兰博基尼转向角
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本范例通过几何作图展示了多边形外角定理。通过旋转、平移、缩放等命令,构造了一个多边形,并通过调整顶点位置来演示多边形外角和的性质。使用了Polygon, Rotate, Dilate, Vector, Translate等命令。适合初中及以上学生学习多边形几何。
GeoGebra 命令及参数
Intersect(xAxis, yAxis) → CPolygon(C, D, 6) → poly1, f, H, g, h, i, j, k, E, F, GRotate(pic1, pi / 3, D) → pic1'Dilate(D, If[0 < a ≤ 1, 1 - a, 0], E) → D'Vector(D, D') → uTranslate(pic1', u) → pic1''Ray(D, E) → lRotate(pic1'', If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], E) → pic1'''Dilate(E, If[2 < a ≤ 3, 3 - a, 0], F) → E'Vector(E, E') → vTranslate(pic1''', v) → pic2Rotate(I, pi / 3, D) → I'Translate(I', u) → I''Rotate(I'', If[1 < a ≤ 2, ((a - 1) * pi / 3), pi / 3], E) → I'''CircleSector(E, I'', I''') → cRotate(pic2, If[3 < a ≤ 4, ((a - 3) * pi / 3), pi / 3], E') → pic2'Translate(I''', v) → JRotate(J, If[3 < a ≤ 4, ((a - 3) * pi / 3), pi / 3], E') → J'CircleSector(F, J, J') → dDilate(E', If[4 < a ≤ 5, 5 - a, 0], G) → E''Vector(E', E'') → wTranslate(pic2', w) → pic2''Translate(J', w) → J''Ray(E, E') → mRotate(pic2'', If[5 < a ≤ 6, ((a - 5) * pi / 3), pi / 3], E'') → pic2'''Rotate(J'', If[5 < a ≤ 6, ((a - 5) * pi / 3), pi / 3], E'') → J'''CircleSector(G, J'', J''') → eRay(E', G) → nDilate(G, If[6 < a ≤ 7, 7 - a, 0], H) → G'Vector(G, G') → bTranslate(pic2''', b) → pic3Translate(J''', b) → KRotate(pic3, If[7 < a ≤ 8, ((a - 7) * pi / 3), pi / 3], H) → pic3'Rotate(K, If[7 < a ≤ 8, ((a - 7) * pi / 3), pi / 3], H) → K'CircleSector(H, K, K') → pRay(E'', H) → qDilate(H, If[8 < a ≤ 9, 9 - a, 0], C) → H'Vector(H, H') → rTranslate(pic3', r) → pic3''Translate(K', r) → K''Rotate(pic3'', If[9 < a ≤ 10, ((a - 9) * pi / 3), pi / 3], C) → pic3'''Rotate(K'', If[9 < a ≤ 10, ((a - 9) * pi / 3), pi / 3], C) → K'''CircleSector(C, K'', K''') → sRay(H, C) → tDilate(C, If[10 < a ≤ 11, 11 - a, 0], D) → C'Vector(C, C') → u_1Translate(pic3''', u_1) → pic4Translate(K''', u_1) → LRotate(pic4, If[11 < a ≤ 12, ((a - 11) * pi / 3), pi / 3], D) → pic4'Rotate(L, If[11 < a ≤ 12, ((a - 11) * pi / 3), pi / 3], D) → L'Ray(C, D) → f_1CircleSector(C', L, L') → c_1Segment(C, D) → g_1Segment(D, E) → h_1Segment(E, F) → i_1Segment(F, G) → j_1Segment(G, H) → k_1Segment(H, C) → l_1Dilate(C, If[13 < a ≤ 14, 14 - a, 0], M) → C'_{1}Dilate(H, If[13 < a ≤ 14, 14 - a, 0], M) → H'_{1}Dilate(G, If[13 < a ≤ 14, 14 - a, 0], M) → G'_{1}Dilate(F, If[13 < a ≤ 14, 14 - a, 0], M) → F'Dilate(E, If[13 < a ≤ 14, 14 - a, 0], M) → E'_{1}Dilate(D, If[13 < a ≤ 14, 14 - a, 0], M) → D'_{1}Vector(H, H'_{1}) → v_1Vector(C, C'_{1}) → w_1Vector(D, D'_{1}) → a_1Vector(E, E'_{1}) → b_1Vector(F, F') → d_1Vector(G, G'_{1}) → e_1Translate(p, v_1) → p'Translate(s, w_1) → s'Translate(c, b_1) → c'Translate(d, d_1) → d'Translate(e, e_1) → e'Translate(c_1, a_1) → p_1CircleArc(E, I'', I''') → q_1CircleArc(F, J, J') → r_1CircleArc(G, J'', J''') → s_1CircleArc(H, K, K') → t_1CircleArc(C, K'', K''') → c_2CircleArc(D, I, I') → d_2
AI 绘图提示语参考
在直角坐标系中取两条坐标轴的交点作为中心,先构造以多边形某个顶点为起点的正多边形(边数取为6),并得到该多边形的各顶点。以其中一个顶点为旋转中心,按固定角度分段旋转、平移复制出外侧构型,使相邻位置形成连续的折转关系;再以若干对应顶点分别作扇形,用每个扇形的两条边所夹的角来刻画外角。最后从外侧各关键点向多边形方向作射线,整体呈现外角逐段展开、并对应于角和定理的几何图景。
以上提示语为根据原始绘图命令整理而来,仅供参考。