正方体截面练习
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①本范例演示如何通过动态交互展示正方体不同角度的截面形状;②涉及的核心数学概念包括立体几何、几何作图、空间想象及不等式表示;③作图要点提炼自构造摘要,使用了Circle(圆)、PointIn(点在路径上)、Sequence(序列)、Element(元素)、Polygon(多边形)、Segment(线段)、Corner(角点)、Line(直线)、Intersect(交点)等GeoGebra命令与对象;④适合高中立体几何教学,用于加深学生对三维图形截面变化的理解与探究。
GeoGebra 命令及参数
Circle(K_1, L) → cPointIn(c) → PSequence(Mat * Element[cube, k], k, 1, 8) → cube'Element(Element[AE, 3], 1) → droite_1Sequence(O + (Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepointsElement(listepoints, 3) → CElement(AB, 3, 1) → avant_1Element(AC, 3, 1) → dessus_1Element(listepoints, 4) → DElement(listepoints, 8) → HElement(listepoints, 7) → GPolygon(D, H, G, C) → dessus, s_{DHdessus}, s_{HGdessus}, s_{GCdessus}, s_{CDdessus}Element(listepoints, 1) → AElement(listepoints, 5) → EPolygon(D, A, E, H) → arrière, s_{DAarrière}, s_{EAarrière}, s_{EHarrière}, s_{HDarrière}Element(listepoints, 6) → FPolygon(H, G, F, E) → droite, s_{HGdroite}, s_{GFdroite}, s_{EFdroite}, s_{EHdroite}Element(listepoints, 2) → BPolygon(D, C, B, A) → gauche, s_{CDgauche}, s_{BCgauche}, s_{BAgauche}, s_{ADgauche}Polygon(F, B, C, G) → avant, s_{FBav}, s_{BCavant}, s_{CGavant}, s_{GFavant}Polygon(B, F, E, A) → dessous, s_{BFdessous}, s_{FEdessous}, s_{EAdessous}, s_{ABdessous}Segment(B, A) → p_{AB}Segment(D, C) → p_{DC}Segment(H, G) → p_{HG}Segment(G, F) → p_{GF}Segment(A, D) → p_{AD}Segment(E, H) → p_{HE}Segment(F, E) → p_{FE}Segment(A, E) → p_{EA}Segment(F, B) → p_{FB}Segment(H, D) → p_{HD}Segment(E, H) → p_{EH}Segment(C, G) → p_{CG}Segment(C, B) → p_{CB3}Segment(A, E) → p_{AE}Segment(C, B) → p_{CB}Corner(1) → coin1'Point(s_{BAgauche}) → IPoint(s_{EAarrière}) → JPoint(s_{CDgauche}) → KSegment(I, K) → aSegment(I, J) → bLine(K, b) → dIntersect(d, s_{HDarrière}) → O_1Segment(J, O_1) → eIntersect(d, p_{HG}) → QSegment(J, Q) → fPolygon(I, J, Q, K) → poly1, j, m, q, nPolygon(I, J, O_1, K) → poly2, j_1, m_1, o, n_1Polygon(I, E, Q, K) → poly3, i, e_1, q_1, kPolygon(B, A, D, C) → poly4, b_1, a_1, d_1, c_1
AI 绘图提示语参考
绘制一个立方体,并展示其从不同角度的截面形状。首先绘制一个立方体,然后通过选择立方体的顶点和面,创建多个截面,包括前、后、上、下、左、右以及对角面。最后,连接这些截面的顶点,形成多个多边形,展示立方体在不同截面下的形状。
以上提示语为根据原始绘图命令整理而来,仅供参考。