三维简单问题2
几何画板及绘图内容加载中,请稍等……
①本范例演示了三维空间中立方体与梯形结合的几何图形构造与性质分析;②涉及核心数学概念包括三角函数、二次函数、三维向量、平移变换、立体几何;③作图要点提炼自构造摘要,使用了Circle(圆)、Point(点)、Segment(线段)、Angle(角)、Line(直线)、Polygon(多边形)、PointIn(点在对象上)、Intersect(交点)、Midpoint(中点)、Mirror(镜像)、Vector(向量)、Translate(平移)等GeoGebra命令及对象;④适合高中及以上学生用于立体几何、向量与变换的学习与可视化理解。
GeoGebra 命令及参数
Circle(O, Radius) → axiscirclePoint(axiscircle) → XSegment(O, X) → OYPoint(axiscircle) → ZAngle(X, O, Z) → αSegment(O, Z) → OZPoint(axiscircle) → YSegment(O, Y) → OXLine(A, OY) → CParallelCBPoint(CParallelCB) → edgeXPtSegment(A, edgeXPt) → edgeXLine(A, OZ) → yaxisPoint(yaxis) → edgeYPtPolygon(edgeYPt, A, edgeXPt) → MaxBase, MaxBaseEdge2, MaxBaseEdge1, MaxBaseEdge3PointIn(MaxBase) → DLine(A, D) → MaxBaseDividerIntersect(MaxBaseEdge3, MaxBaseDivider) → MaxBaseDividerPtPolygon(MaxBaseDividerPt, A, edgeXPt) → MaxBaseLowerHalf, MaxBaseLowerHalfEdge2, MaxBaseLowerHalfEdge1, MaxBaseLowerHalfEdge3PointIn(MaxBaseLowerHalf) → BLine(B, OZ) → BParallelZIntersect(BParallelZ, edgeX) → B_XLine(B, OY) → BParallelXMidpoint(B, D) → MidPointBDMirror(A, MidPointBD) → CPolygon(A, B, C, D) → Base, AB, BD, CD, ACPointIn(Base) → KLine(K, OX) → VerticalFromBasePoint(VerticalFromBase) → VerticalFromBasePtSegment(K, VerticalFromBasePt) → MaxHeightPoint(MaxHeight) → ELine(K, OZ) → KParallelZIntersect(KParallelZ, BParallelX) → K_XLine(K, OY) → KParallelXSegment(A, edgeYPt) → edgeYIntersect(BParallelX, edgeY) → B_ZIntersect(KParallelX, edgeY) → K_ZCircle(B_S, LengthEB / Scale) → CircleAtB_SCircle(A_S, LengthEA / Scale) → CircleAtA_SLine(D, OZ) → CParallelZIntersect(CParallelZ, edgeX) → C_XLine(D, OY) → CParallelXIntersect(CParallelX, edgeY) → C_ZLine(C, OZ) → DParallelZIntersect(DParallelZ, CParallelCB) → D_XLine(C, OY) → DParallelXIntersect(DParallelX, yaxis) → D_ZCircle(A_P, LengthEA / Scale) → CircleAtA_PCircle(D_P, LengthEC / Scale) → CircleAtC_PCircle(B_R, LengthEB / Scale) → CircleAtB_RPoint(OX) → RightAngleDistanceVector(O, RightAngleDistance) → uTranslate(K, u) → DKA3Line(A, OX) → zaxisPoint(zaxis) → edgeZPtSegment(A, edgeZPt) → edgeZSegment(K, E) → KDSegment(A, E) → DASegment(E, D) → DCSegment(E, B) → DBSegment(B_R, C_R) → BC_QCircle(C_R, LengthED / Scale) → CircleAtD_RIntersect(CircleAtB_R, CircleAtD_R) → E_R, D_{Q'}, ,Segment(C_R, E_R) → DC_QSegment(E_R, B_R) → DB_QIntersect(CircleAtA_S, CircleAtB_S) → E_S, T_{R'}, ,Segment(E_S, A_S) → AC_RSegment(A_S, B_S) → AB_RSegment(B_S, E_S) → BC_RCircle(K, KVertical) → CircleAtKCircle(B, BAnglePoint1) → CircleAtBCircle(D, 0.5) → CircleAtCCircle(A, 0.5) → CircleAtAIntersect(CircleAtC_P, CircleAtA_P) → E_P, D_{P'}, ,Segment(E_P, A_P) → DA_PSegment(E_P, D_P) → DC_PSegment(A_P, D_P) → AC_PMidpoint(A, D) → MidPointADMidpoint(A_S, E_S) → MidPointEA_SMidpoint(A, B) → MidPointABMidpoint(A_S, B_S) → MidPointAB_SMidpoint(B_S, E_S) → MidPointEB_SMidpoint(E_R, C_R) → MidPointEC_RMidpoint(E, D) → MidPointEDMidpoint(E, B) → MidPointEBMidpoint(B_R, C_R) → MidPointBC_RMidpoint(B_R, E_R) → MidPointEB_RMidpoint(E, K) → MidPointEKMidpoint(A, E) → MidPointEAMidpoint(A_P, D_P) → MidPointAD_PMidpoint(E_P, A_P) → MidPointAE_PMidpoint(E_P, D_P) → MidPointDE_PAngle(E_P, A_P, D_P) → DAC_PAngle(A_P, D_P, E_P) → DCA_PAngle(E_R, C_R, B_R) → DCB_QAngle(C_R, B_R, E_R) → DBC_QSegment(C, E) → EDAngle(B_S, A_S, E_S) → TAB_RAngle(E_S, B_S, A_S) → TBA_RSegment(A_T, K_T) → AK_SSegment(K_T, E_T) → TK_SSegment(E_T, A_T) → TA_SAngle(E_T, K_T, A_T) → TKA_SCircle(D_Q, LengthED / Scale) → CircleAtD_QCircle(C_Q, LengthEC / Scale) → CircleAtC_QIntersect(CircleAtD_Q, CircleAtC_Q) → E_1, E_Q, ,Segment(C_Q, D_Q) → CD_QSegment(D_Q, E_Q) → TD_QSegment(E_Q, C_Q) → TC_QAngle(E_Q, D_Q, C_Q) → TDC_QAngle(D_Q, C_Q, E_Q) → TCD_QMidpoint(E, C) → MidPointECMidpoint(B, C) → MidPointBCMidpoint(E_Q, D_Q) → MidPointED_QMidpoint(C_Q, D_Q) → MidPointCD_QMidpoint(E_Q, C_Q) → MidPointEC_QMidpoint(C, D) → MidPointCDSegment(A, K) → AKMidpoint(A, K) → MidPointAKMidpoint(E_T, K_T) → MidPointEK_TMidpoint(A_T, K_T) → MidPointAK_TMidpoint(E_T, A_T) → MidPointEA_TIntersect(CircleAtK, KD) → EKA_1,Intersect(CircleAtK, AK) → EKA_2,Line(EKA_2, KD) → ParallelEKLine(EKA_1, AK) → ParallelAKIntersect(ParallelAK, ParallelEK) → EKA_3Segment(EKA_2, EKA_3) → EKA_{L1}Segment(EKA_3, EKA_1) → EKA_{L2}Midpoint(A, C) → MidPointAC
AI 绘图提示语参考
在三维空间中绘制一个结合立方体和平行四边形的几何图形,展示其构造和性质。首先绘制一个圆,标记圆上的点,并连接这些点与圆心形成线段。利用这些线段和点构造角度,并以此为基础绘制平行线和三角形。接着,通过中点和镜像操作创建新的点和多边形,最终形成立方体和平行四边形的组合体,并标注关键点和线段。
以上提示语为根据原始绘图命令整理而来,仅供参考。