勾股螺旋
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①本范例演示了勾股定理在构建螺旋形多边形中的应用;②涉及核心数学概念包括勾股定理、直角三角形、多边形构造;③作图要点——从下方『构造摘要』提炼用到了 Circle(圆)、Point(点)、Segment(线段)、OrthogonalLine(垂线)、Intersect(交点)、Polygon(多边形)、Angle(角度)等 GeoGebra 命令/对象;④适合初中及以上学生学习几何作图与勾股定理的实践应用。
GeoGebra 命令及参数
Circle(A, a) → cPoint(Circle[A, 1]) → CSegment(A, C) → eOrthogonalLine(A, e) → bIntersect(c, b) → B, DPolygon(D, C, A) → poly1, a_1, d, c_1OrthogonalLine(D, a_1) → fCircle(D, a) → gIntersect(g, f) → E, FPolygon(D, F, C) → poly2, c_2, d_1, f_1Circle(F, a) → kOrthogonalLine(F, d_1) → hIntersect(k, h, 2) → GPolygon(G, C, F) → poly3, f_2, g_1, c_3OrthogonalLine(G, f_2) → iCircle(G, a) → pIntersect(p, i, 2) → HPolygon(H, C, G) → poly4, g_2, h_1, c_4OrthogonalLine(H, g_2) → jCircle(H, a) → qIntersect(q, j, 2) → IPolygon(I, C, H) → poly5, h_2, i_1, c_5OrthogonalLine(I, h_2) → lCircle(I, a) → rIntersect(r, l, 2) → JPolygon(I, J, C) → poly6, c_6, i_2, j_1OrthogonalLine(J, i_2) → mCircle(J, a) → sIntersect(s, m, 2) → KPolygon(J, K, C) → poly7, c_7, j_2, k_1OrthogonalLine(K, j_2) → nCircle(K, a) → tIntersect(t, n, 2) → LPolygon(K, L, C) → poly8, c_8, k_2, l_1OrthogonalLine(L, k_2) → b_1Circle(L, a) → e_1Intersect(e_1, b_1, 2) → MPolygon(L, M, C) → poly9, c_9, l_2, m_1OrthogonalLine(M, l_2) → n_1Circle(M, a) → p_1Intersect(p_1, n_1, 2) → NPolygon(M, N, C) → poly10, c_{10}, m_2, n_2OrthogonalLine(N, m_2) → q_1Circle(N, a) → r_1Intersect(r_1, q_1, 2) → OPolygon(N, O, C) → poly11, c_{11}, n_3, oOrthogonalLine(O, n_3) → s_1Circle(O, a) → t_1Intersect(t_1, s_1, 2) → PPolygon(O, P, C) → poly12, c_{12}, o_1, p_2OrthogonalLine(P, o_1) → a_2Circle(P, a) → d_2Intersect(d_2, a_2, 2) → QPolygon(P, Q, C) → poly13, c_{13}, p_3, q_2Angle(C, A, D) → αAngle(C, D, F) → βAngle(C, F, G) → γAngle(C, G, H) → δAngle(C, H, I) → εAngle(C, I, J) → ζAngle(C, J, K) → ηAngle(C, K, L) → θAngle(C, L, M) → ιAngle(C, M, N) → κAngle(C, N, O) → λAngle(C, O, P) → μAngle(C, P, Q) → ν