读取坐标网格上的坐标
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本范例演示如何在笛卡尔坐标系中读取网格上的坐标。核心数学概念包括坐标系、几何图形和二次方程。通过使用GeoGebra命令如Random、Circle、Ray等,可以构造出一个动态的坐标读取模型。适合初中及以上学生学习几何和代数知识。
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
在直角坐标系中给出一个随机中心点,并以该点为基准画出一条与原点相连的射线,再作与这条射线正交的直线。分别取与圆相交形成的两组交点,连成圆弧;同时取若干点的中点并从它们出发再画两条射线,与圆弧继续相交得到新的交点,再用这些点确定另一圆弧。整体叠加一个以坐标原点为圆心的小圆与一系列等半径圆,并在图中添加扇形刻度文字来表达读取的角度信息。
以上提示语为根据原始绘图命令整理而来,仅供参考。