无言证明 by Steve Phelps (3)
几何画板及绘图内容加载中,请稍等……
这是一个几何作图的无言证明范例。通过拖动点和滑块,观察图形的变化,理解其背后的数学原理。构造了三角形、圆弧、多边形等几何对象,使用了点、交点、向量、变换等GeoGebra命令。适合高中及以上学生或教师使用,帮助理解几何变换和证明方法。
GeoGebra 命令及参数
Point(xAxis) → AIntersect(xAxis, yAxis) → BCircleArc(B, D, A) → cPoint(c) → EPolygon(A, E, 4) → poly1, a, b, d, e, F, GPolygon(E, C, 4) → poly2, f, g, h, i, H, IPolygon(C, A, 4) → poly3, j, k, l, m, J, KAngularBisector(A, E, C) → nIntersect(n, j) → LOrthogonalLine(L, a) → pOrthogonalLine(L, f) → qMidpoint(G, E) → MMidpoint(E, H) → NIntersect(p, a) → OIntersect(q, f) → PMirror(O, M) → O'Mirror(P, N) → P'Line(O, j) → rLine(P, j) → sIntersect(r, e) → QIntersect(s, g) → RMirror(Q, M) → Q'Mirror(R, N) → R'Polygon(Q, O, 4) → poly4, t, a_1, b_1, c_1, S, TPolygon(P, R, 4) → poly5, d_1, e_1, f_1, g_1, U, VPolygon(Q, G, O') → poly6, o', q_1, g_2Polygon(O', F, Q') → poly7, q', o'_1, f_2Polygon(Q', O, E) → poly8, e_2, q'_1, oPolygon(O, A, Q) → poly9, q_2, o_1, a_2Polygon(E, P, R') → poly10, r', e_3, p_1Polygon(P, C, R) → poly11, r_1, p_2, c_2Polygon(R, P', H) → poly12, h_1, r_2, p'Polygon(I, R', P') → poly13, p'_1, i_1, r'_1If(0 ≤ u ≤ 1, 1 - u, If[u > 1, 0, 1]) → d1Dilate(O', d1, A) → O''Vector(O', O'') → vTranslate(poly4, v) → poly4'Dilate(R, d1, K) → R'_1Vector(R, R'_1) → wTranslate(poly5, w) → poly5'If(1 ≤ u ≤ 2, 2 - u, If[u > 2, 0, 1]) → d2Dilate(R, d2, J) → R'_2Vector(R, R'_2) → u_1Translate(R, u_1) → R'_3Translate(P', u_1) → P''Translate(H, u_1) → H'Polygon(R'_3, P'', H') → poly12', h', r'_3, p''Dilate(P, d2, W) → P'_1Vector(P, P'_1) → v_1Translate(E, v_1) → E'Translate(P, v_1) → P'_2Translate(R', v_1) → R''Polygon(E', P'_2, R'') → poly10', r'', e', p'_2Dilate(P, d2, L) → P'_3Vector(P, P'_3) → w_1Translate(P, w_1) → P'_4Translate(C, w_1) → C'Translate(R, w_1) → R'_4Polygon(P'_4, C', R'_4) → poly11', r'_4, p'_4, c'Dilate(R', d2, R'') → R''_1Vector(R', R''_1) → j_1Translate(I, j_1) → I'Translate(R', j_1) → R''_2Translate(P', j_1) → P''_1Polygon(I', R''_2, P''_1) → poly13', p''_1, i', r''_2If(2 ≤ u ≤ 3, 3 - u, If[u > 3, 0, 1]) → d3Dilate(G, d3, C') → G'Vector(G, G') → k_1Translate(Q, k_1) → Q'_1Translate(G, k_1) → G'_1Translate(O', k_1) → O''_1Polygon(Q'_1, G'_1, O''_1) → poly6', o''_1, q'_2, g'_1Dilate(O, d3, R'') → O'_1Vector(O, O'_1) → l_1Translate(Q', l_1) → Q''Translate(O, l_1) → O'_2Translate(E, l_1) → E'_1Polygon(Q'', O'_2, E'_1) → poly8', e'_1, q'', o'_2Dilate(A, d3, H') → A'Vector(A, A') → m_1Dilate(F, d3, E') → F'Vector(F, F') → n_1Translate(O, m_1) → O'_3Translate(A, m_1) → A'_1Translate(Q, m_1) → Q'_2Polygon(O'_3, A'_1, Q'_2) → poly9', q'_3, o'_3, a'_1Translate(O', n_1) → O''_2Translate(F, n_1) → F'_1Translate(Q', n_1) → Q''_1Polygon(O''_2, F'_1, Q''_1) → poly7', q''_1, o''_2, f'_1
AI 绘图提示语参考
画一个几何构造图形,包含一个坐标系、点、圆弧、多边形和几何变换。首先在坐标轴上创建点,然后利用这些点构造圆弧和多边形。接着,通过角度平分线和垂线创建新的点和线段。最后,应用镜像和缩放变换,将多边形进行变换并组合,展示几何变换和证明方法。
以上提示语为根据原始绘图命令整理而来,仅供参考。