坐标船游戏:探索坐标与随机过程
几何画板及绘图内容加载中,请稍等……
这个范例演示了如何通过滑块控制坐标系中的船的位置,展示随机过程在几何图形中的应用。核心数学概念包括坐标几何、随机过程和几何作图。作图要点涉及使用GeoGebra命令如Random、Circle、Ray等来构造图形。适合初中生或高中生用于学习坐标几何和随机过程的基础知识。
GeoGebra 命令及参数
Random(-10, 10) → bbRandom(-10, 10) → aaRandom(-10, 10) → ccRandom(4, 15) → rrCircle(A, (1.5 * v - 1) * rr) → c'Ray(A, (0, 0)) → aOrthogonalLine(A, a) → bIntersect(c', b) → B, CIntersect(c', a) → D, TCircumcircleArc(B, D, C) → dMidpoint(C, D) → EMidpoint(B, D) → F_2Ray(A', E) → eRay(A', F_2) → fIntersect(d, e) → G,Intersect(d, f) → H,CircumcircleArc(G, D, H) → gCircle(I, 1) → hSequence(Text[If[s < 10, " ", ""] + (s), (21.6 + 2 * Mod[s - 1, 3], 7.75 - 2 * Div[s - 1, 3])], s, 1, 12) → liste3Circle(J, 1) → kSequence(Text[If[s ≟ 1, " ", If[s < 5, " ", ""]] + (30 * (s - 1)) + "º", (21.25 + 2 * Mod[s - 1, 3], -6.25 - 2 * Div[s - 1, 3])], s, 1, 12) → liste4If(yB > -5, 5*°, (((xB - 3 * yB) / 2 - 19 - 1) * 30)°) → angIf(ang ≟ α ∧ dist ≟ rr, true, false) → razSegment(O, N) → mCircle(A, (2 * v - 1) * rr - n) → pSequence(Circle[A, (1.5 * v - 1) * rr - i], i, 0, n, n / 10) → liste5Polygon(P, Q, R, S) → poly1, p_1, q, r_1, sCircle((0, 0), If[2 * v * rr > 12, 0, 2 * v * rr]) → cMidpoint(K, L) → UMidpoint(U, L) → VMidpoint(U, V) → WMidpoint(V, L) → ZSegment(K, C_1) → lLine(A, l) → iSegment(A, U) → tIntersect(c, t) → A_1, B_1Segment(U, A_1) → a_1Rotate(C_1, 6 * v, U) → L'Segment(U, L') → b_1Mod(v * 100, 2) → abSegment(O, D_1) → jCircle(O, C_1) → g_1Point(g_1) → E_1Segment(O, E_1) → h_1Circle(F_1, 6.5 - abs(r / 4.5)) → q_1Line(F_1, l) → i_1Intersect(q_1, i_1) → G_1, H_1Line(J_1, r_1) → j_1Point(j_1) → N_1Line(N_1, l) → l_1Line(J_1, l) → m_1Point(m_1) → O_1Point(l_1) → P_1Intersect(l_1, r_1) → M_1Polygon(M_1, N_1, J_1, F) → poly2, m_2, n_1, j_2, f_2Point(l_1) → Q_1Point(m_1) → R_1Polygon(P_1, Q_1, R_1, O_1) → poly3, p_2, q_2, r_2, o_1Point(j_1) → S_1Polygon(S_1, T_1, O_1, J_1) → poly4, s_1, t_1, o_2, j_3Midpoint(s_1) → V_1Midpoint(o_2) → W_1Midpoint(S_1, J_1) → Z_1Midpoint(t_1) → A_2Segment(V_1, W_1) → a_2Segment(Z_1, A_2) → b_2Intersect(b_2, a_2) → B_2Circle(B_2, V_1) → c_2Sequence((x(O) + i, y(D_1)), i, -11, 11, 1) → liste1Sequence((x(N) + i, y(N)), i, -11, 11, 1) → liste6Sequence((x(C_1), y(C_1) + i), i, -11, 11, 1) → liste7Sequence((x(E_1), y(E_1) + i), i, -11, 11, 1) → liste8Ray(M_1, T_1) → c_1Sequence(Segment[Element[liste8, i], Element[liste7, i]], i, 0, 22) → liste10Sequence((x(D_1) + i, 0), i, -11, 11) → liste2Sequence(Segment[Element[liste1, i], Element[liste6, i]], i, 0, 22) → liste9Line(S, P) → d_1Line(J_1, S_1) → e_1Line(Q_1, e_1) → f_1Intersect(d_1, s) → MIntersect(d_1, f_1) → C_2Line(R, d_1) → k_1Intersect(e_1, k_1) → D_2Polygon(S, C_2, Q_1, S_1, D_2, R) → poly5, s_2, c_3, q_3, s_3, d_2, r_3Point(d_1) → E_2Line(E_2, p_1) → e_2Intersect(k_1, e_2) → G_2Polygon(E_2, P, Q, G_2) → poly6, e_3, p_3, q_4, g_2Sequence(O + (i, 0), i, -10, 10) → liste11Sequence(O + (0, i), i, -10, 10) → liste12Sequence(i, i, -10, 10) → liste13Sequence(Text[Element[liste13, i], (x(Element[liste11, i] - 0.42), y(Element[liste11, i] - 0.85))], i, 1, Length[liste13], 2) → liste14Sequence(Text[Element[liste13, i], (x(Element[liste12, i] - 1), y(Element[liste12, i] - 0.31))], i, 1, Length[liste13], 2) → liste15
AI 绘图提示语参考
在一个坐标系中,用滑块控制船的位置,展示随机过程在几何图形中的应用。首先绘制一个随机圆和两条射线,然后找到圆与射线的交点,并绘制圆弧和线段。接着,利用圆心、交点和线段的中点绘制新的圆和射线,并找到它们的交点。最后,根据滑块值绘制一系列圆和文本,并连接关键点形成多边形和线段,完成整个图形的构造。
以上提示语为根据原始绘图命令整理而来,仅供参考。