1) → hMidpoint(A1, A5) → B1Midpoint(A3, A7) → B3Midpoint(A1, A2) → B5Midpoint(A2, A3) → B6Midpoint(A3, A4) → B7Midpoint(A4, A1) → B8Midpoint(A5, A6) → BAMidpoint(A6, A7) → BBMidpoint(A7, A8) → BCMidpoint(A8, A5) → BDMidpoint(A1, A6) → O1Midpoint(A2, A7) → O2Midpoint(A3, A8) → O3Midpoint(A8, A1) → O4Midpoint(A5, A7) → O5Vector(A1, A6) → u1Vector(A2, A5) → u2Vector(A3, A6) → u3Polygon(A1, A6, A7, A4) → c1, a_1, b_1, c_1, d_1Polygon(A5, A6, A3, A4) → c3, e_1, f_2, g_2, h_2Translate(c1, u1) → c1'Polygon(A8, A5, A2, A3) → c2, f, g, i, jTranslate(c2, u2) → c2'Translate(c3, u3) → c3'Translate(c1', Vector[((-sl(1)) * u1)]) → c1''Translate(c2', Vector[((-sl(2)) * u2)]) → c2''Translate(c3', Vector[((-sl(3)) * u3)]) → c3''Line(B1, B2) → t_1Polygon(A1, A2, A7, A8) → c4, a1, p_2, a7, q_2Vector(A2, A7) → u4Translate(c4, u4) → c4'Translate(c4', Vector[((-sl(4)) * u4)]) → c4''Point(a7) → APolygon(centro, A6, A7) → t1, l, a_2, c_2Polygon(centro, A1, A4) → t2, a4, m, nPolygon(A4, A8, centro) → t3, p, q, a8Polygon(A1, centro, A5) → t4, a5, s, ePolygon(A1, A5, A2) → t5, a2, f_1, g_1Polygon(A4, A8, A3) → t6, a3, h_1, i_1Polygon(A3, centro, A8) → t7, j_1, k_1, l_1Polygon(A2, centro, A5) → t8, m_1, n_1, p_1Polygon(A2, A6, centro) → t9, q_1, r_1, s_1Polygon(A3, centro, A7) → t10, i_2, j_2, d_2Polygon(A2, A3, A7, A6) → c5, k_2, l_2, m_2, b_2Polygon(A1, A2, A3, A4) → c6, n_2, r_2, s_2, t_2Translate(ll1, Vector[(sl(7) * v / 2)]) → ll2Mirror(ll2, centro) → ll3
AI 绘图提示语参考
画一个立方体的模块截面,展示三角形。先画一个圆在底面上,然后得到圆上的点和旋转点,以此构建立方体的几个面。接着找到各面的中点和线段的中点,连接这些点形成线段和三角形。利用向量平移这些三角形,并画出连接中点的线段,最终呈现一个包含多个三角形和立方体面的几何图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。