缺失正方形悖论(Curry)第二部分:几何面积与斜率的关系
几何画板及绘图内容加载中,请稍等……
这个范例演示了缺失正方形悖论在几何图形中的表现,揭示了面积计算与斜率之间的微妙关系。核心数学概念包括面积差、斜率、几何作图和参数曲线。作图要点涉及使用Polygon、Segment、Circle、Point、Line、OrthogonalLine和Intersect等GeoGebra命令来构造图形。适合高中生或大学低年级学生用于学习几何和数学分析。
GeoGebra 命令及参数
Polygon(A, B, C) → t1, c, a, bPolygon(J, K, L, O) → poly2, j, k, l, mPolygon(P, Q, F_1) → t2, p, q, rSegment(F_1, Q) → i_2Circle(B_1, 3) → dPoint(d) → GLine(B_1, G) → fOrthogonalLine(G, f) → gCircle(G, 2) → eIntersect(e, g, 2) → HOrthogonalLine(H, g) → hOrthogonalLine(B_1, f) → iIntersect(h, i) → IPolygon(B_1, G, H, I) → q1, n, g_2, h_2, i_3Circle(D, 3) → c_1Point(c_1) → ELine(D, E) → m_1OrthogonalLine(E, m_1) → n_1Circle(E, 2) → d_1Intersect(d_1, n_1, 2) → FOrthogonalLine(F, n_1) → p_1OrthogonalLine(D, m_1) → e_1Intersect(p_1, e_1) → RPolygon(D, E, F, R) → q2, d_2, e_2, f_2, r_2Polygon(C_1, D_1, K_1, L_1) → q3, j_2, k_2, l_2, s_2Circle(N_1, 2) → c_2Point(c_2) → O_1Line(N_1, O_1) → t_2OrthogonalLine(O_1, t_2) → a_2Circle(O_1, 1) → c_3Intersect(c_3, a_2, 2) → P_1OrthogonalLine(P_1, a_2) → b_2OrthogonalLine(N_1, t_2) → f_3Intersect(b_2, f_3) → Q_1Polygon(N_1, O_1, P_1, Q_1) → q4, g_3, o_1, h_3, j_3Segment(S, T) → sSegment(T, U) → tSegment(U, S) → f_1Segment(V, W) → g_1Segment(W, Z) → h_1Segment(Z, A_1) → i_1Segment(A_1, E_1) → j_1Segment(E_1, V) → k_1Segment(A, B) → l_1Segment(B, C) → q_1Segment(A, C) → r_1Segment(P, Q) → s_1Segment(Q, F_1) → t_1Segment(P, F_1) → a_1Segment(J, K) → b_1Segment(K, L) → m_2Segment(L, O) → n_2Segment(O, J) → p_2Segment(B_1, G) → q_2Segment(G, H) → k_3Segment(H, I) → l_3Segment(I, B_1) → m_3Segment(D, E) → n_3Segment(E, F) → p_3Segment(F, R) → q_3Segment(R, D) → r_3Segment(N_1, O_1) → s_3Segment(O_1, P_1) → t_3Segment(P_1, Q_1) → a_3Segment(Q_1, N_1) → b_3Segment(C_1, D_1) → d_3Segment(K_1, D_1) → e_3Segment(K_1, L_1) → f_4Segment(C_1, L_1) → g_4
AI 绘图提示语参考
绘制一个由多个四边形和三角形组成的几何图形,包括一个缺角的正方形和两个直角三角形。首先画出一个缺角的正方形,然后构造两个直角三角形,它们的直角边分别与缺角正方形的边相接。接着,通过构造圆和垂线,生成一系列的小三角形和四边形,最终形成一个复杂的几何图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。