数轴整数加法的几何表示:用向量平移构造
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该范例通过数轴(实数直线)上的图形操作演示“整数的加法”如何从量的位移得到结果。核心数学概念包括:整数的正负表示、实数轴上的位置刻画、向量与平移(Translate)对应加法、以及用线段长度/端点位置理解代数运算。作图要点:依据构造摘要使用了 Line 与 Point 生成数轴与关键端点位置;用 Segment 与 Midpoint 构造与刻画必要的线段与其中点;通过 Circle、OrthogonalLine、Intersect 形成辅助几何关系并定位相应交点;用 Vector 表示位移方向与大小;再用 Translate 实现从某点按向量平移到新位置,从而对应整数相加的几何结果。该资源适合初中到高中阶段的函数与数与代数衔接教学,也适用于数学建模或教学演示,用几何直观帮助理解整数加法的运算意义。
GeoGebra 命令及参数
Line(A, B) → aPoint(a) → CCircle(C, 2) → pOrthogonalLine(C, a) → dPoint(a) → DPoint(a) → EPoint(a) → FPoint(a) → GPoint(a) → HPoint(a) → IPoint(a) → JPoint(a) → KPoint(a) → LPoint(a) → MPoint(a) → NPoint(a) → OPoint(a) → PPoint(a) → QPoint(a) → RPoint(a) → SPoint(a) → TPoint(a) → UPoint(a) → VPoint(a) → WPoint(a) → YPoint(a) → ZPoint(a) → A_1Point(a) → B_1Point(a) → C_1Point(a) → D_1Point(a) → E_1Point(a) → F_1Point(a) → G_1Point(a) → H_1Intersect(p, d) → I_1, L_5OrthogonalLine(I_1, d) → eVector(I_1, L_1) → vOrthogonalLine(L_5, d) → hCircle(C, 4) → kIntersect(k, d, 1) → J_1OrthogonalLine(J_1, d) → fVector(J_1, K_1) → uVector(L_5, M_1) → wCircle(L_5, 1) → gIntersect(g, d, 1) → N_1OrthogonalLine(N_1, d) → iCircle(M_1, 1) → qIntersect(q, i) → O_1, P_1Translate(O_1, v) → Q_1Vector(O_1, Q_1) → zIntersect(k, d, 2) → R_1Circle(R_1, N_1) → rIntersect(r, d, 2) → S_1OrthogonalLine(S_1, d) → jVector(S_1, T_1) → lSegment(J_1, S_1) → mSegment(M_1, O_1) → tOrthogonalLine(K_1, a) → nIntersect(n, a) → U_1OrthogonalLine(L_1, a) → sOrthogonalLine(T_1, a) → a_1Intersect(s, a) → W_1Intersect(a_1, a) → Y_1Segment(K_1, U_1) → b_1Segment(T_1, Y_1) → c_1Segment(L_1, W_1) → d_1Segment(I_1, L_1) → b_2Segment(J_1, K_1) → e_1Segment(L_5, M_1) → f_1Segment(Q_1, O_1) → g_1Segment(T_1, S_1) → h_1Midpoint(J_1, K_1) → Z_1Midpoint(I_1, L_1) → A_2Midpoint(L_5, M_1) → B_2Midpoint(Q_1, O_1) → C_2Segment(Q_1, Y_1) → i_1Point(a) → V_1Point(a) → D_2Point(a) → E_2Point(a) → F_2Point(a) → G_2Point(a) → H_2Point(a) → I_2Point(a) → J_2Point(a) → K_2Point(a) → L_2
AI 绘图提示语参考
画一条数轴,以点C为原点,向右为正方向。在数轴上依次标记点D到Z。以点C为圆心,半径为2画圆,与垂直于数轴的直线d相交于点I1和L5。以I1为起点,L1为方向画向量v。以L5为圆心,半径为4画圆,与垂直于数轴的直线d相交于点J1,再以J1为起点,K1为方向画向量u。以L5为圆心,半径为1画圆,与垂直于数轴的直线d相交于点N1,再以N1为起点,M1为方向画向量w。以M1为圆心,半径为1画圆,与垂直于数轴的直线d相交于点O1和P1。
以上提示语为根据原始绘图命令整理而来,仅供参考。