佩里加尔的分割
几何画板及绘图内容加载中,请稍等……
①本范例演示了佩里加尔分割,即将两个半圆分割成若干部分,拼接后能完全重合成一个正方形的过程;②涉及的核心数学概念包括坐标几何、减法、几何作图和特殊点;③作图要点:使用Point, Semicircle, Polygon, Angle, Midpoint, Line, OrthogonalLine, Intersect, If, Translate等GeoGebra命令和对象进行构造;④适合高中及以上数学学习者,用于理解几何变换和优化问题。
GeoGebra 命令及参数
Point(xAxis) → APoint(xAxis) → BSemicircle(A, B) → cPoint(c) → CPolygon(A, C, 4) → poly1, a, b, d, e, D, EPolygon(C, B, 4) → poly2, f, g, h, i, F, GPolygon(B, A, 4) → poly3, j, k, l, m, H, IAngle(A, C, B) → αMidpoint(C, F) → JMidpoint(C, E) → KLine(J, j) → nLine(K, j) → pOrthogonalLine(J, j) → qOrthogonalLine(K, j) → rIntersect(n, i) → LIntersect(q, f) → MIntersect(n, g) → NIntersect(q, h) → OIntersect(r, d) → PIntersect(p, e) → QIntersect(p, b) → RIntersect(r, a) → SPolygon(O, G, L, J) → poly4, o, g_1, l_1, j_1Polygon(L, C, M, J) → poly5, l_2, c_1, m_1, j_2Polygon(O, J, N, F) → poly6, o_1, j_3, n_1, f_1Polygon(J, M, B, N) → poly7, j_4, m_2, b_1, n_2Polygon(P, K, Q, E) → poly8, p_1, k_1, q_1, e_1Polygon(Q, A, S, K) → poly9, q_2, a_1, s, k_2Polygon(K, S, C, R) → poly10, k_3, s_1, c_2, r_1Polygon(K, P, D, R) → poly11, k_4, p_2, d_1, r_2Midpoint(H, B) → TIf(t ≤ 1, t, 1) → t1If(t ≤ 1, 0, If[t ≤ 2, t - 1, 1]) → t2If(t ≤ 2, 0, If[t ≤ 3, t - 2, 1]) → t3If(t ≤ 3, 0, If[t ≤ 4, t - 3, 1]) → t4If(t ≤ 4, 0, If[t ≤ 5, t - 4, 1]) → t5Translate(Element[list1, 5], Vector[(t5 * Vector[K, T])]) → list1eTranslate(Element[list1, 1], Vector[(t1 * Vector[J, I])]) → list1aTranslate(Element[list1, 2], Vector[(t2 * Vector[J, B])]) → list1bTranslate(Element[list1, 4], Vector[(t3 * Vector[J, A])]) → list1dTranslate(Element[list1, 3], Vector[(t4 * Vector[J, H])]) → list1cTranslate(Element[list2, 1], Vector[(t1 * Vector[K, I])]) → list2aTranslate(Element[list2, 2], Vector[(t2 * Vector[K, B])]) → list2bTranslate(Element[list2, 3], Vector[(t3 * Vector[K, A])]) → list2cTranslate(Element[list2, 4], Vector[(t4 * Vector[K, H])]) → list2dTranslate(Element[list2, 5], Vector[(t5 * Vector[J, T])]) → list2e
AI 绘图提示语参考
绘制一个由两个半圆组成的图形,通过切割和重新排列,可以形成一个正方形。首先在x轴上创建点A和B,以A和B为直径画两个半圆,然后在每个半圆上创建四个顶点,形成三个四边形。接着找到关键角度和中点,利用这些点画出一系列线段和垂线,最终通过平移操作将这些四边形重新排列成一个正方形。
以上提示语为根据原始绘图命令整理而来,仅供参考。