欧拉公式
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该范例演示了欧拉公式,涉及复数与指数函数的关系。通过点、圆、向量等对象的构造,展示了欧拉公式在解析几何中的应用。使用了Point、Circle、Vector等GeoGebra命令,适合高中数学教学。
GeoGebra 命令及参数
Point(yAxis) → ACircle(A, 1) → cVector(A, B) → uVector(B, C) → vCircle(C, t02) → dOrthogonalLine(C, yAxis) → fIntersect(d, f, 2) → DVector(C, D) → wCircle(D, t03) → eOrthogonalLine(D, w) → gIntersect(e, g) → E, FVector(D, F) → aCircle(F, t04) → hOrthogonalLine(F, yAxis) → iIntersect(h, i, 1) → GVector(F, G) → bOrthogonalLine(G, b) → jCircle(G, t05) → kIntersect(k, j) → H, IVector(G, I) → lCircle(I, t06) → pOrthogonalLine(I, l) → mIntersect(p, m, 2) → JVector(I, J) → nCircle(J, t07) → qOrthogonalLine(J, n) → rIntersect(q, r, 2) → KVector(J, K) → sCircle(K, t08) → tOrthogonalLine(K, s) → f_1Intersect(t, f_1, 2) → LVector(K, L) → u_1Circle(L, t09) → c_1OrthogonalLine(L, u_1) → g_1Intersect(c_1, g_1, 2) → MVector(L, M) → v_1Circle(M, t10) → d_1OrthogonalLine(M, v_1) → h_1Intersect(d_1, h_1, 2) → NVector(M, N) → w_1Circle(N, t11) → e_1OrthogonalLine(N, w_1) → i_1Intersect(e_1, i_1, 2) → OVector(N, O) → a_1Circle(O, t12) → k_1OrthogonalLine(O, a_1) → j_1Intersect(k_1, j_1, 2) → PVector(O, P) → b_1Circle(P, t13) → p_1OrthogonalLine(P, b_1) → l_1Intersect(p_1, l_1, 2) → QVector(P, Q) → m_1Circle(Q, t14) → q_1OrthogonalLine(Q, m_1) → n_1Intersect(q_1, n_1, 2) → RVector(Q, R) → r_1Circle(R, t15) → s_1OrthogonalLine(R, r_1) → t_1Intersect(s_1, t_1, 2) → SVector(R, S) → u_2Circle(S, t16) → c_2OrthogonalLine(S, u_2) → f_2Intersect(c_2, f_2, 2) → TVector(S, T) → v_2Circle(T, t17) → d_2OrthogonalLine(T, v_2) → g_2Intersect(d_2, g_2, 2) → UVector(T, U) → w_2Circle(U, t18) → e_2OrthogonalLine(U, w_2) → h_2Intersect(e_2, h_2, 2) → VVector(U, V) → a_2
AI 绘图提示语参考
画一个展示欧拉公式的图形,包含一个点在y轴上,以此点为圆心画一个单位圆,再从圆上点向y轴作向量,接着以向量终点为圆心画圆,交点作向量,重复此过程,展示复数与指数函数的关系,适合高中数学教育。
以上提示语为根据原始绘图命令整理而来,仅供参考。