康威多边形艺术:反射旋转与相似变换的数学之美
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本范例演示了利用GeoGebra康威(Conway)多边形命令(Dardo1~4、Cometa1~4)构建的一组几何艺术图案。核心数学概念包括:①多边形(poly1~5)的构造与叠加;②反射变换实现对称图案;③旋转变换创造动态视觉效果;④相似变换产生层次感。作图要点:从构造摘要可见,共构建了5个多边形对象(poly1~5),通过反射(Reflejo)、旋转(Rotación)、相似变换(Transformación de Semejanza)等几何变换,结合对称(Simetría)手法,最终形成具有数学美感的复杂图案。该范例适合用于中学数学课堂展示几何变换的视觉效果,或作为数学艺术教学的案例,帮助学生理解抽象的变换概念。
GeoGebra 命令及参数
Dardo4Conway(A, B) → poly1, C, D, a, b, c, d, e, fCometa2Conway(D, C) → poly2, E, F, g, h, i, j, k, pCometa1Conway(C, B) → poly3, G, H, l, m, n, q, r, sCometa2Conway(D, F) → poly4, I, J, t, a1, b1, c1, d1, e1Cometa1Conway(G, B) → poly5, K, L, f1, g1, h1, i1, k1, p1Dardo1Conway(D, J) → poly6, M, N, j1, l1, m1, n1, q1, r1Dardo2Conway(K, B) → poly7, O, P, s1, t1, a2, b2, c2, d2Cometa3Conway(J, I) → poly8, Q, R, e2, f2, g2, h2, k2, p2Cometa4Conway(L, K) → poly9, S, T, i2, j2, l2, m2, q2, r2Dardo2Conway(T, O) → poly10, U, V, s2, t2, n2, a3, b3, c3Dardo1Conway(N, Q) → poly11, W, Z, d3, e3, f3, g3, h3, k3Cometa4Conway(L, T) → poly12, A1, B1, i3, j3, l3, m3, p3, q3Cometa3Conway(Q, I) → poly13, C1, D1, n3, r3, s3, t3, c4, d4Cometa3Conway(V, O) → poly14, E1, F1, a4, b4, e4, f4, g4, h4Cometa4Conway(N, W) → poly15, G1, H1, i4, j4, k4, l4, p4, q4Cometa3Conway(E1, S) → poly16, I1, J1, m4, n4, r4, s4, t4, c5Cometa4Conway(N, H1) → poly17, K1, L1, a5, b5, d5, e5, f5, g5Dardo1Conway(J1, H1) → poly18, M1, N1, h5, i5, j5, k5, p5, q5Dardo1Conway(F1, E1) → poly19, O1, P1, l5, m5, n5, r5, s5, t5Cometa3Conway(G, L) → poly20, Q1, R1, a6, b6, c6, d6, e6, f6Cometa3Conway(Q1, L) → poly21, S1, T1, g6, h6, i6, j6, k6, p6Cometa3Conway(C1, I) → poly22, U1, V1, l6, m6, n6, q6, r6, s6Cometa3Conway(U1, I) → poly23, W1, Z1, t6, a7, b7, c7, d7, e7Dardo4Conway(F, E) → poly24, A2, B2, f7, g7, h7, i7, k7, p7Dardo3Conway(E, G) → poly25, C2, D2, j7, l7, m7, n7, q7, r7Cometa1Conway(A2, E) → poly26, E2, F2, s7, t7, a8, b8, c8, d8Cometa2Conway(B2, A2) → poly27, G2, H2, e8, f8, g8, h8, k8, p8Cometa4Conway(F2, D2) → poly28, I2, J2, i8, j8, l8, m8, q8, r8Cometa4Conway(F2, J2) → poly29, K2, L2, n8, s8, t8, a9, c9, d9Cometa4Conway(F2, L2) → poly30, M2, N2, b9, e9, f9, g9, h9, k9Cometa2Conway(Z1, F) → poly31, O2, P2, i9, j9, l9, m9, p9, q9Cometa3Conway(P2, B2) → poly32, Q2, R2, n9, r9, s9, t9, c10, d10Dardo4Conway(Q2, B2) → poly33, S2, T2, a10, b10, e10, f10, g10, h10Cometa4Conway(C2, G) → poly34, U2, V2, i10, j10, k10, l10, p10, q10Cometa4Conway(C2, V2) → poly35, W2, Z2, m10, n10, r10, s10, t10, c11Dardo3Conway(C2, Z2) → poly36, A3, B3, a11, b11, d11, e11, f11, g11Dardo1Conway(Z1, P2) → poly37, C3, D3, h11, i11, j11, k11, p11, q11Dardo1Conway(W2, V2) → poly38, E3, F3, l11, m11, n11, r11, s11, t11Dardo1Conway(R1, Q1) → poly39, G3, H3, a12, b12, c12, d12, e12, f12Dardo1Conway(V1, U1) → poly40, I3, J3, g12, h12, i12, j12, k12, p12Dardo4Conway(M1, G1) → poly41, K3, L3, l12, m12, n12, q12, r12, s12Dardo4Conway(M1, L3) → poly42, M3, N3, t12, a13, b13, c13, d13, e13Dardo4Conway(M1, N3) → poly43, O3, P3, f13, g13, h13, i13, k13, p13Dardo4Conway(E3, T1) → poly44, Q3, R3, j13, l13, m13, n13, q13, r13Dardo4Conway(E3, R3) → poly45, S3, T3, s13, t13, a14, b14, c14, d14Dardo4Conway(E3, T3) → poly46, U3, V3, e14, f14, g14, h14, k14, p14Dardo4Conway(C3, R2) → poly47, W3, Z3, i14, j14, l14, m14, q14, r14Dardo4Conway(C3, Z3) → poly48, A4, B4, n14, s14, t14, a15, c15, d15Dardo4Conway(C3, B4) → poly49, C4, D4, b15, e15, f15, g15, h15, k15Cometa2Conway(N3, M3) → poly50, E4, F4, i15, j15, l15, m15, p15, q15Cometa4Conway(E4, M3) → poly51, G4, H4, n15, r15, s15, t15, c16, d16Cometa4Conway(E4, H4) → poly52, I4, J4, a16, b16, e16, f16, g16, h16Cometa4Conway(E4, J4) → poly53, K4, L4, i16, j16, k16, l16, p16, q16Cometa4Conway(E4, L4) → poly54, M4, N4, m16, n16, r16, s16, t16, c17Cometa2Conway(T3, S3) → poly55, O4, P4, a17, b17, d17, e17, f17, g17Cometa2Conway(B4, A4) → poly56, Q4, R4, h17, i17, j17, k17, p17, q17Cometa4Conway(O4, S3) → poly57, S4, T4, l17, m17, n17, r17, s17, t17Cometa4Conway(O4, T4) → poly58, U4, V4, a18, b18, c18, d18, e18, f18Cometa4Conway(O4, V4) → poly59, W4, Z4, g18, h18, i18, j18, k18, p18Cometa4Conway(O4, Z4) → poly60, A5, B5, l18, m18, n18, q18, r18, s18Cometa4Conway(Q4, A4) → poly61, C5, D5, t18, a19, b19, c19, d19, e19Cometa4Conway(Q4, D5) → poly62, E5, F5, f19, g19, h19, i19, k19, p19Cometa4Conway(Q4, F5) → poly63, G5, H5, j19, l19, m19, n19, q19, r19Cometa4Conway(Q4, H5) → poly64, I5, J5, s19, t19, a20, b20, c20, d20Cometa2Conway(F1, O3) → poly65, K5, L5, e20, f20, g20, h20, k20, p20Cometa2Conway(N3, F4) → poly66, M5, N5, i20, j20, l20, m20, q20, r20Cometa2Conway(W2, U3) → poly67, O5, P5, n20, s20, t20, a21, c21, d21Cometa2Conway(T3, P4) → poly68, Q5, R5, b21, e21, f21, g21, h21, k21Cometa2Conway(V1, C4) → poly69, S5, T5, i21, j21, l21, m21, p21, q21Cometa2Conway(B4, R4) → poly70, U5, V5, n21, r21, s21, t21, c22, d22Cometa2Conway(Z3, W3) → poly71, W5, Z5, a22, b22, e22, f22, g22, h22Cometa2Conway(R2, Q2) → poly72, A6, B6, i22, j22, k22, l22, p22, q22Cometa2Conway(R3, Q3) → poly73, C6, D6, m22, n22, r22, s22, t22, c23Cometa2Conway(T1, B1) → poly74, E6, F6, a23, b23, d23, e23, f23, g23Cometa2Conway(L3, K3) → poly75, G6, H6, h23, i23, j23, k23, p23, q23Cometa2Conway(G1, W) → poly76, I6, J6, l23, m23, n23, r23, s23, t23Dardo4Conway(W, Z) → poly77, K6, L6, a24, b24, c24, d24, e24, f24Dardo4Conway(W, L6) → poly78, M6, N6, g24, h24, i24, j24, k24, p24Cometa2Conway(G6, M6) → poly79, P6, Q6, l24, m24, n24, q24, r24, s24Cometa3Conway(Q6, P6) → poly80, R6, S6, t24, a25, b25, c25, d25, e25Cometa3Conway(R6, P6) → poly81, T6, U6, f25, g25, h25, i25, k25, p25Cometa3Conway(T6, P6) → poly82, V6, W6, j25, l25, m25, n25, q25, r25Cometa3Conway(V6, P6) → poly83, Z6, A7, s25, t25, a26, b26, c26, d26Dardo4Conway(H4, G6) → poly84, B7, C7, e26, f26, g26, h26, k26, p26Dardo3Conway(U, V) → poly85, D7, E7, i26, j26, l26, m26, q26, r26Dardo3Conway(D7, V) → poly86, F7, G7, n26, s26, t26, a27, c27, d27Cometa1Conway(G7, K5) → poly87, H7, I7, b27, e27, f27, g27, h27, k27Cometa4Conway(I7, H7) → poly88, J7, K7, i27, j27, l27, m27, p27, q27Cometa4Conway(I7, K7) → poly89, L7, M7, n27, r27, s27, t27, c28, d28Cometa4Conway(I7, M7) → poly90, N7, O7, a28, b28, e28, f28, g28, h28Cometa4Conway(I7, O7) → poly91, P7, Q7, i28, j28, k28, l28, p28, q28Dardo1Conway(J7, H7) → poly92, O6, R7, m28, n28, r28, s28, t28, c29Cometa1Conway(B1, U) → poly93, S7, T7, a29, b29, d29, e29, f29, g29Cometa1Conway(E7, D7) → poly94, U7, V7, h29, i29, j29, k29, p29, q29Cometa1Conway(K6, Z) → poly95, W7, Z7, l29, m29, n29, r29, s29, t29Cometa1Conway(V6, L6) → poly96, A8, B8, a30, b30, c30, d30, e30, f30Dardo3Conway(C6, B1) → poly97, C8, D8, g30, h30, i30, j30, k30, p30Dardo3Conway(T7, O7) → poly98, E8, F8, l30, m30, n30, q30, r30, s30Dardo3Conway(Z7, C1) → poly99, G8, H8, t30, a31, b31, c31, d31, e31Dardo4Conway(V6, Z7) → poly100, I8, J8, f31, g31, h31, i31, k31, p31Cometa2Conway(T7, F8) → poly101, K8, L8, j31, l31, m31, n31, q31, r31Cometa4Conway(K8, F8) → poly102, M8, N8, s31, t31, a32, b32, c32, d32Cometa4Conway(K8, N8) → poly103, O8, P8, e32, f32, g32, h32, k32, p32Cometa4Conway(K8, P8) → poly104, Q8, R8, i32, j32, l32, m32, q32, r32Cometa4Conway(K8, R8) → poly105, S8, T8, n32, s32, t32, a33, c33, d33Cometa2Conway(Z7, H8) → poly106, U8, V8, b33, e33, f33, g33, h33, k33Cometa3Conway(I8, U8) → poly107, W8, Z8, i33, j33, l33, m33, p33, q33Cometa3Conway(W8, U8) → poly108, A9, B9, n33, r33, s33, t33, c34, d34Cometa3Conway(A9, U8) → poly109, C9, D9, a34, b34, e34, f34, g34, h34Cometa3Conway(C9, U8) → poly110, E9, F9, i34, j34, k34, l34, p34, q34Dardo1Conway(D9, C9) → poly111, G9, H9, m34, n34, r34, s34, t34, c35Dardo1Conway(G5, F5) → poly112, I9, J9, a35, b35, d35, e35, f35, g35Cometa2Conway(E5, D5) → poly113, K9, L9, h35, i35, j35, k35, p35, q35Cometa3Conway(L9, K9) → poly114, M9, N9, l35, m35, n35, r35, s35, t35Dardo3Conway(K9, D5) → poly115, O9, P9, a36, b36, c36, d36, e36, f36Dardo4Conway(M9, K9) → poly116, Q9, R9, g36, h36, i36, j36, k36, p36Cometa2Conway(R9, Q9) → poly117, S9, T9, l36, m36, n36, q36, r36, s36Cometa4Conway(S9, Q9) → poly118, U9, V9, t36, a37, b37, c37, d37, e37Cometa4Conway(S9, P9) → poly119, W9, Z9, f37, g37, h37, i37, k37, p37Cometa4Conway(S9, Z9) → poly120, A10, B10, j37, l37, m37, n37, q37, r37Cometa4Conway(S9, B10) → poly121, C10, D10, s37, t37, a38, b38, c38, d38Dardo1Conway(A10, Z9) → poly122, E10, F10, e38, f38, g38, h38, k38, p38Dardo1Conway(R9, T9) → poly123, G10, H10, i38, j38, l38, m38, q38, r38Cometa2Conway(C10, B10) → poly124, I10, J10, n38, s38, t38, a39, c39, d39Cometa3Conway(J10, I10) → poly125, K10, L10, b39, e39, f39, g39, h39, k39Dardo3Conway(I10, B10) → poly126, M10, N10, i39, j39, l39, m39, p39, q39Cometa2Conway(I10, N10) → poly127, O10, P10, n39, r39, s39, t39, c40, d40Cometa4Conway(O10, N10) → poly128, Q10, R10, a40, b40, e40, f40, g40, h40Cometa4Conway(O10, R10) → poly129, S10, T10, i40, j40, k40, l40, p40, q40Cometa4Conway(O10, T10) → poly130, U10, V10, m40, n40, r40, s40, t40, c41Cometa4Conway(O10, V10) → poly131, W10, Z10, a41, b41, d41, e41, f41, g41Dardo1Conway(S10, R10) → poly132, A11, B11, h41, i41, j41, k41, p41, q41Dardo1Conway(U10, T10) → poly133, C11, D11, l41, m41, n41, r41, s41, t41Dardo1Conway(I10, P10) → poly134, E11, F11, a42, b42, c42, d42, e42, f42Cometa3Conway(L2, M10) → poly135, G11, H11, g42, h42, i42, j42, k42, p42Cometa3Conway(G11, M10) → poly136, I11, J11, l42, m42, n42, q42, r42, s42Dardo1Conway(M2, G11) → poly137, K11, L11, t42, a43, b43, c43, d43, e43Dardo1Conway(C10, J10) → poly138, M11, N11, f43, g43, h43, i43, k43, p43Dardo1Conway(W10, V10) → poly139, O11, P11, j43, l43, m43, n43, q43, r43Cometa3Conway(O11, U10) → poly140, Q11, R11, s43, t43, a44, b44, c44, d44Cometa3Conway(Q11, U10) → poly141, S11, T11, e44, f44, g44, h44, k44, p44Cometa3Conway(C11, S10) → poly142, U11, V11, i44, j44, l44, m44, q44, r44Cometa3Conway(U11, S10) → poly143, W11, Z11, n44, s44, t44, a45, c45, d45Cometa2Conway(T11, C11) → poly144, A12, B12, b45, e45, f45, g45, h45, k45Cometa4Conway(A12, C11) → poly145, C12, D12, i45, j45, l45, m45, p45, q45Cometa4Conway(A12, D12) → poly146, E12, F12, n45, r45, s45, t45, c46, d46Cometa4Conway(A12, F12) → poly147, G12, H12, a46, b46, e46, f46, g46, h46Cometa4Conway(A12, H12) → poly148, I12, J12, i46, j46, k46, l46, p46, q46Dardo1Conway(O5, D12) → poly149, K12, L12, m46, n46, r46, s46, t46, c47Dardo1Conway(V11, U11) → poly150, M12, N12, a47, b47, d47, e47, f47, g47Dardo1Conway(G12, F12) → poly151, O12, P12, h47, i47, j47, k47, p47, q47Dardo1Conway(C6, R8) → poly152, Q12, R12, l47, m47, n47, r47, s47, t47Dardo1Conway(Q8, P8) → poly153, S12, T12, a48, b48, c48, d48, e48, f48Dardo1Conway(O8, N8) → poly154, U12, V12, g48, h48, i48, j48, k48, p48Dardo1Conway(W4, V4) → poly155, W12, Z12, l48, m48, n48, q48, r48, s48Dardo1Conway(I12, H12) → poly156, A13, B13, t48, a49, b49, c49, d49, e49Dardo1Conway(R11, Q11) → poly157, C13, D13, f49, g49, h49, i49, k49, p49Dardo1Conway(T11, B12) → poly158, E13, F13, j49, l49, m49, n49, q49, r49Dardo1Conway(E5, L9) → poly159, G13, H13, s49, t49, a50, b50, c50, d50Dardo1Conway(I5, H5) → poly160, I13, J13, e50, f50, g50, h50, k50, p50Cometa3Conway(A13, G12) → poly161, K13, L13, i50, j50, l50, m50, q50, r50Cometa3Conway(K13, G12) → poly162, M13, N13, n50, s50, t50, a51, c51, d51Dardo1Conway(L13, K13) → poly163, O13, P13, b51, e51, f51, g51, h51, k51Dardo1Conway(A5, Z4) → poly164, Q13, R13, i51, j51, l51, m51, p51, q51Cometa2Conway(U4, T4) → poly165, S13, T13, n51, r51, s51, t51, c52, d52Cometa3Conway(T13, Q8) → poly166, U13, V13, a52, b52, e52, f52, g52, h52Dardo4Conway(W12, U4) → poly167, W13, Z13, i52, j52, k52, l52, p52, q52Cometa1Conway(O7, N7) → poly168, A14, B14, m52, n52, r52, s52, t52, c53Cometa3Conway(U12, E8) → poly169, C14, D14, a53, b53, d53, e53, f53, g53Dardo1Conway(D14, A14) → poly170, E14, F14, h53, i53, j53, k53, p53, q53Dardo1Conway(N7, M7) → poly171, G14, H14, l53, m53, n53, r53, s53, t53Dardo1Conway(L7, K7) → poly172, I14, J14, a54, b54, c54, d54, e54, f54Dardo1Conway(M4, L4) → poly173, K14, L14, g54, h54, i54, j54, k54, p54Dardo1Conway(S6, R6) → poly174, M14, N14, l54, m54, n54, q54, r54, s54Dardo1Conway(U6, T6) → poly175, O14, P14, t54, a55, b55, c55, d55, e55Dardo1Conway(J8, W8) → poly176, Q14, R14, f55, g55, h55, i55, k55, p55Dardo1Conway(B9, A9) → poly177, S14, T14, j55, l55, m55, n55, q55, r55Dardo1Conway(K4, J4) → poly178, U14, V14, s55, t55, a56, b56, c56, d56Dardo4Conway(U14, I4) → poly188, Q15, R15, a59, b59, d59, e59, f59, g59Dardo3Conway(M4, K14) → poly190, U15, V15, l59, m59, n59, r59, s59, t59Cometa3Conway(H4, S6) → poly192, A16, B16, g60, h60, i60, j60, k60, p60Cometa3Conway(Q15, S6) → poly193, C16, D16, l60, m60, n60, q60, r60, s60Cometa4Conway(J7, F4) → poly199, O16, P16, i62, j62, l62, m62, q62, r62Cometa4Conway(J7, V15) → poly200, Q16, R16, n62, s62, t62, a63, c63, d63Cometa3Conway(V6, J8) → poly206, E17, F17, m64, n64, r64, s64, t64, c65Cometa3Conway(E17, J8) → poly207, G17, H17, a65, b65, d65, e65, f65, g65Dardo1Conway(W6, E17) → poly208, I17, J17, h65, i65, j65, k65, p65, q65Cometa1Conway(R4, I5) → poly209, K17, L17, l65, m65, n65, r65, s65, t65Cometa4Conway(D9, K17) → poly210, M17, N17, a66, b66, c66, d66, e66, f66Dardo3Conway(I5, I13) → poly211, O17, P17, g66, h66, i66, j66, k66, p66Dardo4Conway(E14, D14) → poly225, S18, T18, m70, n70, r70, s70, t70, c71
AI 绘图提示语参考
绘制一个由多个多边形构成的复杂几何艺术图案,这些多边形通过反射、旋转和相似变换相互组合,形成具有对称性和动态视觉效果的美学结构。首先创建五个基础多边形,然后应用反射和旋转变换,再通过相似变换创建层叠效果,最终形成包含多种变换特征的复杂图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。