随机旋转对称问题
几何画板及绘图内容加载中,请稍等……
所属专题
Randomised Questions
该范例演示了随机旋转对称图形的生成过程。核心数学概念包括旋转对称性和几何变换。通过使用GeoGebra命令Polygon、Random、If和Rotate,可以构造出具有不同旋转对称性的多边形。适合初中及以上学生学习旋转对称性和几何变换。
GeoGebra 命令及参数
Polygon(A1, B1, C1, D1) → E1, F1, G1, H1, I1Polygon(A2, B2, C2, D2) → E2, F2, G2, H2, I2Polygon(A3, B3, C3, D3) → E3, F3, G3, H3, I3Polygon(A4, B4, C4, D4) → E4, F4, G4, H4, I4Polygon(A5, B5, C5, D5) → E5, F5, G5, H5, I5Random(4, 5) → sizePolygon(A6, B6, C6, D6) → E6, F6, G6, H6, I6Polygon(A7, B7, C7, D7) → E7, F7, G7, H7, I7Polygon(A8, B8, C8, D8) → E8, F8, G8, H8, I8Polygon(A9, B9, C9, D9) → E9, F9, G9, H9, I9Polygon(A10, B10, C10, D10) → E10, F10, G10, H10, I10Polygon(A11, B11, C11, D11) → E11, F11, G11, H11, I11Polygon(A12, B12, C12, D12) → E12, F12, G12, H12, I12Polygon(A13, B13, C13, D13) → E13, F13, G13, H13, I13Polygon(A14, B14, C14, D14) → E14, F14, G14, H14, I14Polygon(A15, B15, C15, D15) → E15, F15, G15, H15, I15Polygon(A16, B16, C16, D16) → E16, F16, G16, H16, I16Polygon(A17, B17, C17, D17) → E17, F17, G17, H17, I17Polygon(A18, B18, C18, D18) → E18, F18, G18, H18, I18Polygon(A19, B19, C19, D19) → E19, F19, G19, H19, I19Polygon(A20, B20, C20, D20) → E20, F20, G20, H20, I20Polygon(A21, B21, C21, D21) → E21, F21, G21, H21, I21Polygon(A22, B22, C22, D22) → E22, F22, G22, H22, I22Polygon(A23, B23, C23, D23) → E23, F23, G23, H23, I23Polygon(A24, B24, C24, D24) → E24, F24, G24, H24, I24Polygon(A25, B25, C25, D25) → E25, F25, G25, H25, I25If(size ≟ 4, centre_4, centre_5) → centreRotate(A1, 180*°, centre) → A1'Rotate(B1, 180*°, centre) → B1'Rotate(C1, 180*°, centre) → C1'Rotate(D1, 180*°, centre) → D1'Rotate(A1, 180*°, centre) → J1Rotate(B1, 180*°, centre) → K1Rotate(C1, 180*°, centre) → L1Rotate(D1, 180*°, centre) → M1Polygon(J1, K1, L1, M1) → N1, O1, P1, Q1, R1Rotate(A2, 180*°, centre) → J2Rotate(B2, 180*°, centre) → K2Rotate(C2, 180*°, centre) → L2Rotate(D2, 180*°, centre) → M2Rotate(A3, 180*°, centre) → J3Rotate(B3, 180*°, centre) → K3Rotate(C3, 180*°, centre) → L3Rotate(D3, 180*°, centre) → M3Rotate(A4, 180*°, centre) → J4Rotate(B4, 180*°, centre) → K4Rotate(C4, 180*°, centre) → L4Rotate(D4, 180*°, centre) → M4Rotate(A5, 180*°, centre) → J5Rotate(B5, 180*°, centre) → K5Rotate(C5, 180*°, centre) → L5Rotate(D5, 180*°, centre) → M5Rotate(A6, 180*°, centre) → J6Rotate(B6, 180*°, centre) → K6Rotate(C6, 180*°, centre) → L6Rotate(D6, 180*°, centre) → M6Rotate(A7, 180*°, centre) → J7Rotate(B7, 180*°, centre) → K7Rotate(C7, 180*°, centre) → L7Rotate(D7, 180*°, centre) → M7Rotate(A8, 180*°, centre) → J8Rotate(B8, 180*°, centre) → K8Rotate(C8, 180*°, centre) → L8Rotate(D8, 180*°, centre) → M8Rotate(A9, 180*°, centre) → J9Rotate(B9, 180*°, centre) → K9Rotate(C9, 180*°, centre) → L9Rotate(D9, 180*°, centre) → M9Rotate(A10, 180*°, centre) → J10Rotate(B10, 180*°, centre) → K10Rotate(C10, 180*°, centre) → L10Rotate(D10, 180*°, centre) → M10Rotate(A11, 180*°, centre) → J11Rotate(B11, 180*°, centre) → K11Rotate(C11, 180*°, centre) → L11Rotate(D11, 180*°, centre) → M11Rotate(A12, 180*°, centre) → J12Rotate(B12, 180*°, centre) → K12Rotate(C12, 180*°, centre) → L12Rotate(D12, 180*°, centre) → M12Rotate(A13, 180*°, centre) → J13Rotate(B13, 180*°, centre) → K13Rotate(C13, 180*°, centre) → L13Rotate(D13, 180*°, centre) → M13Rotate(A14, 180*°, centre) → J14Rotate(B14, 180*°, centre) → K14Rotate(C14, 180*°, centre) → L14Rotate(D14, 180*°, centre) → M14Rotate(A15, 180*°, centre) → J15Rotate(B15, 180*°, centre) → K15Rotate(C15, 180*°, centre) → L15Rotate(D15, 180*°, centre) → M15Rotate(A16, 180*°, centre) → J16Rotate(B16, 180*°, centre) → K16Rotate(C16, 180*°, centre) → L16Rotate(D16, 180*°, centre) → M16Rotate(A17, 180*°, centre) → J17Rotate(B17, 180*°, centre) → K17Rotate(C17, 180*°, centre) → L17Rotate(D17, 180*°, centre) → M17Rotate(A18, 180*°, centre) → J18Rotate(B18, 180*°, centre) → K18Rotate(C18, 180*°, centre) → L18Rotate(D18, 180*°, centre) → M18Rotate(A19, 180*°, centre) → J19Rotate(B19, 180*°, centre) → K19Rotate(C19, 180*°, centre) → L19Rotate(D19, 180*°, centre) → M19Rotate(A20, 180*°, centre) → J20Rotate(B20, 180*°, centre) → K20Rotate(C20, 180*°, centre) → L20Rotate(D20, 180*°, centre) → M20Rotate(A21, 180*°, centre) → J21Rotate(B21, 180*°, centre) → K21Rotate(C21, 180*°, centre) → L21Rotate(D21, 180*°, centre) → M21Rotate(A22, 180*°, centre) → J22Rotate(B22, 180*°, centre) → K22Rotate(C22, 180*°, centre) → L22Rotate(D22, 180*°, centre) → M22Rotate(A23, 180*°, centre) → J23Rotate(B23, 180*°, centre) → K23Rotate(C23, 180*°, centre) → L23Rotate(D23, 180*°, centre) → M23Rotate(A24, 180*°, centre) → J24Rotate(B24, 180*°, centre) → K24Rotate(C24, 180*°, centre) → L24Rotate(D24, 180*°, centre) → M24Rotate(A25, 180*°, centre) → J25Rotate(B25, 180*°, centre) → K25Rotate(C25, 180*°, centre) → L25Rotate(D25, 180*°, centre) → M25Polygon(J2, K2, L2, M2) → N2, O2, P2, Q2, R2Polygon(J3, K3, L3, M3) → N3, O3, P3, Q3, R3Polygon(J4, K4, L4, M4) → N4, O4, P4, Q4, R4Polygon(J5, K5, L5, M5) → N5, O5, P5, Q5, R5Polygon(J6, K6, L6, M6) → N6, O6, P6, Q6, R6Polygon(J7, K7, L7, M7) → N7, O7, P7, Q7, R7Polygon(J8, K8, L8, M8) → N8, O8, P8, Q8, R8Polygon(J9, K9, L9, M9) → N9, O9, P9, Q9, R9Polygon(J10, K10, L10, M10) → N10, O10, P10, Q10, R10Polygon(J11, K11, L11, M11) → N11, O11, P11, Q11, R11Polygon(J12, K12, L12, M12) → N12, O12, P12, Q12, R12Polygon(J13, K13, L13, M13) → N13, O13, P13, Q13, R13Polygon(J14, K14, L14, M14) → N14, O14, P14, Q14, R14Polygon(J15, K15, L15, M15) → N15, O15, P15, Q15, R15Polygon(J16, K16, L16, M16) → N16, O16, P16, Q16, R16Polygon(J17, K17, L17, M17) → N17, O17, P17, Q17, R17Polygon(J18, K18, L18, M18) → N18, O18, P18, Q18, R18Polygon(J19, K19, L19, M19) → N19, O19, P19, Q19, R19Polygon(J20, K20, L20, M20) → N20, O20, P20, Q20, R20Polygon(J21, K21, L21, M21) → N21, O21, P21, Q21, R21Polygon(J22, K22, L22, M22) → N22, O22, P22, Q22, R22Polygon(J23, K23, L23, M23) → N23, O23, P23, Q23, R23Polygon(J24, K24, L24, M24) → N24, O24, P24, Q24, R24Polygon(J25, K25, L25, M25) → N25, O25, P25, Q25, R25Polygon((1, 1 + size), (1, 1), 4) → poly1Rotate(A1, 90*°, centre) → T1Rotate(B1, 90*°, centre) → U1Rotate(C1, 90*°, centre) → V1Rotate(D1, 90*°, centre) → W1Polygon(T1, U1, V1, W1) → X1, Y1, Z1, AA1, AB1Rotate(A1, 270*°, centre) → AD1Rotate(B1, 270*°, centre) → AE1Rotate(C1, 270*°, centre) → AF1Rotate(D1, 270*°, centre) → AG1Polygon(AD1, AE1, AF1, AG1) → AH1, AI1, AJ1, AK1, AL1Rotate(A2, 90*°, centre) → T2Rotate(B2, 90*°, centre) → U2Rotate(C2, 90*°, centre) → V2Rotate(D2, 90*°, centre) → W2Rotate(A3, 90*°, centre) → T3Rotate(B3, 90*°, centre) → U3Rotate(C3, 90*°, centre) → V3Rotate(D3, 90*°, centre) → W3Rotate(A4, 90*°, centre) → T4Rotate(B4, 90*°, centre) → U4Rotate(C4, 90*°, centre) → V4Rotate(D4, 90*°, centre) → W4Rotate(A5, 90*°, centre) → T5Rotate(B5, 90*°, centre) → U5Rotate(C5, 90*°, centre) → V5Rotate(D5, 90*°, centre) → W5Rotate(A6, 90*°, centre) → T6Rotate(B6, 90*°, centre) → U6Rotate(C6, 90*°, centre) → V6Rotate(D6, 90*°, centre) → W6Rotate(A7, 90*°, centre) → T7Rotate(B7, 90*°, centre) → U7Rotate(C7, 90*°, centre) → V7Rotate(D7, 90*°, centre) → W7Rotate(A8, 90*°, centre) → T8Rotate(B8, 90*°, centre) → U8Rotate(C8, 90*°, centre) → V8Rotate(D8, 90*°, centre) → W8Rotate(A9, 90*°, centre) → T9Rotate(B9, 90*°, centre) → U9Rotate(C9, 90*°, centre) → V9Rotate(D9, 90*°, centre) → W9Rotate(A10, 90*°, centre) → T10Rotate(B10, 90*°, centre) → U10Rotate(C10, 90*°, centre) → V10Rotate(D10, 90*°, centre) → W10Rotate(A11, 90*°, centre) → T11Rotate(B11, 90*°, centre) → U11Rotate(C11, 90*°, centre) → V11Rotate(D11, 90*°, centre) → W11Rotate(A12, 90*°, centre) → T12Rotate(B12, 90*°, centre) → U12Rotate(C12, 90*°, centre) → V12Rotate(D12, 90*°, centre) → W12Rotate(A13, 90*°, centre) → T13Rotate(B13, 90*°, centre) → U13Rotate(C13, 90*°, centre) → V13Rotate(D13, 90*°, centre) → W13Rotate(A14, 90*°, centre) → T14Rotate(B14, 90*°, centre) → U14Rotate(C14, 90*°, centre) → V14Rotate(D14, 90*°, centre) → W14Rotate(A15, 90*°, centre) → T15Rotate(B15, 90*°, centre) → U15Rotate(C15, 90*°, centre) → V15Rotate(D15, 90*°, centre) → W15Rotate(A16, 90*°, centre) → T16Rotate(B16, 90*°, centre) → U16Rotate(C16, 90*°, centre) → V16Rotate(D16, 90*°, centre) → W16Rotate(A17, 90*°, centre) → T17Rotate(B17, 90*°, centre) → U17Rotate(C17, 90*°, centre) → V17Rotate(D17, 90*°, centre) → W17Rotate(A18, 90*°, centre) → T18Rotate(B18, 90*°, centre) → U18Rotate(C18, 90*°, centre) → V18Rotate(D18, 90*°, centre) → W18Rotate(A19, 90*°, centre) → T19Rotate(B19, 90*°, centre) → U19Rotate(C19, 90*°, centre) → V19Rotate(D19, 90*°, centre) → W19Rotate(A20, 90*°, centre) → T20Rotate(B20, 90*°, centre) → U20Rotate(C20, 90*°, centre) → V20Rotate(D20, 90*°, centre) → W20Rotate(A21, 90*°, centre) → T21Rotate(B21, 90*°, centre) → U21Rotate(C21, 90*°, centre) → V21Rotate(D21, 90*°, centre) → W21Rotate(A22, 90*°, centre) → T22Rotate(B22, 90*°, centre) → U22Rotate(C22, 90*°, centre) → V22Rotate(D22, 90*°, centre) → W22Rotate(A23, 90*°, centre) → T23Rotate(B23, 90*°, centre) → U23Rotate(C23, 90*°, centre) → V23Rotate(D23, 90*°, centre) → W23Rotate(A24, 90*°, centre) → T24Rotate(B24, 90*°, centre) → U24Rotate(C24, 90*°, centre) → V24Rotate(D24, 90*°, centre) → W24Rotate(A25, 90*°, centre) → T25Rotate(B25, 90*°, centre) → U25Rotate(C25, 90*°, centre) → V25Rotate(D25, 90*°, centre) → W25Rotate(A2, 270*°, centre) → AD2Rotate(B2, 270*°, centre) → AE2Rotate(C2, 270*°, centre) → AF2Rotate(D2, 270*°, centre) → AG2Rotate(A3, 270*°, centre) → AD3Rotate(B3, 270*°, centre) → AE3Rotate(C3, 270*°, centre) → AF3Rotate(D3, 270*°, centre) → AG3Rotate(A4, 270*°, centre) → AD4Rotate(B4, 270*°, centre) → AE4Rotate(C4, 270*°, centre) → AF4Rotate(D4, 270*°, centre) → AG4Rotate(A5, 270*°, centre) → AD5Rotate(B5, 270*°, centre) → AE5Rotate(C5, 270*°, centre) → AF5Rotate(D5, 270*°, centre) → AG5Rotate(A6, 270*°, centre) → AD6Rotate(B6, 270*°, centre) → AE6Rotate(C6, 270*°, centre) → AF6Rotate(D6, 270*°, centre) → AG6Rotate(A7, 270*°, centre) → AD7Rotate(B7, 270*°, centre) → AE7Rotate(C7, 270*°, centre) → AF7Rotate(D7, 270*°, centre) → AG7Rotate(A8, 270*°, centre) → AD8Rotate(B8, 270*°, centre) → AE8Rotate(C8, 270*°, centre) → AF8Rotate(D8, 270*°, centre) → AG8Rotate(A9, 270*°, centre) → AD9Rotate(B9, 270*°, centre) → AE9Rotate(C9, 270*°, centre) → AF9Rotate(D9, 270*°, centre) → AG9Rotate(A10, 270*°, centre) → AD10Rotate(B10, 270*°, centre) → AE10Rotate(C10, 270*°, centre) → AF10Rotate(D10, 270*°, centre) → AG10Rotate(A11, 270*°, centre) → AD11Rotate(B11, 270*°, centre) → AE11Rotate(C11, 270*°, centre) → AF11Rotate(D11, 270*°, centre) → AG11Rotate(A12, 270*°, centre) → AD12Rotate(B12, 270*°, centre) → AE12Rotate(C12, 270*°, centre) → AF12Rotate(D12, 270*°, centre) → AG12Rotate(A13, 270*°, centre) → AD13Rotate(B13, 270*°, centre) → AE13Rotate(C13, 270*°, centre) → AF13Rotate(D13, 270*°, centre) → AG13Rotate(A14, 270*°, centre) → AD14Rotate(B14, 270*°, centre) → AE14Rotate(C14, 270*°, centre) → AF14Rotate(D14, 270*°, centre) → AG14Rotate(A15, 270*°, centre) → AD15Rotate(B15, 270*°, centre) → AE15Rotate(C15, 270*°, centre) → AF15Rotate(D15, 270*°, centre) → AG15Rotate(A16, 270*°, centre) → AD16Rotate(B16, 270*°, centre) → AE16Rotate(C16, 270*°, centre) → AF16Rotate(D16, 270*°, centre) → AG16Rotate(A17, 270*°, centre) → AD17Rotate(B17, 270*°, centre) → AE17Rotate(C17, 270*°, centre) → AF17Rotate(D17, 270*°, centre) → AG17Rotate(A18, 270*°, centre) → AD18Rotate(B18, 270*°, centre) → AE18Rotate(C18, 270*°, centre) → AF18Rotate(D18, 270*°, centre) → AG18Rotate(A19, 270*°, centre) → AD19Rotate(B19, 270*°, centre) → AE19Rotate(C19, 270*°, centre) → AF19Rotate(D19, 270*°, centre) → AG19Rotate(A20, 270*°, centre) → AD20Rotate(B20, 270*°, centre) → AE20Rotate(C20, 270*°, centre) → AF20Rotate(D20, 270*°, centre) → AG20Rotate(A21, 270*°, centre) → AD21Rotate(B21, 270*°, centre) → AE21Rotate(C21, 270*°, centre) → AF21Rotate(D21, 270*°, centre) → AG21Rotate(A22, 270*°, centre) → AD22Rotate(B22, 270*°, centre) → AE22Rotate(C22, 270*°, centre) → AF22Rotate(D22, 270*°, centre) → AG22Rotate(A23, 270*°, centre) → AD23Rotate(B23, 270*°, centre) → AE23Rotate(C23, 270*°, centre) → AF23Rotate(D23, 270*°, centre) → AG23Rotate(A24, 270*°, centre) → AD24Rotate(B24, 270*°, centre) → AE24Rotate(C24, 270*°, centre) → AF24Rotate(D24, 270*°, centre) → AG24Rotate(A25, 270*°, centre) → AD25Rotate(B25, 270*°, centre) → AE25Rotate(C25, 270*°, centre) → AF25Rotate(D25, 270*°, centre) → AG25Polygon(AD2, AE2, AF2, AG2) → AH2, AI2, AJ2, AK2, AL2Polygon(AD3, AE3, AF3, AG3) → AH3, AI3, AJ3, AK3, AL3Polygon(AD4, AE4, AF4, AG4) → AH4, AI4, AJ4, AK4, AL4Polygon(AD5, AE5, AF5, AG5) → AH5, AI5, AJ5, AK5, AL5Polygon(AD6, AE6, AF6, AG6) → AH6, AI6, AJ6, AK6, AL6Polygon(AD7, AE7, AF7, AG7) → AH7, AI7, AJ7, AK7, AL7Polygon(AD8, AE8, AF8, AG8) → AH8, AI8, AJ8, AK8, AL8Polygon(AD9, AE9, AF9, AG9) → AH9, AI9, AJ9, AK9, AL9Polygon(AD10, AE10, AF10, AG10) → AH10, AI10, AJ10, AK10, AL10Polygon(AD11, AE11, AF11, AG11) → AH11, AI11, AJ11, AK11, AL11Polygon(AD12, AE12, AF12, AG12) → AH12, AI12, AJ12, AK12, AL12Polygon(AD13, AE13, AF13, AG13) → AH13, AI13, AJ13, AK13, AL13Polygon(AD14, AE14, AF14, AG14) → AH14, AI14, AJ14, AK14, AL14Polygon(AD15, AE15, AF15, AG15) → AH15, AI15, AJ15, AK15, AL15Polygon(AD16, AE16, AF16, AG16) → AH16, AI16, AJ16, AK16, AL16Polygon(AD17, AE17, AF17, AG17) → AH17, AI17, AJ17, AK17, AL17Polygon(AD18, AE18, AF18, AG18) → AH18, AI18, AJ18, AK18, AL18Polygon(AD19, AE19, AF19, AG19) → AH19, AI19, AJ19, AK19, AL19Polygon(AD20, AE20, AF20, AG20) → AH20, AI20, AJ20, AK20, AL20Polygon(AD21, AE21, AF21, AG21) → AH21, AI21, AJ21, AK21, AL21Polygon(AD22, AE22, AF22, AG22) → AH22, AI22, AJ22, AK22, AL22Polygon(AD23, AE23, AF23, AG23) → AH23, AI23, AJ23, AK23, AL23Polygon(AD24, AE24, AF24, AG24) → AH24, AI24, AJ24, AK24, AL24Polygon(AD25, AE25, AF25, AG25) → AH25, AI25, AJ25, AK25, AL25Polygon(T2, U2, V2, W2) → X2, Y2, Z2, AA2, AB2Polygon(T3, U3, V3, W3) → X3, Y3, Z3, AA3, AB3Polygon(T4, U4, V4, W4) → X4, Y4, Z4, AA4, AB4Polygon(T5, U5, V5, W5) → X5, Y5, Z5, AA5, AB5Polygon(T6, U6, V6, W6) → X6, Y6, Z6, AA6, AB6Polygon(T7, U7, V7, W7) → X7, Y7, Z7, AA7, AB7Polygon(T8, U8, V8, W8) → X8, Y8, Z8, AA8, AB8Polygon(T9, U9, V9, W9) → X9, Y9, Z9, AA9, AB9Polygon(T10, U10, V10, W10) → X10, Y10, Z10, AA10, AB10Polygon(T11, U11, V11, W11) → X11, Y11, Z11, AA11, AB11Polygon(T12, U12, V12, W12) → X12, Y12, Z12, AA12, AB12Polygon(T13, U13, V13, W13) → X13, Y13, Z13, AA13, AB13Polygon(T14, U14, V14, W14) → X14, Y14, Z14, AA14, AB14Polygon(T15, U15, V15, W15) → X15, Y15, Z15, AA15, AB15Polygon(T16, U16, V16, W16) → X16, Y16, Z16, AA16, AB16Polygon(T17, U17, V17, W17) → X17, Y17, Z17, AA17, AB17Polygon(T18, U18, V18, W18) → X18, Y18, Z18, AA18, AB18Polygon(T19, U19, V19, W19) → X19, Y19, Z19, AA19, AB19Polygon(T20, U20, V20, W20) → X20, Y20, Z20, AA20, AB20Polygon(T21, U21, V21, W21) → X21, Y21, Z21, AA21, AB21Polygon(T22, U22, V22, W22) → X22, Y22, Z22, AA22, AB22Polygon(T23, U23, V23, W23) → X23, Y23, Z23, AA23, AB23Polygon(T24, U24, V24, W24) → X24, Y24, Z24, AA24, AB24Polygon(T25, U25, V25, W25) → X25, Y25, Z25, AA25, AB25
AI 绘图提示语参考
绘制多个随机多边形,每个多边形随机选择四或五条边,然后以其中一个多边形为中心,将其他多边形绕其中心旋转180度,展示旋转对称性。
以上提示语为根据原始绘图命令整理而来,仅供参考。