旋转图案
几何画板及绘图内容加载中,请稍等……
①本范例演示了通过旋转和几何构造创建的复杂图案;②涉及的核心数学概念包括旋转、多边形构造、函数图像、立体几何;③作图要点使用了GeoGebra的Polygon(多边形)、Midpoint(中点)、Semicircle(半圆)、Sequence(数列)等命令和对象;④适合高中数学教学和几何作图学习。
GeoGebra 命令及参数
Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, EMidpoint(E, A) → FMidpoint(A, B) → GMidpoint(B, C) → HMidpoint(C, D) → IMidpoint(D, E) → JSemicircle(J, I) → cSemicircle(I, H) → dSemicircle(H, G) → eSemicircle(G, F) → kSemicircle(F, J) → pSemicircle(J, F) → qSemicircle(F, G) → rSemicircle(G, H) → sSemicircle(H, I) → tSemicircle(I, J) → c_1Polygon(A, B, 3) → poly2, l, m, n, KPolygon(B, C, 3) → poly3, a, b, f_1, LPolygon(C, D, 3) → poly4, g_1, h_1, i_1, MPolygon(D, E, 3) → poly5, j_1, k_1, l_1, NPolygon(E, A, 3) → poly6, m_1, n_1, p_1, OPolygon(M, N, 5) → poly7, q_1, r_1, s_1, t_1, a_1, P, Q, RSemicircle(F, A) → d_1Semicircle(B, H) → e_1Semicircle(H, C) → c_2Semicircle(C, I) → d_2Semicircle(I, D) → e_2Semicircle(D, J) → f_2Semicircle(J, E) → g_2Semicircle(E, F) → h_2Semicircle(A, G) → k_2Semicircle(G, B) → p_2Sequence(Rotate[c, ((i * 2) * π / w), S], i, 1, w) → L_1Sequence(Rotate[c_1, ((i * 2) * π / w), S], i, 1, w) → L_2Sequence(Rotate[c_2, ((i * 2) * π / w), S], i, 1, w) → L_3Sequence(Rotate[d_2, ((i * 2) * π / w), S], i, 1, w) → L_4Sequence(Rotate[d_1, ((i * 2) * π / w), S], i, 1, w) → L_5Sequence(Rotate[d, ((i * 2) * π / w), S], i, 1, w) → L_6Sequence(Rotate[e, ((i * 2) * π / w), S], i, 1, w) → L_7Sequence(Rotate[e_1, ((i * 2) * π / w), S], i, 1, w) → L_8Sequence(Rotate[e_2, ((i * 2) * π / w), S], i, 1, w) → L_9Sequence(Rotate[f_2, ((i * 2) * π / w), S], i, 1, w) → L_{10}Sequence(Rotate[g_2, ((i * 2) * π / w), S], i, 1, w) → L_{11}Sequence(Rotate[h_2, ((i * 2) * π / w), S], i, 1, w) → L_{12}Sequence(Rotate[k_2, ((i * 2) * π / w), S], i, 1, w) → L_{13}Sequence(Rotate[p_2, ((i * 2) * π / w), S], i, 1, w) → L_{14}Sequence(Rotate[p, ((i * 2) * π / w), S], i, 1, w) → L_{15}Sequence(Rotate[k, ((i * 2) * π / w), S], i, 1, w) → L_{16}Sequence(Rotate[q, ((i * 2) * π / w), S], i, 1, w) → L_{17}Sequence(Rotate[r, ((i * 2) * π / w), S], i, 1, w) → L_{18}Sequence(Rotate[s, ((i * 2) * π / w), S], i, 1, w) → L_{19}Sequence(Rotate[t, ((i * 2) * π / w), S], i, 1, w) → L_{20}Sequence(Rotate[poly7, ((i * 2) * π / w), S], i, 1, w) → L_{21}
AI 绘图提示语参考
绘制一个由五个点A、B、C、D、E构成的正五边形,然后依次找到每两点的中点,连接这些中点形成新的正五边形。接着,以每个中点为圆心,以中点到原五边形顶点的距离为半径,画出一系列半圆。最后,围绕每个半圆旋转这些半圆,形成复杂的旋转图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。