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Christmas Card 2：几何图形与函数作图示例

Christmas Card 2：几何图形与函数作图示例
几何画板及绘图内容加载中，请稍等……
2021-07-09 21:23
函数解析几何几何作图
所属专题 STEAM like Leonardo
本范例展示了如何通过GeoGebra构造一个包含三角形、多边形和函数的几何图形。核心数学概念包括三角形性质、函数图像与几何关系的结合。作图要点涉及使用Point、Polygon、Segment等命令创建图形对象，并利用Sequence和参数化构造函数。适合初中生或高中生学习几何与函数的基础应用，以及动手实践几何作图技能。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 5) → wielokąt1, f, g, h, i, j, C, D, E
  4. Polygon(H, I, 5) → wielokąt2, k, l, m, n_{1}, p, F, G, J
  5. Segment(C, I) → q
  6. Segment(A, I) → r
  7. Segment(D, F) → s
  8. Segment(B, F) → t
  9. Segment(E, G) → a_{1}
  10. Segment(C, G) → b
  11. Segment(A, J) → c
  12. Segment(D, J) → d
  13. Segment(B, H) → e
  14. Segment(E, H) → f_1
  15. Sequence(I + (i / n * (C - I)), i, 1, n) → l1, {(14.836377715357154, -9.666867907865745), (14.432755430714305, -9.373735815731488), (14.029133146071459, -9.080603723597232), (13.625510861428612, -8.787471631462974), (13.221888576785766, -8.494339539328719), (12.818266292142917, -8.201207447194461), (12.41464400750007, -7.908075355060205), (12.011021722857222, -7.614943262925948), (11.607399438214376, -7.321811170791692), (11.20377715357153, -7.028679078657435), (10.800154868928681, -6.735546986523179), (10.396532584285834, -6.442414894388922), (9.992910299642986, -6.149282802254666), (9.58928801500014, -5.856150710120409), (9.185665730357293, -5.5630186179861525), (8.782043445714447, -5.269886525851896), (8.3784211610716, -4.976754433717639), (7.974798876428752, -4.683622341583383), (7.571176591785904, -4.390490249449126), (7.1675543071430585, -4.097358157314869), (6.76393202250021, -3.804226065180613)}
  16. Sequence(I + (i / n * (A - I)), i, 1, n) → l2, {(15.085714285714285, -9.485714285714286), (14.931428571428572, -9.011428571428572), (14.777142857142858, -8.537142857142857), (14.622857142857143, -8.062857142857144), (14.468571428571428, -7.588571428571429), (14.314285714285715, -7.114285714285716), (14.16, -6.640000000000001), (14.005714285714285, -6.165714285714286), (13.851428571428572, -5.691428571428572), (13.697142857142858, -5.217142857142858), (13.542857142857143, -4.742857142857143), (13.388571428571428, -4.26857142857143), (13.234285714285715, -3.7942857142857145), (13.08, -3.3200000000000003), (12.925714285714285, -2.845714285714286), (12.771428571428572, -2.371428571428572), (12.617142857142857, -1.8971428571428568), (12.462857142857143, -1.4228571428571435), (12.30857142857143, -0.9485714285714284), (12.154285714285715, -0.4742857142857151), (12, 0)}
  17. Sequence(F + (i / n * (D - F)), i, 1, n) → l3, {(18.074760096237572, -0.2863772028041141), (17.671022091425694, -0.5798266963814337), (17.267284086613813, -0.8732761899587533), (16.863546081801935, -1.1667256835360729), (16.459808076990058, -1.4601751771133924), (16.05607007217818, -1.7536246706907122), (15.6523320673663, -2.0470741642680315), (15.248594062554421, -2.340523657845351), (14.844856057742543, -2.633973151422671), (14.441118052930666, -2.9274226449999903), (14.037380048118784, -3.2208721385773105), (13.633642043306907, -3.51432163215463), (13.229904038495029, -3.8077711257319495), (12.826166033683151, -4.101220619309268), (12.422428028871272, -4.394670112886589), (12.018690024059392, -4.688119606463908), (11.614952019247514, -4.981569100041228), (11.211214014435637, -5.275018593618547), (10.807476009623757, -5.568468087195867), (10.40373800481188, -5.861917580773186), (10, -6.155367074350506)}
  18. Sequence(F + (i / n * (B - F)), i, 1, n) → l4, {(17.979522000999477, 0.006735515022100458), (17.4805459009495, 0.006398739270995435), (16.98156980089953, 0.006061963519890412), (16.482593700849556, 0.005725187768785389), (15.983617600799581, 0.005388412017680366), (15.484641500749607, 0.005051636266575343), (14.985665400699634, 0.0047148605154703205), (14.48668930064966, 0.004378084764365298), (13.987713200599686, 0.004041309013260275), (13.488737100549713, 0.003704533262155252), (12.989761000499737, 0.003367757511050229), (12.490784900449764, 0.003030981759945206), (11.99180880039979, 0.002694206008840183), (11.492832700349817, 0.0023574302577351602), (10.993856600299843, 0.0020206545066301373), (10.49488050024987, 0.0016838787555251145), (9.995904400199896, 0.0013471030044200916), (9.496928300149921, 0.0010103272533150687), (8.997952200099947, 0.0006735515022100458), (8.498976100049974, 0.0003367757511050229), (8, 0)}
  19. Sequence(G + (i / n * (E - G)), i, 1, n) → l5, {(10.154098475119039, 5.6922385062279), (10.308196950238077, 5.217415277657475), (10.462295425357114, 4.742592049087048), (10.616393900476151, 4.267768820516623), (10.77049237559519, 3.792945591946197), (10.924590850714226, 3.3181223633757715), (11.078689325833265, 2.8432991348053456), (11.232787800952302, 2.36847590623492), (11.386886276071339, 1.8936526776644946), (11.540984751190377, 1.4188294490940683), (11.695083226309414, 0.9440062205236428), (11.849181701428453, 0.46918299195321733), (12.00328017654749, -0.005640236617209027), (12.157378651666527, -0.4804634651876345), (12.311477126785565, -0.95528669375806), (12.465575601904602, -1.4301099223284854), (12.619674077023639, -1.904933150898911), (12.773772552142677, -2.3797563794693364), (12.927871027261714, -2.8545796080397636), (13.081969502380751, -3.329402836610189), (13.23606797749979, -3.8042260651806146)}
  20. Sequence(G + (i / n * (C - G)), i, 1, n) → l6, {(9.845901524880965, 5.6922385062279), (9.691803049761926, 5.217415277657475), (9.53770457464289, 4.742592049087049), (9.38360609952385, 4.267768820516623), (9.229507624404814, 3.7929455919461974), (9.075409149285775, 3.318122363375772), (8.921310674166739, 2.8432991348053465), (8.7672121990477, 2.3684759062349205), (8.613113723928663, 1.8936526776644955), (8.459015248809624, 1.4188294490940692), (8.304916773690588, 0.9440062205236437), (8.150818298571549, 0.4691829919532182), (7.996719823452512, -0.005640236617208139), (7.842621348333474, -0.4804634651876327), (7.688522873214437, -0.9552866937580591), (7.534424398095399, -1.4301099223284846), (7.380325922976361, -1.904933150898911), (7.226227447857323, -2.3797563794693346), (7.072128972738286, -2.854579608039762), (6.918030497619248, -3.3294028366101873), (6.76393202250021, -3.804226065180613)}
  21. Sequence(G + (i / n * (E - G)), i, 1, n) → l7, {(10.154098475119039, 5.6922385062279), (10.308196950238077, 5.217415277657475), (10.462295425357114, 4.742592049087048), (10.616393900476151, 4.267768820516623), (10.77049237559519, 3.792945591946197), (10.924590850714226, 3.3181223633757715), (11.078689325833265, 2.8432991348053456), (11.232787800952302, 2.36847590623492), (11.386886276071339, 1.8936526776644946), (11.540984751190377, 1.4188294490940683), (11.695083226309414, 0.9440062205236428), (11.849181701428453, 0.46918299195321733), (12.00328017654749, -0.005640236617209027), (12.157378651666527, -0.4804634651876345), (12.311477126785565, -0.95528669375806), (12.465575601904602, -1.4301099223284854), (12.619674077023639, -1.904933150898911), (12.773772552142677, -2.3797563794693364), (12.927871027261714, -2.8545796080397636), (13.081969502380751, -3.329402836610189), (13.23606797749979, -3.8042260651806146)}
  22. Sequence(J + (i / n * (A - J)), i, 1, n) → l8, {(2.0204779990005255, 0.006735515022104265), (2.5194540990504994, 0.006398739270999051), (3.018430199100473, 0.006061963519893838), (3.517406299150447, 0.005725187768788624), (4.01638239920042, 0.005388412017683412), (4.515358499250394, 0.005051636266578199), (5.014334599300367, 0.004714860515472985), (5.513310699350342, 0.004378084764367771), (6.012286799400315, 0.004041309013262559), (6.511262899450289, 0.0037045332621573456), (7.010238999500263, 0.003367757511052132), (7.509215099550236, 0.003030981759946919), (8.00819119960021, 0.0026942060088417054), (8.507167299650185, 0.0023574302577364925), (9.006143399700157, 0.002020654506631279), (9.50511949975013, 0.001683878755526066), (10.004095599800106, 0.0013471030044208531), (10.503071699850079, 0.0010103272533156403), (11.002047799900053, 0.0006735515022104266), (11.501023899950026, 0.0003367757511052137), (12, 0)}
  23. Sequence(J + (i / n * (D - J)), i, 1, n) → l9, {(1.9252399037624304, -0.2863772028041103), (2.3289779085743088, -0.57982669638143), (2.7327159133861874, -0.8732761899587498), (3.1364539181980655, -1.1667256835360695), (3.540191923009944, -1.4601751771133893), (3.9439299278218227, -1.753624670690709), (4.347667932633701, -2.047074164268029), (4.751405937445579, -2.3405236578453485), (5.1551439422574585, -2.6339731514226683), (5.558881947069336, -2.927422644999988), (5.962619951881216, -3.2208721385773083), (6.3663579566930935, -3.5143216321546276), (6.770095961504972, -3.8077711257319478), (7.173833966316851, -4.101220619309267), (7.577571971128729, -4.394670112886587), (7.981309975940607, -4.688119606463907), (8.385047980752486, -4.981569100041227), (8.788785985564363, -5.275018593618546), (9.192523990376243, -5.568468087195866), (9.59626199518812, -5.861917580773186), (10, -6.155367074350506)}
  24. Sequence(H + (i / n * (B - H)), i, 1, n) → l10, {(4.914285714285714, -9.485714285714286), (5.0685714285714285, -9.011428571428572), (5.222857142857142, -8.537142857142857), (5.377142857142857, -8.062857142857144), (5.531428571428571, -7.588571428571429), (5.685714285714285, -7.114285714285716), (5.84, -6.640000000000001), (5.994285714285714, -6.165714285714286), (6.148571428571429, -5.691428571428572), (6.3028571428571425, -5.217142857142858), (6.457142857142857, -4.742857142857143), (6.611428571428571, -4.26857142857143), (6.765714285714285, -3.7942857142857145), (6.92, -3.3200000000000003), (7.074285714285715, -2.845714285714286), (7.228571428571428, -2.371428571428572), (7.382857142857143, -1.8971428571428568), (7.537142857142857, -1.4228571428571435), (7.691428571428571, -0.9485714285714284), (7.845714285714285, -0.4742857142857151), (8, 0)}
  25. Sequence(H + (i / n * (E - H)), i, 1, n) → l11, {(5.163622284642847, -9.666867907865745), (5.567244569285694, -9.373735815731488), (5.970866853928541, -9.080603723597232), (6.374489138571388, -8.787471631462974), (6.778111423214235, -8.494339539328719), (7.181733707857083, -8.201207447194463), (7.585355992499929, -7.908075355060205), (7.988978277142777, -7.61494326292595), (8.392600561785624, -7.321811170791692), (8.79622284642847, -7.0286790786574365), (9.199845131071319, -6.735546986523179), (9.603467415714166, -6.442414894388923), (10.007089700357014, -6.149282802254666), (10.41071198499986, -5.85615071012041), (10.814334269642707, -5.563018617986153), (11.217956554285553, -5.269886525851898), (11.6215788389284, -4.97675443371764), (12.025201123571248, -4.683622341583384), (12.428823408214097, -4.390490249449128), (12.832445692856941, -4.097358157314871), (13.23606797749979, -3.8042260651806146)}
  26. Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l12, {9.575864707060978, 8.688817677085293, 7.8162844890063665, 6.963722901601629, 6.1394586843840155, 5.356570924946615, 4.636068815329039, 4.011707728225869, 3.5348050275376943, 3.2705163382044398, 3.2707935587524366, 3.535574456753598, 4.01283762744998, 4.637437628590395, 5.358094114852, 6.141082980868683, 6.965415325878003, 7.818024302584074, 8.69059147465649, 9.57766355708461, NaN}
  27. Sequence(Segment[Element[l3, i], Element[l4, n - i]], i, 1, n) → l13, {9.580075367508414, 8.692475014494674, 7.819386546424963, 6.9662684632114305, 6.141448761894992, 5.358012294009208, 4.636982299389437, 4.012146582725139, 3.534889222029449, 3.2704693359045307, 3.270917882871498, 3.536134071300212, 4.013974439163354, 4.639196447729736, 5.3604759879440325, 6.144075862841034, 6.969005657458741, 7.822200314065279, 8.695343691157865, 9.582984520267145, NaN}
  28. Sequence(Segment[Element[l5, i], Element[l6, n - i]], i, 1, n) → l14, {9.58447434520042, 8.696507194829538, 7.823041805637955, 6.96953266603413, 6.144301820401952, 5.360425442499227, 4.638915150777352, 4.0135474850499335, 3.5357106556546682, 3.2707175135418867, 3.270717513541887, 3.5357106556546687, 4.013547485049934, 4.638915150777352, 5.360425442499228, 6.144301820401952, 6.969532666034128, 7.823041805637957, 8.69650719482954, 9.58447434520042, NaN}
  29. Sequence(Segment[Element[l8, i], Element[l9, n - i]], i, 1, n) → l15, {9.582984520267145, 8.695343691157866, 7.822200314065279, 6.969005657458741, 6.144075862841034, 5.360475987944033, 4.639196447729736, 4.013974439163355, 3.536134071300212, 3.2709178828714984, 3.2704693359045294, 3.5348892220294474, 4.012146582725138, 4.6369822993894365, 5.358012294009204, 6.141448761894989, 6.966268463211431, 7.819386546424961, 8.69247501449467, 9.580075367508412, NaN}
  30. Sequence(Segment[Element[l10, i], Element[l11, n - i]], i, 1, n) → l16, {9.57766355708461, 8.690591474656488, 7.818024302584074, 6.965415325878002, 6.141082980868682, 5.358094114852, 4.637437628590395, 4.012837627449981, 3.535574456753597, 3.2707935587524366, 3.2705163382044415, 3.5348050275376943, 4.01170772822587, 4.636068815329039, 5.356570924946617, 6.1394586843840155, 6.963722901601629, 7.8162844890063665, 8.688817677085293, 9.575864707060978, NaN}

AI 绘图提示语参考

在坐标平面上绘制一个由两个正五边形组成的几何图形，两个五边形分别位于上下两侧，并通过多条线段连接对应顶点，形成对称的网状结构。在五边形的各边之间，用一系列平行线段填充，这些线段从一条边均匀分布到另一条边，构成密集的曲线网格。整体图形类似一个装饰性的星形或雪花图案，包含三角形、多边形和函数曲线的几何关系，适合用于数学教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。