人形与水壶
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①本范例演示了如何通过 GeoGebra 绘制人形与水壶的几何图形;②涉及的核心数学概念包括解析几何、几何作图、向量与变换;③作图要点提炼了以下 GeoGebra 命令/对象:Intersect(交点)、Point(点)、Rotate(旋转)、Segment(线段)、Polygon(多边形)、Circle(圆)、Distance(距离)、CircleArc(圆弧)、Plane(平面)、Mirror(镜像)、Vector(向量);④适合高中阶段学习几何作图、向量与变换的学生使用。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → APoint(xAxis) → BPoint(yAxis) → DRotate(A, (-(22.5°)), B) → A'Segment(A', B) → fRotate(A, 22.5°, D) → A'_1Segment(D, A'_1) → gIntersect(f, g) → EPolygon(A, B, E, D) → vierhoek1, a, b, e, dCircle(B, 0.2) → cIntersect(c, b, 1) → FSegment(A, B) → hSegment(G, H) → iSegment(H, B) → jSegment(G, A) → kDistance(E, F) → lCircleArc(I, J, K) → boog0Segment(K, F) → vertmiddenSegment(B, F) → onderSegment(H, L) → bovenSegment(L, J) → vertkleinPlane(E, A, G) → diagSegment(G, M) → mSegment(M, D) → nMirror(boog0, diag) → boog0'Mirror(H, diag) → H'Mirror(L, diag) → L'Segment(H', L') → boven'Mirror(K, diag) → K'Mirror(F, diag) → F'Segment(K', F') → vertmidden'Mirror(B, diag) → B'Mirror(F, diag) → F'_1Segment(B', F'_1) → onder'Segment(L, O) → pSegment(N, H) → qSegment(P, M) → rSegment(O, N) → sSegment(O, P) → tSegment(N, Q) → boven1CircleArc(S, T, V) → boog1Segment(U, V) → vertmidden1Segment(U, H) → onder1Segment(T, Q) → vertklein1Mirror(boog1, diag) → boog1'Mirror(N, diag) → N'Mirror(Q, diag) → Q'Segment(N', Q') → boven1'Mirror(U, diag) → U'Mirror(V, diag) → V'Segment(U', V') → vertmidden1'Mirror(U, diag) → U'_1Mirror(H, diag) → H'_1Segment(U'_1, H'_1) → onder1'Segment(D, C) → f_1Segment(C, B) → g_1Vector(A, B) → uVector(A, D) → vVector(D, E) → wVector(B, E) → u_1Vector(B, C) → v_1Vector(D, C) → w_1Vector(L, M) → a_1Vector(L, H) → b_1Vector(H, R) → c_1Vector(M, R) → d_1Vector(A_1, W) → e_1Vector(A_1, Z) → h_1Polygon(G, H, L, M) → vierhoek2, g_2, h_2, l_1, m_1Polygon(B', E, B, C) → vierhoek3, b', e_2, b_2, c_2Polygon(P, O, N, Q') → vierhoek4, p_1, o_1, n_1, q'Point(boog1) → B_1Vector(B_1, T) → i_1Point(boog1') → C_1Vector(C_1, T) → j_1Point(boog0) → D_1Point(boog0') → E_1Vector(D_1, J) → k_1Vector(E_1, J) → q_1
AI 绘图提示语参考
画一个双足人物和一个水壶,首先绘制坐标轴并找到它们的交点,然后旋转其中一个轴创建一个角度,用线段连接这些点形成四边形,接着画一个圆并找到其与线段的交点,再通过旋转和镜像操作创建对称图形,最后用弧线和线段完善水壶的形状,整个过程中注意运用向量和平面进行变换。
以上提示语为根据原始绘图命令整理而来,仅供参考。