折纸制作纸盒
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①本范例演示如何通过折纸将正方形纸片制作成立方体纸盒的过程;②涉及的核心数学概念包括多边形、立体几何、向量运算和几何变换;③作图要点提炼自构造摘要,使用了Point, Intersect, Midpoint, Segment, Circle, Line, OrthogonalLine, Mirror, Polygon, Prism, Vector等GeoGebra命令和对象;④适合高中阶段学生学习和理解空间几何与几何作图。
GeoGebra 命令及参数
Point(xAxis) → FIntersect(xAxis, yAxis) → BMidpoint(B, F) → IPoint(yAxis) → ESegment(B, E) → cMidpoint(B, E) → HMin(Distance[B, I], Distance[B, H]) → mRadCircle(B, mRad) → hIntersect(h, c) → J,Segment(B, J) → gPoint(g) → KDistance(B, K) → HeightIntersect(yAxis, zAxis) → OLine(A, yAxis) → aLine(C, xAxis) → bIntersect(a, b) → DSegment(B, F) → dOrthogonalLine(F, xAxis) → eOrthogonalLine(E, yAxis) → fIntersect(e, f) → GMirror(K, H) → K'Mirror(K, i) → BRMirror(BR, I) → LOrthogonalLine(I, xAxis) → jMirror(K, j) → K'_2Mirror(K', j) → K''OrthogonalLine(H, c) → kMirror(BR, k) → MMirror(L, k) → L'Segment(E, G) → lSegment(G, F) → mLine(L, L') → nLine(M, BR) → pLine(K, K'_2) → qLine(K', K'') → rIntersect(p, r) → NIntersect(r, n) → PIntersect(n, q) → QIntersect(q, p) → RPolygon(B, BR, R, K) → poly1, b_1, k'_1, r_1, k_1Polygon(L, F, K'_2, Q) → poly2, l_1, f_1, k'_2, q_1Polygon(P, K'', G, L') → poly3, p_1, k'', g_1, l'Polygon(K', N, M, E) → poly4, k', n_1, m_1, e_1Prism(O, A, D, C, V) → Volume, S, edgeAO, edgeAD, edgeCD, edgeCO, edgeOV, edgeAS, edgeDT, edgeCU, edgeSV, edgeST, T, edgeTU, edgeUV, U, faceADCO, faceAOVS, faceADTS, faceCDTU, faceCOVU, faceSTUVDistance(B, E) → w_ODistance(B, F) → l_OIntersect(s, xAxis) → Z, root2, B_1Polygon(K', K, M, N, R, BR, L, Q, K'_2, K'', P, L') → poly5, k'_3, l'_1, m_2, n_2, k_2, r_2, k'_4, l_2, q_2, k'_5, k''_1, p_2Midpoint(BL, BRL) → A_1Vector(BL, BRL) → uVector(BRL, BL) → vSegment(W, (0, y(W))) → a_1Segment(W, (x(W), 0)) → c_1
AI 绘图提示语参考
绘制一个正方形纸张折叠成一个立方体盒子的过程。首先在x轴上取点F,在y轴上取点E,连接BE并取其中点H。以B为圆心,BH为半径画圆h,与BE交于J,连接BJ。接着构造正方形纸张的四个角点B、E、F、G,以及立方体的各个面和棱。最后通过镜像和旋转操作,形成完整的立方体盒子。
以上提示语为根据原始绘图命令整理而来,仅供参考。