斜二测六面体
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所属专题
Surface Area
该范例演示了斜二测六面体的绘制方法。涉及的核心数学概念包括立体几何中的六面体及其投影。通过使用GeoGebra命令如Point, Segment, Polygon等,可以构造出六面体的各个面,并通过变换命令如Translate实现六面体的平移。适合高中阶段的学生学习立体几何。
GeoGebra 命令及参数
Point(xAxis) → OOrthogonalLine(O, xAxis) → kPoint(k) → TPoint(k) → SOrthogonalLine(S, k) → g_1Point(g_1) → PSequence(Mat * Element[cube, k], k, 1, 9) → cube'Sequence(I + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 9) → listepointsElement(listepoints, 1) → MElement(listepoints, 7) → LElement(listepoints, 8) → KElement(listepoints, 4) → JSegment(M, J) → m'Element(listepoints, 5) → NElement(listepoints, 2) → ASegment(A, M) → a'_1Element(listepoints, 6) → QPolygon(K, L, Q, N) → poly6, k_3, l_2, q_1, n_2Point(n_2) → RElement(listepoints, 3) → CPolygon(Q, A, C, L) → poly2, q, a_2, c_1, lPolygon(J, K, L, C) → poly4, j_2, k_1, l_1, c_5Line(R, k_1) → eIntersect(e, l_2) → FLine(F, q) → fIntersect(f, a_2) → GLine(G, a'_1) → gIntersect(g, m') → HElement(Element[AE, 3], 1) → droiteElement(AB, 3, 1) → avantElement(AC, 3, 1) → dessusPolygon(J, M, N, K) → poly5, j_3, m_1, n_1, k_2Polygon(J, C, A, M) → poly1, j, c, a_1, mPolygon(A, Q, N, M) → poly3, a_3, q_2, n, m_2Segment(J, C) → j'_1Segment(K, L) → k'_3Segment(L, Q) → l'_2Segment(N, K) → n'_2Segment(Q, N) → q'_1Segment(M, N) → m'_1Segment(Q, A) → q'Segment(K, J) → j'Segment(N, K) → l'Segment(C, L) → l''Segment(C, A) → l''''Segment(M, N) → k''''If(i ≟ 1, true, false) → hSegment(C, A) → k'''PointIn(poly2) → EPolygon(A, M, J, C) → poly10, p, s, t, b_1Polygon(C, F', A) → poly7, a_4, c_2, f'Polygon(J, R', M) → poly8, m_3, j_1, r'Segment(R, M) → d_1Line(J, M) → f_1Line(C, A) → h_1Segment(R, H) → e_1Translate(R_2, A - M) → Q_2Polygon(A, Q_2, R_2, M) → poly9, a_5, q_3, r_2, m_4Translate(R_3, C - J) → F_3Polygon(J, R_3, F_3, C) → poly11, j_4, r_3, f_3, c_3Angle(Line[M, J], Line[M, R']) → angAngle(Line[C, A], Line[C, F']) → ang2Angle(Line[A, M], Line[A, F']) → ang3Angle(Line[J, C], Line[J, R']) → ang4Angle(Line[C, J], Line[C, A]) → ang5
AI 绘图提示语参考
绘制一个斜投影棱柱,首先在x轴上取点O,通过O作x轴的垂线得到点T和S,再通过S作垂线得到点P。接着构造棱柱的各个面,包括顶面、底面和侧面,使用Translate命令将顶面平移得到棱柱的各个侧面。最后连接各个点形成棱柱的各个面,包括顶面、底面和侧面,确保所有线段和多边形正确连接。
以上提示语为根据原始绘图命令整理而来,仅供参考。