积极 AI Logo 积极 AI

圣诞贺卡8

圣诞贺卡8
几何画板及绘图内容加载中，请稍等……
2021-09-13 03:57
函数三角函数解析几何
所属专题 STEAM like Leonardo
这是一个展示圣诞贺卡图案的GeoGebra范例。它涉及到了对数、圆、余弦函数和微积分等核心数学概念。通过使用Segment, Sequence, Point, Intersect等命令，可以构造出复杂的几何图形。适合高中数学教学和学习使用。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Sequence(A + (i / n * (B - A)), i, 1, n) → l1, {(3.885, 4.886428571428572), (3.77, 4.772857142857143), (3.6550000000000002, 4.659285714285715), (3.54, 4.545714285714285), (3.425, 4.432142857142857), (3.31, 4.3185714285714285), (3.1950000000000003, 4.205), (3.08, 4.091428571428572), (2.965, 3.977857142857143), (2.85, 3.8642857142857143), (2.7350000000000003, 3.750714285714286), (2.62, 3.637142857142857), (2.505, 3.5235714285714286), (2.39, 3.41), (2.2750000000000004, 3.2964285714285717), (2.16, 3.1828571428571433), (2.0450000000000004, 3.069285714285715), (1.9300000000000002, 2.955714285714286), (1.815, 2.842142857142857), (1.7000000000000002, 2.7285714285714286), (1.585, 2.615), (1.4700000000000002, 2.501428571428572), (1.3550000000000004, 2.3878571428571433), (1.2400000000000002, 2.2742857142857145), (1.125, 2.160714285714286), (1.0100000000000002, 2.047142857142857), (0.895, 1.9335714285714287), (0.7800000000000002, 1.8200000000000003)}
  4. Sequence(A + (i / n * (C - A)), i, 1, n) → l2, {(4.117857142857143, 4.883571428571429), (4.235714285714286, 4.767142857142857), (4.353571428571429, 4.650714285714286), (4.4714285714285715, 4.534285714285715), (4.589285714285714, 4.417857142857143), (4.707142857142857, 4.301428571428572), (4.825, 4.1850000000000005), (4.942857142857143, 4.0685714285714285), (5.060714285714286, 3.9521428571428574), (5.178571428571429, 3.835714285714286), (5.296428571428571, 3.7192857142857143), (5.414285714285715, 3.602857142857143), (5.532142857142857, 3.486428571428571), (5.65, 3.37), (5.767857142857142, 3.253571428571429), (5.885714285714285, 3.1371428571428575), (6.003571428571428, 3.020714285714286), (6.121428571428572, 2.9042857142857144), (6.239285714285714, 2.787857142857143), (6.357142857142858, 2.6714285714285717), (6.475, 2.555), (6.5928571428571425, 2.4385714285714286), (6.710714285714285, 2.3221428571428575), (6.828571428571428, 2.205714285714286), (6.946428571428571, 2.0892857142857144), (7.064285714285714, 1.9728571428571429), (7.182142857142857, 1.8564285714285718), (7.3, 1.7400000000000002)}
  5. Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l3, {4.477951654541188, 4.323461387285301, 4.175931278267917, 4.03612463147712, 3.904871107648361, 3.7830610648531913, 3.6716345134013535, 3.5715634260254223, 3.483826479429696, 3.409376027656555, 3.3490982642606153, 3.3037690288393895, 3.2740092752913625, 3.2602453895374204, 3.262679817548257, 3.2812765062097533, 3.3157635252083395, 3.3656524369772067, 3.4302713047935147, 3.50880641372242, 3.6003472054789385, 3.7039295184372802, 3.818573566350745, 3.9433146732469755, 4.077226197966916, 4.2194351106589165, 4.369131282447954, NaN}
  6. Segment(D, E) → h
  7. Segment(D, F) → i
  8. Sequence(D + (i / n * (E - D)), i, 1, n) → l4, {(3.862857142857143, 3.2035714285714283), (3.725714285714286, 3.087142857142857), (3.5885714285714285, 2.9707142857142856), (3.4514285714285715, 2.854285714285714), (3.314285714285714, 2.737857142857143), (3.177142857142857, 2.6214285714285714), (3.04, 2.505), (2.902857142857143, 2.388571428571429), (2.7657142857142856, 2.272142857142857), (2.6285714285714286, 2.1557142857142857), (2.4914285714285715, 2.039285714285714), (2.3542857142857145, 1.9228571428571428), (2.217142857142857, 1.8064285714285713), (2.08, 1.69), (1.942857142857143, 1.5735714285714286), (1.805714285714286, 1.4571428571428573), (1.668571428571429, 1.3407142857142857), (1.5314285714285711, 1.2242857142857142), (1.3942857142857141, 1.1078571428571427), (1.2571428571428571, 0.9914285714285715), (1.12, 0.875), (0.9828571428571431, 0.7585714285714285), (0.8457142857142861, 0.6421428571428573), (0.7085714285714291, 0.5257142857142858), (0.5714285714285712, 0.40928571428571425), (0.43428571428571416, 0.2928571428571427), (0.29714285714285715, 0.1764285714285716), (0.16000000000000014, 0.06000000000000005)}
  9. Sequence(D + (i / n * (F - D)), i, 1, n) → l5, {(4.150714285714286, 3.209285714285714), (4.301428571428572, 3.0985714285714283), (4.452142857142857, 2.987857142857143), (4.602857142857143, 2.8771428571428572), (4.753571428571429, 2.7664285714285715), (4.904285714285715, 2.6557142857142857), (5.055, 2.545), (5.2057142857142855, 2.434285714285714), (5.356428571428571, 2.3235714285714284), (5.507142857142857, 2.2128571428571426), (5.657857142857143, 2.102142857142857), (5.808571428571429, 1.9914285714285715), (5.9592857142857145, 1.8807142857142856), (6.11, 1.77), (6.260714285714286, 1.6592857142857145), (6.411428571428571, 1.5485714285714287), (6.562142857142858, 1.4378571428571432), (6.7128571428571435, 1.327142857142857), (6.863571428571429, 1.2164285714285712), (7.014285714285714, 1.1057142857142859), (7.165000000000001, 0.9950000000000001), (7.315714285714286, 0.8842857142857143), (7.466428571428572, 0.773571428571429), (7.617142857142857, 0.6628571428571433), (7.767857142857144, 0.552142857142857), (7.918571428571429, 0.4414285714285713), (8.069285714285716, 0.33071428571428596), (8.22, 0.2200000000000002)}
  10. Sequence(Segment[Element[l4, i], Element[l5, n - i]], i, 1, n) → l6, {5.0938540899593825, 4.9578074894090856, 4.82865580019271, 4.706966612785514, 4.59333306798771, 4.488367049998273, 4.392689950360713, 4.306920866110587, 4.231662299419289, 4.167483702207276, 4.11490353744155, 4.074370866671771, 4.046247757906991, 4.030793966453755, 4.0281553103227825, 4.038356909760731, 4.0613020054647295, 4.096776482921714, 4.144458619035538, 4.203933046710484, 4.274707592338919, 4.356231520617849, 4.447913808168719, 4.549140309005692, 4.659288999363727, 4.777742828011178, 4.903899999396565, NaN}
  11. Segment(G, H) → j
  12. Segment(G, I) → k
  13. Sequence(G + (i / n * (H - G)), i, 1, n) → l7, {(3.9457142857142853, 1.54), (3.791428571428571, 1.42), (3.637142857142857, 1.2999999999999998), (3.4828571428571427, 1.18), (3.3285714285714283, 1.06), (3.1742857142857144, 0.94), (3.0199999999999996, 0.82), (2.8657142857142857, 0.7), (2.711428571428571, 0.5799999999999998), (2.557142857142857, 0.45999999999999996), (2.402857142857143, 0.3400000000000001), (2.2485714285714287, 0.21999999999999997), (2.0942857142857143, 0.09999999999999987), (1.94, -0.020000000000000018), (1.7857142857142856, -0.1399999999999999), (1.6314285714285717, -0.26), (1.4771428571428573, -0.37999999999999967), (1.3228571428571425, -0.5000000000000002), (1.1685714285714286, -0.6199999999999999), (1.0142857142857142, -0.74), (0.8600000000000003, -0.8600000000000001), (0.705714285714286, -0.9799999999999998), (0.5514285714285716, -1.0999999999999999), (0.3971428571428577, -1.22), (0.24285714285714288, -1.34), (0.08857142857142897, -1.4600000000000002), (-0.06571428571428584, -1.5799999999999998), (-0.21999999999999975, -1.7)}
  14. Sequence(G + (i / n * (I - G)), i, 1, n) → l8, {(4.268571428571429, 1.5457142857142856), (4.437142857142857, 1.4314285714285713), (4.605714285714285, 1.3171428571428572), (4.774285714285714, 1.2028571428571428), (4.942857142857143, 1.0885714285714285), (5.111428571428571, 0.9742857142857142), (5.279999999999999, 0.8599999999999999), (5.448571428571428, 0.7457142857142857), (5.617142857142857, 0.6314285714285712), (5.785714285714286, 0.5171428571428569), (5.954285714285714, 0.4028571428571428), (6.122857142857143, 0.2885714285714285), (6.291428571428572, 0.17428571428571416), (6.46, 0.05999999999999983), (6.628571428571428, -0.05428571428571449), (6.797142857142857, -0.1685714285714286), (6.965714285714285, -0.2828571428571429), (7.134285714285715, -0.39714285714285746), (7.3028571428571425, -0.5114285714285718), (7.4714285714285715, -0.6257142857142861), (7.640000000000001, -0.7400000000000004), (7.808571428571429, -0.8542857142857143), (7.977142857142857, -0.9685714285714286), (8.145714285714286, -1.082857142857143), (8.314285714285715, -1.1971428571428577), (8.482857142857142, -1.3114285714285716), (8.651428571428571, -1.425714285714286), (8.82, -1.5400000000000003)}
  15. Sequence(Segment[Element[l7, i], Element[l8, n - i]], i, 1, n) → l9, {5.56230241566074, 5.428646616020669, 5.302017328819479, 5.182929594705438, 5.071914664832891, 4.96951358848353, 4.876269065586928, 4.792715561034224, 4.719367823454878, 4.6567081304549145, 4.605172779226704, 4.565138529762089, 4.53690985367884, 4.520707909166439, 4.516662123149559, 4.52480510348123, 4.545071338206667, 4.577299801125959, 4.621240225793266, 4.6765624912636286, 4.74286833045152, 4.819704453636983, 4.906576178550412, 5.002960756045424, 5.1083197445192186, 5.222109980942686, 5.343792889790882, NaN}
  16. Segment(J, K) → l
  17. Segment(J, L) → m
  18. Sequence(J + (i / n * (K - J)), i, 1, n) → l10, {(4.060714285714286, -0.18928571428571428), (3.8814285714285717, -0.31857142857142856), (3.7021428571428574, -0.44785714285714284), (3.522857142857143, -0.5771428571428572), (3.343571428571429, -0.7064285714285714), (3.1642857142857146, -0.8357142857142856), (2.9850000000000003, -0.9650000000000001), (2.805714285714286, -1.0942857142857143), (2.6264285714285713, -1.2235714285714288), (2.447142857142857, -1.352857142857143), (2.2678571428571432, -1.4821428571428572), (2.0885714285714285, -1.6114285714285714), (1.9092857142857143, -1.7407142857142859), (1.73, -1.87), (1.5507142857142857, -1.9992857142857143), (1.3714285714285714, -2.1285714285714286), (1.1921428571428572, -2.257857142857143), (1.0128571428571425, -2.3871428571428575), (0.8335714285714282, -2.5164285714285715), (0.6542857142857139, -2.645714285714286), (0.47499999999999964, -2.775), (0.2957142857142858, -2.9042857142857144), (0.1164285714285711, -3.033571428571429), (-0.06285714285714317, -3.162857142857143), (-0.24214285714285744, -3.2921428571428573), (-0.4214285714285717, -3.4214285714285717), (-0.600714285714286, -3.5507142857142857), (-0.7800000000000002, -3.68)}
  19. Sequence(J + (i / n * (L - J)), i, 1, n) → l11, {(4.428571428571429, -0.18214285714285713), (4.617142857142857, -0.30428571428571427), (4.805714285714286, -0.4264285714285714), (4.994285714285715, -0.5485714285714285), (5.182857142857143, -0.6707142857142858), (5.371428571428572, -0.7928571428571427), (5.5600000000000005, -0.915), (5.748571428571428, -1.0371428571428571), (5.937142857142858, -1.1592857142857145), (6.1257142857142854, -1.2814285714285716), (6.314285714285714, -1.4035714285714285), (6.502857142857143, -1.5257142857142856), (6.691428571428571, -1.647857142857143), (6.88, -1.77), (7.0685714285714285, -1.8921428571428571), (7.257142857142856, -2.0142857142857142), (7.445714285714285, -2.136428571428571), (7.634285714285714, -2.258571428571429), (7.822857142857143, -2.380714285714286), (8.01142857142857, -2.502857142857143), (8.2, -2.625), (8.388571428571428, -2.747142857142857), (8.577142857142857, -2.869285714285714), (8.765714285714285, -2.991428571428571), (8.954285714285714, -3.113571428571429), (9.142857142857142, -3.2357142857142858), (9.331428571428571, -3.357857142857143), (9.52, -3.48)}
  20. Sequence(Segment[Element[l10, i], Element[l11, n - i]], i, 1, n) → l12, {6.149819020068138, 6.016008066918169, 5.889909782407363, 5.772029671667691, 5.662880973353346, 5.562977656629879, 5.472826052415698, 5.39291523147523, 5.323706367728775, 5.2656214626343125, 5.21903193971402, 5.184247726507281, 5.1615075020654135, 5.150970782289489, 5.152712432123809, 5.1667200348351905, 5.192894330776647, 5.23105268993708, 5.280935339617832, 5.34221386501812, 5.414501362083125, 5.497363561058062, 5.590330253834632, 5.692906434631557, 5.804582681127113, 5.924844439531984, 6.053180012630231, NaN}
  21. Point(l6) → R
  22. Intersect(j, k) → S
  23. Point(l12) → V
  24. Point(l9) → B_1
  25. Point(l12) → C_1

AI 绘图提示语参考

绘制一张圣诞贺卡图案：从顶部到底部依次排列四组对称的扇形网格，每组由两条从同一点出发的边和一系列连接对应等分点的线段构成，形成类似编织或放射的曲线簇。每组网格的顶点分别位于不同高度，整体呈倒置的树形或锥形结构。在每组网格的交叉区域或边界上标记若干点，并用细线连接部分点以增强装饰效果。图形以坐标轴为背景，线条简洁，适合数学教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。