勾股定理探索 by Veronika Havelková
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①本范例通过移动点演示直角三角形三边关系;②涉及核心数学概念为勾股定理、直角三角形、坐标几何;③作图要点:使用Point, Semicircle, Midpoint, OrthogonalLine, Intersect, Circle, CircleArc, Polygon, Segment等GeoGebra命令构建图形;④适合初中及以上学生学习和理解勾股定理的证明及应用。
GeoGebra 命令及参数
Point(xAxis) → APoint(xAxis) → BSemicircle(A, B) → cMidpoint(A, B) → COrthogonalLine(C, xAxis) → aIntersect(c, a) → D,Circle(D, 0.1) → dIntersect(d, c) → E, F, ,CircleArc(C, F, A) → ePoint(e) → GPolygon(A, B, G) → mnohoúhelník1, g, a_1, bPolygon(G, B, 4) → mnohoúhelník2, f, h, i, j, H, IPolygon(A, G, 4) → mnohoúhelník3, k, l, m, n, J, KPolygon(B, A, 4) → mnohoúhelník4, p, q, r, s, L, MSegment(G, H) → tSegment(B, I) → b_1Intersect(t, b_1) → NOrthogonalLine(N, g) → c_1OrthogonalLine(N, c_1) → d_1Intersect(d_1, j) → OIntersect(d_1, h) → PIntersect(f, c_1) → QIntersect(c_1, i) → RSegment(Q, B) → e_1Segment(B, H) → f_1Segment(H, I) → g_1Segment(I, G) → h_1Segment(G, Q) → i_1Segment(Q, N) → j_1Segment(N, P) → k_1Segment(N, R) → l_1Segment(N, O) → m_1Circle(L, Segment[N, P]) → p_1Circle(M, Segment[N, Q]) → q_1Circle(B, Segment[N, Q]) → r_1Circle(A, Segment[N, Q]) → s_1Intersect(p_1, r) → S,Intersect(q_1, s) → T,Intersect(r_1, g) → U,Intersect(s_1, q) → V,Circle(Q, Segment[B, Q]) → t_1Circle(S, Segment[Q, B]) → c_2Circle(T, Segment[Q, B]) → d_2Circle(U, Segment[B, Q]) → e_2Circle(V, Segment[Q, B]) → f_2Intersect(t_1, j_1) → W,Intersect(c_2, r) → Z, A_1Intersect(d_2, s) → B_1, C_1Intersect(g, p) → D_1Intersect(e_2, g) → E_1, F_1Intersect(e_2, f_2) → G_1, N_1, ,Intersect(f_2, q) → H_1, I_1Circle(Z, Segment[B, W]) → g_2Circle(B_1, Segment[B, W]) → h_2Circle(F_1, Segment[B, W]) → k_2Circle(H_1, Segment[B, W]) → p_2Intersect(c_2, g_2, 2) → J_1Intersect(d_2, h_2, 2) → K_1Intersect(e_2, k_2, 2) → L_1Intersect(f_2, p_2, 2) → M_1Segment(L, S) → n_1Segment(S, J_1) → a_2Segment(J_1, V) → b_2Segment(V, L) → i_2Segment(S, M) → j_2Segment(M, B) → l_2Segment(B, A) → m_2Segment(A, L) → n_2Segment(S, K_1) → q_2Segment(T, L_1) → r_2Segment(U, M_1) → s_2Polygon(L, S, J_1, V) → mnohoúhelník5, l_3, s_3, j_3, vPolygon(S, M, T, K_1) → mnohoúhelník6, s_4, m_3, t_2, k_3Polygon(T, B, U, L_1) → mnohoúhelník7, t_3, b_3, u, l_4Polygon(U, A, V, M_1) → mnohoúhelník8, u_1, a_3, v_1, m_4Polygon(Q, B, P, N) → mnohoúhelník9, q_3, b_4, p_3, n_3Polygon(Q, G, O, N) → mnohoúhelník10, q_4, g_3, o, n_4Polygon(N, P, H, R) → mnohoúhelník11, n_5, p_4, h_3, r_3Polygon(N, O, I, R) → mnohoúhelník12, n_6, o_1, i_3, r_4Polygon(M_1, J_1, K_1, L_1) → mnohoúhelník13, m_5, j_4, k_4, l_5Polygon(A, B, G) → mnohoúhelník14, g_4, a_4, b_5Segment(A, K) → c_3Segment(K, J) → d_3Segment(J, G) → e_3Segment(G, A) → f_3Segment(L, M) → c_4
AI 绘图提示语参考
在坐标平面上,先画一条水平线段作为直角三角形的一条边,并以其为直径作一个半圆。在半圆上取一点,连接该点与线段两端点,构成一个直角三角形。接着,以该直角三角形的三条边为边,分别向外作正方形。然后,在图形内部添加辅助线段和交点,构造出若干小三角形和四边形,以展示勾股定理的几何证明。最后,在关键位置绘制一些圆,用于标记或辅助说明。整体图形应清晰展示直角三角形三边上的正方形面积关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。