圣诞贺卡3：几何对称与算术平均的节日图案

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Point(c) → C
3. Point(c) → D
4. Point(c) → E
5. Point(c) → F
6. Point(c) → G
7. Point(c) → H
8. Point(c) → I
9. Segment(A, B) → f
10. Sequence(A + (i / n * (B - A)), i, 1, n) → l1, {(-6.3014, -2.452913432835821), (-6.3014, -2.278226865671642), (-6.3014, -2.103540298507463), (-6.3014, -1.9288537313432839), (-6.3014, -1.7541671641791048), (-6.3014, -1.5794805970149255), (-6.3014, -1.4047940298507464), (-6.3014, -1.2301074626865673), (-6.3014, -1.055420895522388), (-6.3014, -0.8807343283582092), (-6.3014, -0.7060477611940299), (-6.3014, -0.5313611940298508), (-6.3014, -0.35667462686567175), (-6.3014, -0.18198805970149268), (-6.3014, -0.007301492537313159), (-6.3014, 0.16738507462686547), (-6.3014, 0.342071641791045), (-6.3014, 0.5167582089552241), (-6.3014, 0.6914447761194027), (-6.3014, 0.8661313432835818), (-6.3014, 1.0408179104477613), (-6.3014, 1.2155044776119404), (-6.3014, 1.3901910447761194), (-6.3014, 1.5648776119402985), (-6.3014, 1.7395641791044776), (-6.3014, 1.9142507462686567), (-6.3014, 2.0889373134328357), (-6.3014, 2.263623880597015), (-6.3014, 2.438310447761194), (-6.3014, 2.612997014925374), (-6.3014, 2.787683582089552), (-6.3014, 2.962370149253731), (-6.3014, 3.13705671641791)}
11. Segment(A, C) → g
12. Sequence(A + (i / n * (C - A)), i, 1, n) → l2, {(-6.175521715248428, -2.5064800009263233), (-6.049643430496857, -2.385360001852646), (-5.923765145745286, -2.264240002778969), (-5.797886860993714, -2.1431200037052918), (-5.672008576242143, -2.022000004631615), (-5.546130291490571, -1.9008800055579376), (-5.420252006738999, -1.7797600064842607), (-5.294373721987428, -1.6586400074105834), (-5.1684954372358565, -1.5375200083369065), (-5.042617152484285, -1.4164000092632294), (-4.916738867732713, -1.2952800101895523), (-4.790860582981142, -1.1741600111158752), (-4.66498229822957, -1.053040012042198), (-4.539104013477999, -0.931920012968521), (-4.413225728726427, -0.8108000138948439), (-4.287347443974856, -0.6896800148211668), (-4.161469159223284, -0.5685600157474897), (-4.035590874471713, -0.44744001667381283), (-3.9097125897201415, -0.3263200176001355), (-3.78383430496857, -0.20520001852645864), (-3.657956020216998, -0.08408001945278132), (-3.5320777354654265, 0.03703997962089556), (-3.406199450713855, 0.15815997869457243), (-3.2803211659622837, 0.27927997776824975), (-3.154442881210712, 0.4003999768419271), (-3.0285645964591406, 0.521519975915604), (-2.902686311707569, 0.6426399749892808), (-2.776808026955998, 0.7637599740629581), (-2.6509297422044265, 0.884879973136635), (-2.525051457452854, 1.0059999722103123), (-2.399173172701283, 1.1271199712839892), (-2.273294887949712, 1.2482399703576665), (-2.14741660319814, 1.3693599694313434)}
13. Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l3, {5.644940391411102, 5.353652878114178, 5.066018159313959, 4.782695325447797, 4.50449807370638, 4.232437235257201, 3.9677752883904116, 3.7120951310997494, 3.4673842475142806, 3.2361320294278384, 3.0214303298719565, 2.827052475468831, 2.6574619271480797, 2.5176726999019508, 2.4128699691082476, 2.347743786323403, 2.3256298112594624, 2.3477437863234036, 2.412869969108247, 2.5176726999019508, 2.6574619271480797, 2.8270524754688307, 3.021430329871957, 3.2361320294278384, 3.46738424751428, 3.712095131099749, 3.967775288390411, 4.2324372352572, 4.50449807370638, 4.782695325447798, 5.066018159313958, 5.353652878114178, 5.644940391411101}
14. Segment(A, D) → h
15. Sequence(A + (i / n * (D - A)), i, 1, n) → l4, {(-6.126718847878435, -2.6262245578573107), (-5.95203769575687, -2.624849115714621), (-5.777356543635305, -2.6234736735719317), (-5.60267539151374, -2.6220982314292423), (-5.4279942393921745, -2.620722789286553), (-5.25331308727061, -2.6193473471438633), (-5.078631935149044, -2.617971905001174), (-4.903950783027479, -2.6165964628584844), (-4.729269630905915, -2.615221020715795), (-4.554588478784349, -2.6138455785731054), (-4.379907326662784, -2.612470136430416), (-4.2052261745412185, -2.6110946942877264), (-4.030545022419654, -2.609719252145037), (-3.8558638702980885, -2.6083438100023475), (-3.6811827181765233, -2.606968367859658), (-3.5065015660549586, -2.6055929257169685), (-3.3318204139333933, -2.604217483574279), (-3.157139261811828, -2.6028420414315896), (-2.9824581096902634, -2.6014665992889), (-2.807776957568698, -2.6000911571462106), (-2.6330958054471325, -2.598715715003521), (-2.4584146533255677, -2.5973402728608317), (-2.2837335012040025, -2.595964830718142), (-2.1090523490824378, -2.5945893885754527), (-1.9343711969608721, -2.5932139464327633), (-1.7596900448393074, -2.591838504290074), (-1.5850088927177426, -2.5904630621473843), (-1.410327740596177, -2.589087620004695), (-1.2356465884746122, -2.5877121778620054), (-1.0609654363530465, -2.586336735719316), (-0.8862842842314818, -2.5849612935766264), (-0.711603132109917, -2.583585851433937), (-0.5369219799883513, -2.582210409291248)}
16. Sequence(Segment[Element[l2, i], Element[l4, n - i]], i, 1, n) → l5, {5.639108268975346, 5.341719546610919, 5.047680217336353, 4.757611339186605, 4.472285539793912, 4.192671279812797, 3.919990967860639, 3.6557965113057787, 3.402065445059307, 3.1613181853907464, 2.936749608414459, 2.732351747522141, 2.5529739713276935, 2.4042230222653367, 2.29206954513366, 2.2220619872299587, 2.1982307355871593, 2.222061987229959, 2.29206954513366, 2.4042230222653367, 2.5529739713276935, 2.7323517475221415, 2.936749608414459, 3.161318185390747, 3.402065445059308, 3.6557965113057787, 3.9199909678606404, 4.192671279812798, 4.472285539793912, 4.757611339186606, 5.047680217336353, 5.341719546610919, 5.639108268975347}
17. Segment(A, E) → i
18. Sequence(A + (i / n * (E - A)), i, 1, n) → l6, {(-6.174489544446484, -2.747638048213074), (-6.047579088892967, -2.867676096426147), (-5.92066863333945, -2.9877141446392206), (-5.793758177785934, -3.1077521928522938), (-5.666847722232417, -3.2277902410653674), (-5.5399372666789, -3.347828289278441), (-5.413026811125383, -3.467866337491514), (-5.286116355571867, -3.5879043857045874), (-5.1592059000183506, -3.707942433917661), (-5.032295444464834, -3.8279804821307346), (-4.905384988911317, -3.9480185303438082), (-4.7784745333578, -4.068056578556881), (-4.6515640778042835, -4.188094626769955), (-4.524653622250767, -4.308132674983028), (-4.39774316669725, -4.428170723196102), (-4.270832711143734, -4.5482087714091755), (-4.143922255590217, -4.668246819622249), (-4.0170118000367, -4.788284867835322), (-3.890101344483184, -4.908322916048395), (-3.7631908889296675, -5.028360964261468), (-3.6362804333761503, -5.148399012474543), (-3.509369977822634, -5.268437060687615), (-3.382459522269117, -5.388475108900689), (-3.2555490667156004, -5.508513157113763), (-3.1286386111620836, -5.628551205326836), (-3.001728155608567, -5.74858925353991), (-2.8748177000550506, -5.8686273017529835), (-2.747907244501534, -5.988665349966056), (-2.6209967889480175, -6.108703398179129), (-2.4940863333945003, -6.2287414463922035), (-2.367175877840984, -6.348779494605276), (-2.240265422287467, -6.46881754281835), (-2.113354966733951, -6.5888555910314235)}
19. Sequence(Segment[Element[l4, i], Element[l6, n - i]], i, 1, n) → l7, {5.639994179744307, 5.343533164364803, 5.050468852847458, 4.761428484425344, 4.477191465060505, 4.1987334091512825, 3.9272837548660258, 3.6644003281771678, 3.412063666295544, 3.1727911662071855, 2.9497636735286825, 2.7469408983040413, 2.5691125883620436, 2.4217909299491818, 2.3108179826387993, 2.241598718144816, 2.2180456490543716, 2.2415987181448163, 2.3108179826387985, 2.4217909299491827, 2.5691125883620427, 2.746940898304041, 2.949763673528682, 3.172791166207185, 3.412063666295543, 3.6644003281771664, 3.927283754866023, 4.1987334091512825, 4.477191465060503, 4.761428484425342, 5.050468852847458, 5.3435331643648025, 5.639994179744306}
20. Segment(A, F) → j
21. Sequence(A + (i / n * (F - A)), i, 1, n) → l8, {(-6.3037227543085335, -2.8022711240017295), (-6.306045508617068, -2.9769422480034584), (-6.308368262925601, -3.1516133720051878), (-6.310691017234134, -3.3262844960069167), (-6.313013771542669, -3.500955620008646), (-6.315336525851202, -3.6756267440103754), (-6.317659280159736, -3.8502978680121043), (-6.31998203446827, -4.024968992013834), (-6.322304788776803, -4.199640116015563), (-6.324627543085337, -4.374311240017292), (-6.3269502973938705, -4.548982364019022), (-6.329273051702404, -4.72365348802075), (-6.331595806010938, -4.8983246120224795), (-6.333918560319471, -5.072995736024209), (-6.336241314628005, -5.247666860025938), (-6.338564068936539, -5.422337984027667), (-6.340886823245072, -5.597009108029397), (-6.343209577553606, -5.771680232031125), (-6.34553233186214, -5.946351356032855), (-6.347855086170673, -6.121022480034584), (-6.3501778404792075, -6.295693604036313), (-6.352500594787741, -6.470364728038042), (-6.354823349096274, -6.645035852039771), (-6.3571461034048085, -6.8197069760415), (-6.359468857713342, -6.99437810004323), (-6.361791612021875, -7.169049224044959), (-6.364114366330409, -7.343720348046688), (-6.366437120638943, -7.5183914720484175), (-6.368759874947476, -7.693062596050146), (-6.37108262925601, -7.867733720051876), (-6.373405383564544, -8.042404844053605), (-6.375728137873077, -8.217075968055333), (-6.378050892181611, -8.391747092057063)}
22. Sequence(Segment[Element[l6, i], Element[l8, n - i]], i, 1, n) → l9, {5.6477786891036414, 5.359455269421782, 5.074925480413547, 4.794864717752368, 4.520103745968714, 4.2516701741871294, 3.990840995179148, 3.7392078854365236, 3.498755572370974, 3.2719499817175213, 3.061825271550244, 2.872045000887739, 2.70689160546241, 2.571115132252843, 2.469565764634411, 2.406580206722229, 2.3852154409818342, 2.406580206722231, 2.46956576463441, 2.571115132252843, 2.7068916054624097, 2.8720450008877383, 3.061825271550244, 3.271949981717522, 3.4987555723709742, 3.7392078854365236, 3.99084099517915, 4.251670174187129, 4.520103745968714, 4.794864717752367, 5.074925480413545, 5.359455269421783, 5.6477786891036414}
23. Segment(A, G) → k
24. Sequence(A + (i / n * (G - A)), i, 1, n) → l10, {(-6.429984140984296, -2.7458434583177267), (-6.558568281968592, -2.8640869166354537), (-6.687152422952888, -2.98233037495318), (-6.815736563937183, -3.1005738332709067), (-6.94432070492148, -3.2188172915886337), (-7.072904845905775, -3.3370607499063603), (-7.201488986890071, -3.455304208224087), (-7.330073127874368, -3.5735476665418138), (-7.458657268858663, -3.6917911248595403), (-7.587241409842959, -3.8100345831772673), (-7.715825550827255, -3.928278041494994), (-7.844409691811551, -4.04652149981272), (-7.972993832795847, -4.164764958130447), (-8.101577973780142, -4.283008416448174), (-8.230162114764438, -4.401251874765901), (-8.358746255748734, -4.519495333083627), (-8.48733039673303, -4.637738791401354), (-8.615914537717327, -4.7559822497190805), (-8.744498678701621, -4.874225708036807), (-8.873082819685917, -4.9924691663545335), (-9.001666960670214, -5.110712624672261), (-9.13025110165451, -5.2289560829899875), (-9.258835242638806, -5.347199541307714), (-9.3874193836231, -5.465442999625441), (-9.516003524607399, -5.583686457943168), (-9.644587665591693, -5.7019299162608945), (-9.77317180657599, -5.820173374578621), (-9.901755947560286, -5.938416832896348), (-10.03034008854458, -6.056660291214074), (-10.158924229528877, -6.174903749531801), (-10.287508370513173, -6.293147207849527), (-10.41609251149747, -6.411390666167254), (-10.544676652481765, -6.52963412448498)}
25. Sequence(Segment[Element[l8, i], Element[l10, n - i]], i, 1, n) → l11, {5.646142479941703, 5.356110744086045, 5.069791991548261, 4.7878523899302685, 4.511113090302242, 4.240592323576118, 3.977559092155681, 3.7236004812478387, 3.4807033616568264, 3.251347778274461, 3.0386016511337295, 2.8461919732857357, 2.6785049260475216, 2.540440840576044, 2.437039561766237, 2.3728369354639622, 2.351046480725428, 2.3728369354639622, 2.437039561766237, 2.540440840576044, 2.6785049260475238, 2.846191973285736, 3.03860165113373, 3.2513477782744626, 3.480703361656826, 3.723600481247839, 3.977559092155682, 4.240592323576119, 4.511113090302244, 4.78785238993027, 5.069791991548262, 5.356110744086044, 5.6461424799417035}
26. Segment(A, H) → l
27. Sequence(A + (i / n * (H - A)), i, 1, n) → l12, {(-6.476076890042206, -2.6294387041057075), (-6.650753780084412, -2.631277408211415), (-6.825430670126618, -2.6331161123171225), (-7.000107560168824, -2.6349548164228302), (-7.17478445021103, -2.6367935205285375), (-7.349461340253236, -2.638632224634245), (-7.524138230295442, -2.6404709287399526), (-7.698815120337647, -2.64230963284566), (-7.873492010379854, -2.644148336951367), (-8.04816890042206, -2.645987041057075), (-8.222845790464266, -2.6478257451627822), (-8.397522680506471, -2.64966444926849), (-8.572199570548678, -2.6515031533741973), (-8.746876460590883, -2.6533418574799046), (-8.92155335063309, -2.6551805615856123), (-9.096230240675295, -2.6570192656913196), (-9.270907130717502, -2.6588579697970274), (-9.445584020759707, -2.6606966739027347), (-9.620260910801914, -2.662535378008442), (-9.794937800844119, -2.6643740821141497), (-9.969614690886326, -2.666212786219857), (-10.144291580928531, -2.6680514903255648), (-10.318968470970738, -2.669890194431272), (-10.493645361012943, -2.6717288985369794), (-10.668322251055148, -2.673567602642687), (-10.842999141097355, -2.6754063067483944), (-11.017676031139562, -2.6772450108541017), (-11.192352921181767, -2.6790837149598095), (-11.367029811223972, -2.6809224190655168), (-11.541706701266179, -2.6827611231712245), (-11.716383591308386, -2.684599827276932), (-11.89106048135059, -2.686438531382639), (-12.065737371392796, -2.688277235488347)}
28. Sequence(Segment[Element[l10, i], Element[l12, n - i]], i, 1, n) → l13, {5.636047226919828, 5.335450496935829, 5.038036286468966, 4.744403144721819, 4.45529872543443, 4.171664682523288, 3.8946963516184017, 3.6259215485928986, 3.367302843394704, 3.121365688134104, 2.8913479618217544, 2.681349710676287, 2.4964281409445586, 2.342529532833918, 2.226097418991669, 2.15321823855055, 2.1283706923736725, 2.153218238550549, 2.226097418991668, 2.342529532833917, 2.496428140944559, 2.681349710676287, 2.8913479618217526, 3.121365688134104, 3.3673028433947056, 3.6259215485928995, 3.8946963516184003, 4.1716646825232875, 4.455298725434429, 4.744403144721818, 5.038036286468964, 5.33545049693583, 5.636047226919829}
29. Segment(A, I) → m
30. Sequence(A + (i / n * (I - A)), i, 1, n) → l14, {(-6.42605417550702, -2.50522053572486), (-6.55070835101404, -2.38284107144972), (-6.67536252652106, -2.26046160717458), (-6.80001670202808, -2.1380821428994397), (-6.9246708775351005, -2.015702678624299), (-7.0493250530421205, -1.893323214349159), (-7.17397922854914, -1.7709437500740188), (-7.29863340405616, -1.6485642857988787), (-7.42328757956318, -1.5261848215237386), (-7.5479417550702, -1.4038053572485985), (-7.67259593057722, -1.281425892973458), (-7.79725010608424, -1.159046428698318), (-7.92190428159126, -1.0366669644231776), (-8.04655845709828, -0.9142875001480377), (-8.1712126326053, -0.7919080358728974), (-8.29586680811232, -0.6695285715977572), (-8.42052098361934, -0.5471491073226171), (-8.54517515912636, -0.424769643047477), (-8.66982933463338, -0.30239017877233687), (-8.7944835101404, -0.18001071449719674), (-8.91913768564742, -0.057631250222056174), (-9.04379186115444, 0.06474821405308395), (-9.16844603666146, 0.18712767832822408), (-9.293100212168481, 0.3095071426033642), (-9.417754387675501, 0.4318866068785048), (-9.542408563182521, 0.5542660711536449), (-9.667062738689541, 0.676645535428785), (-9.79171691419656, 0.7990249997039247), (-9.916371089703581, 0.9214044639790648), (-10.041025265210601, 1.0437839282542054), (-10.165679440717621, 1.1661633925293455), (-10.29033361622464, 1.2885428568044857), (-10.414987791731662, 1.4109223210796262)}
31. Sequence(Segment[Element[l12, i], Element[l14, n - i]], i, 1, n) → l15, {5.642653303658193, 5.348974882504858, 5.0588325338343765, 4.772871173667326, 4.491889379626131, 4.216882673314689, 3.949099528441313, 3.690112872785772, 3.4419089566101615, 3.206992335603151, 2.9884980741120737, 2.790286716568016, 2.6169710555660295, 2.4737892743754384, 2.3662179877791605, 2.2992607683110853, 2.2765041003761497, 2.2992607683110853, 2.3662179877791614, 2.4737892743754384, 2.61697105556603, 2.790286716568015, 2.9884980741120746, 3.20699233560315, 3.4419089566101593, 3.6901128727857717, 3.949099528441313, 4.216882673314689, 4.491889379626128, 4.772871173667325, 5.0588325338343765, 5.348974882504856, 5.642653303658191}
32. Sequence(Segment[Element[l14, i], Element[l1, n - i]], i, 1, n) → l16, {5.643654069263912, 5.351022112439773, 5.061977659288176, 4.77717194367742, 4.4974103122572275, 4.223695187291514, 3.957281432311104, 3.699746669015573, 3.4530780871973232, 3.2197740477688335, 3.002951105513035, 2.8064318175453864, 2.634763278166205, 2.4930842942885096, 2.386741470267743, 2.320597805389056, 2.298126907694626, 2.320597805389056, 2.3867414702677436, 2.49308429428851, 2.634763278166205, 2.8064318175453873, 3.002951105513035, 3.2197740477688344, 3.4530780871973237, 3.6997466690155743, 3.9572814323111043, 4.223695187291512, 4.4974103122572275, 4.77717194367742, 5.0619776592881776, 5.351022112439773, 5.6436540692639126}