等值分数的可视化
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①本范例通过动态图形演示等值分数的几何意义;②涉及核心数学概念包括分数、几何表示、相似三角形;③构造要点:使用 Point, Circle, OrthogonalLine, Intersect, Rotate, CircleSector, Segment, Vector, Translate, Polygon 等命令及 Slider 动态展示分数关系;④适合初中及以上数学教学,用于分数概念的可视化教学与理解。
GeoGebra 命令及参数
Point(xAxis) → ACircle(A, 3) → eOrthogonalLine(A, xAxis) → fIntersect(e, f, 2) → CRotate(C, (360 * ° / Slider), A) → C'Rotate(C', (360 * ° / Slider), A) → C''Rotate(C'', (360 * ° / Slider), A) → C'''Rotate(C''', (360 * ° / Slider), A) → DRotate(D, (360 * ° / Slider), A) → D'Rotate(D', (360 * ° / Slider), A) → D''Rotate(D'', (360 * ° / Slider), A) → D'''Rotate(D''', (360 * ° / Slider), A) → ERotate(E, (360 * ° / Slider), A) → E'Rotate(E', (360 * ° / Slider), A) → E''Rotate(E'', (360 * ° / Slider), A) → E'''Rotate(E''', (360 * ° / Slider), A) → FRotate(F, (360 * ° / Slider), A) → F'Rotate(F', (360 * ° / Slider), A) → F''Rotate(F'', (360 * ° / Slider), A) → F'''Rotate(F''', (360 * ° / Slider), A) → GRotate(G, (360 * ° / Slider), A) → G'Rotate(G', (360 * ° / Slider), A) → G''Rotate(G'', (360 * ° / Slider), A) → G'''CircleSector(A, C, C') → gCircleSector(A, C', C'') → hCircleSector(A, C'', C''') → kCircleSector(A, C''', D) → pCircleSector(A, D, D') → qCircleSector(A, D', D'') → rCircleSector(A, D'', D''') → sCircleSector(A, D''', E) → tCircleSector(A, E, E') → c_1CircleSector(A, E', E'') → d_1CircleSector(A, E'', E''') → e_1CircleSector(A, E''', F) → f_1CircleSector(A, F, F') → g_1CircleSector(A, F', F'') → h_1CircleSector(A, F'', F''') → k_1CircleSector(A, F''', G) → p_1CircleSector(A, G, G') → q_1CircleSector(A, G', G'') → r_1CircleSector(A, G'', G''') → s_1CircleSector(A, G''', C) → t_1Segment(A, C) → iSegment(A, C') → jSegment(A, C'') → lSegment(A, C''') → mSegment(A, D) → nSegment(A, D') → a_1Segment(A, D'') → b_1Segment(A, D''') → i_1Segment(A, E) → j_1Segment(A, E') → l_1Segment(A, E'') → m_1Segment(A, E''') → n_1Segment(A, F) → a_2Segment(A, F') → b_2Segment(A, F'') → c_2Segment(A, F''') → d_2Segment(A, G) → e_2Segment(A, G') → f_2Segment(A, G'') → g_2Segment(A, G''') → h_2Intersect(e, xAxis, 1) → HIntersect(e, xAxis, 2) → IOrthogonalLine(H, xAxis) → i_2OrthogonalLine(I, xAxis) → j_2OrthogonalLine(J, i_2) → k_2OrthogonalLine(K, i_2) → l_2Intersect(j_2, k_2) → LIntersect(j_2, l_2) → MSegment(J, L) → m_2Segment(K, M) → n_2Segment(K, J) → p_2Segment(M, L) → q_2Vector(J, L) → uTranslate(i_2, Vector[u / Slider]) → r_2Translate(i_2, Vector[(u * 2 / Slider)]) → s_2Translate(i_2, Vector[(u * 18 / Slider)]) → t_2Translate(i_2, Vector[(u * 19 / Slider)]) → a_3Translate(i_2, Vector[(u * 17 / Slider)]) → b_3Translate(i_2, Vector[(u * 16 / Slider)]) → c_3Translate(i_2, Vector[(u * 15 / Slider)]) → d_3Translate(i_2, Vector[(u * 14 / Slider)]) → e_3Translate(i_2, Vector[(u * 13 / Slider)]) → f_3Translate(i_2, Vector[(u * 12 / Slider)]) → h_3Translate(i_2, Vector[(u * 11 / Slider)]) → i_3Translate(i_2, Vector[(u * 10 / Slider)]) → j_3Translate(i_2, Vector[(u * 9 / Slider)]) → k_3Translate(i_2, Vector[(u * 8 / Slider)]) → l_3Translate(i_2, Vector[(u * 7 / Slider)]) → m_3Translate(i_2, Vector[(u * 6 / Slider)]) → n_3Translate(i_2, Vector[(u * 5 / Slider)]) → p_3Translate(i_2, Vector[(u * 4 / Slider)]) → q_3Translate(i_2, Vector[(u * 3 / Slider)]) → r_3Intersect(r_2, n_2) → NIntersect(r_2, m_2) → OIntersect(s_2, m_2) → PIntersect(r_3, m_2) → QIntersect(q_3, m_2) → RIntersect(p_3, m_2) → SIntersect(n_3, m_2) → TIntersect(m_3, m_2) → UIntersect(l_3, m_2) → VIntersect(k_3, m_2) → WIntersect(j_3, m_2) → ZIntersect(i_3, m_2) → A_1Intersect(h_3, m_2) → B_1Intersect(m_2, f_3) → D_1Intersect(e_3, m_2) → E_1Intersect(d_3, m_2) → F_1Intersect(c_3, m_2) → G_1Intersect(b_3, m_2) → H_1Intersect(t_2, m_2) → I_1Intersect(a_3, m_2) → J_1Intersect(a_3, n_2) → K_1Intersect(t_2, n_2) → L_1Intersect(b_3, n_2) → M_1Intersect(c_3, n_2) → N_1Intersect(d_3, n_2) → O_1Intersect(e_3, n_2) → P_1Intersect(n_2, h_3) → R_1Intersect(i_3, n_2) → S_1Intersect(j_3, n_2) → T_1Intersect(k_3, n_2) → U_1Intersect(l_3, n_2) → V_1Intersect(m_3, n_2) → W_1Intersect(n_3, n_2) → Z_1Intersect(p_3, n_2) → A_2Intersect(q_3, n_2) → B_2Intersect(r_3, n_2) → C_2Intersect(s_2, n_2) → D_2Intersect(f_3, n_2) → C_1Polygon(J, O, N, K) → poly1, j_4, o, n_4, k_4Polygon(N, D_2, P, O) → poly2, n_5, d_4, p_4, o_1Polygon(D_2, C_2, Q, P) → poly3, d_5, c_4, q_4, p_5Polygon(C_2, B_2, R, Q) → poly4, c_5, b_4, r_4, q_5Polygon(A_2, B_2, R, S) → poly5, a_4, b_5, r_5, s_3Polygon(A_2, Z_1, T, S) → poly6, a_5, z_1, t_3, s_4Polygon(Z_1, W_1, U, T) → poly7, z_2, w_1, u_1, t_4Polygon(W_1, V_1, V, U) → poly8, w_2, v_1, v, u_2Polygon(V_1, U_1, W, V) → poly9, v_2, u_3, w, v_3Polygon(U_1, T_1, Z, W) → poly10, u_4, t_5, z, w_3Polygon(T_1, S_1, A_1, Z) → poly11, t_6, s_5, a_6, z_3Polygon(S_1, R_1, B_1, A_1) → poly12, s_6, r_6, b_6, a_7Polygon(R_1, C_1, D_1, B_1) → poly13, r_7, c_6, d_6, b_7Polygon(C_1, P_1, E_1, D_1) → poly14, c_7, p_6, e_4, d_7Polygon(P_1, O_1, F_1, E_1) → poly15, p_7, o_2, f_4, e_5Polygon(O_1, N_1, G_1, F_1) → poly16, o_3, n_6, g_3, f_5Polygon(M_1, N_1, G_1, H_1) → poly17, m_4, n_7, g_4, h_4Polygon(M_1, L_1, I_1, H_1) → poly18, m_5, l_4, i_4, h_5Polygon(L_1, K_1, J_1, I_1) → poly19, l_5, k_5, j_5, i_5Polygon(K_1, M, L, J_1) → poly20, k_6, m_6, l_6, j_6
AI 绘图提示语参考
画一个圆形,从圆心向外作一条水平线,并在圆上找到与水平线成一定角度的点。以圆心为轴,将这个点旋转多次,每次旋转的角度由一个滑动条控制,形成多个扇形。用线段连接圆心和这些点,展示出不同角度下的扇形区域,直观表达分数的几何意义和旋转关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。