积极 AI Logo 积极 AI

圣诞卡片9

圣诞卡片9
几何画板及绘图内容加载中，请稍等……
2021-09-13 03:58
多边形函数几何作图滑块动画
所属专题 STEAM like Leonardo
①这个范例演示了一个复杂的几何图形构造，结合了多边形、直线和函数图像；②涉及的核心数学概念包括多边形构造、直线方程、函数图像、导数等；③作图要点使用了GeoGebra的Segment（线段）、Sequence（数列）、Polygon（多边形）、Point（点）等命令；④适合高中阶段学习几何作图和函数图像的学生使用。

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, {(1.3133588980711708, 5.543239535272778), (1.185532811114649, 5.424109100490169), (1.0577067241581273, 5.30497866570756), (0.9298806372016056, 5.185848230924951), (0.8020545502450839, 5.066717796142343), (0.6742284632885621, 4.947587361359734), (0.5464023763320404, 4.828456926577125), (0.4185762893755187, 4.709326491794517), (0.29075020241899696, 4.590196057011908), (0.1629241154624752, 4.4710656222292995), (0.03509802850595345, 4.35193518744669), (-0.09272805845056831, 4.232804752664082), (-0.22055414540708984, 4.113674317881474), (-0.3483802323636118, 3.9945438830988644), (-0.4762063193201336, 3.8754134483162557), (-0.6040324062766551, 3.756283013533647), (-0.7318584932331769, 3.6371525787510386), (-0.8596845801896986, 3.5180221439684294), (-0.9875106671462204, 3.3988917091858206), (-1.1153367541027421, 3.2797612744032123), (-1.243162841059264, 3.1606308396206035), (-1.3709889280157856, 3.0415004048379948), (-1.4988150149723074, 2.922369970055386)}
  4. Sequence(A + (i / n * (C - A)), i, 1, n) → l2, {(1.5672204204612712, 5.534440840922543), (1.6932558558948496, 5.4065117117897), (1.8192912913284283, 5.278582582656858), (1.9453267267620067, 5.150653453524015), (2.0713621621955856, 5.022724324391172), (2.197397597629164, 4.894795195258329), (2.3234330330627424, 4.766866066125486), (2.4494684684963213, 4.638936936992643), (2.5755039039298997, 4.511007807859801), (2.701539339363478, 4.3830786787269576), (2.827574774797057, 4.2551495495941145), (2.9536102102306354, 4.127220420461272), (3.079645645664214, 3.9992912913284293), (3.2056810810977927, 3.871362162195586), (3.3317165165313716, 3.743433033062743), (3.4577519519649496, 3.6155039039299), (3.5837873873985284, 3.4875747747970576), (3.709822822832107, 3.3596456456642145), (3.8358582582656857, 3.2317165165313715), (3.961893693699264, 3.103787387398529), (4.087929129132842, 2.9758582582656863), (4.213964564566421, 2.847929129132843), (4.34, 2.72)}
  5. Sequence(Segment[Element[l1, i], Element[l2, n - i]], i, 1, n) → l3, {3.959572125615415, 3.7970826397773396, 3.644111002392254, 3.50190472333615, 3.37182616010994, 3.2553294588703894, 3.15392000321615, 3.069093702820832, 3.0022565173235845, 2.9546295036838943, 2.9271505054193363, 2.9203883179851187, 2.9344861634332453, 2.9691469192426845, 3.023663519941566, 3.0969875693506506, 3.1878215440500157, 3.2947175383963256, 3.416168085447962, 3.550679989433008, 3.6968277828155207, 3.8532877122456592, NaN}
  6. Segment(E, D) → h
  7. Segment(D, F) → i
  8. Sequence(D + (i / n * (E - D)), i, 1, n) → l4, {(1.2617391304347825, 4.194782608695652), (1.0834782608695652, 4.029565217391305), (0.9052173913043479, 3.8643478260869566), (0.7269565217391305, 3.699130434782609), (0.5486956521739131, 3.533913043478261), (0.3704347826086958, 3.3686956521739133), (0.1921739130434783, 3.2034782608695656), (0.013913043478261056, 3.0382608695652173), (-0.16434782608695642, 2.87304347826087), (-0.34260869565217367, 2.707826086956522), (-0.5208695652173911, 2.542608695652174), (-0.6991304347826084, 2.3773913043478263), (-0.8773913043478259, 2.2121739130434785), (-1.0556521739130433, 2.0469565217391303), (-1.2339130434782608, 1.8817391304347826), (-1.4121739130434778, 1.7165217391304348), (-1.5904347826086953, 1.551304347826087), (-1.7686956521739128, 1.3860869565217393), (-1.9469565217391303, 1.2208695652173915), (-2.1252173913043473, 1.0556521739130438), (-2.3034782608695648, 0.890434782608696), (-2.4817391304347822, 0.7252173913043478), (-2.6599999999999997, 0.56)}
  9. Sequence(D + (i / n * (F - D)), i, 1, n) → l5, {(1.6052173913043477, 4.2034782608695656), (1.7704347826086957, 4.046956521739131), (1.9356521739130435, 3.890434782608696), (2.1008695652173914, 3.7339130434782613), (2.266086956521739, 3.5773913043478265), (2.431304347826087, 3.4208695652173917), (2.596521739130435, 3.2643478260869565), (2.7617391304347825, 3.107826086956522), (2.9269565217391307, 2.951304347826087), (3.092173913043478, 2.794782608695652), (3.257391304347826, 2.6382608695652174), (3.422608695652174, 2.4817391304347827), (3.5878260869565217, 2.325217391304348), (3.75304347826087, 2.1686956521739127), (3.9182608695652177, 2.0121739130434784), (4.0834782608695654, 1.8556521739130436), (4.248695652173913, 1.6991304347826088), (4.413913043478261, 1.5426086956521736), (4.579130434782609, 1.3860869565217389), (4.7443478260869565, 1.229565217391304), (4.909565217391304, 1.0730434782608698), (5.074782608695653, 0.9165217391304346), (5.24, 0.7599999999999998)}
  10. Sequence(Segment[Element[l4, i], Element[l5, n - i]], i, 1, n) → l6, {5.02854799082501, 4.8352830519853365, 4.656286276675777, 4.493263178210002, 4.348010865638754, 4.222363720420545, 4.11811664333233, 4.036927840501238, 3.9802085989924434, 3.9490134203784266, 3.9439480090285937, 3.9651125081475844, 4.012091836856729, 4.083995226886597, 4.179536519741007, 4.297139330673508, 4.4350490116062655, 4.59143609824142, 4.764481456976744, 4.952439203490762, 5.153678004631772, 5.366704043203295, NaN}
  11. Segment(G, H) → j
  12. Segment(G, I) → k
  13. Sequence(G + (i / n * (H - G)), i, 1, n) → l7, {(1.2608695652173911, 2.5930434782608693), (1.0817391304347825, 2.406086956521739), (0.9026086956521738, 2.2191304347826084), (0.7234782608695651, 2.0321739130434784), (0.5443478260869564, 1.8452173913043477), (0.3652173913043477, 1.6582608695652172), (0.1860869565217389, 1.4713043478260868), (0.006956521739130306, 1.2843478260869565), (-0.1721739130434785, 1.0973913043478258), (-0.3513043478260871, 0.9104347826086956), (-0.5304347826086959, 0.7234782608695651), (-0.7095652173913045, 0.5365217391304347), (-0.8886956521739129, 0.34956521739130464), (-1.0678260869565221, 0.16260869565217373), (-1.2469565217391305, -0.024347826086956736), (-1.4260869565217393, -0.21130434782608676), (-1.6052173913043477, -0.3982608695652172), (-1.784347826086957, -0.5852173913043481), (-1.9634782608695653, -0.7721739130434782), (-2.142608695652174, -0.9591304347826086), (-2.3217391304347825, -1.146086956521739), (-2.500869565217392, -1.3330434782608696), (-2.68, -1.52)}
  14. Sequence(G + (i / n * (I - G)), i, 1, n) → l8, {(1.6199999999999999, 2.589565217391304), (1.8, 2.3991304347826086), (1.98, 2.2086956521739127), (2.16, 2.0182608695652173), (2.34, 1.8278260869565215), (2.52, 1.6373913043478259), (2.7, 1.4469565217391303), (2.88, 1.2565217391304346), (3.0600000000000005, 1.0660869565217388), (3.24, 0.8756521739130434), (3.4200000000000004, 0.6852173913043478), (3.6, 0.49478260869565194), (3.7800000000000002, 0.30434782608695654), (3.9600000000000004, 0.1139130434782607), (4.140000000000001, -0.07652173913043514), (4.32, -0.26695652173913054), (4.5, -0.45739130434782593), (4.680000000000001, -0.6478260869565222), (4.86, -0.8382608695652176), (5.040000000000001, -1.028695652173913), (5.220000000000001, -1.2191304347826084), (5.4, -1.4095652173913042), (5.58, -1.6)}
  15. Sequence(Segment[Element[l7, i], Element[l8, n - i]], i, 1, n) → l9, {5.757888252359025, 5.501581968742279, 5.2598841333634265, 5.034898999931231, 4.82896310692997, 4.644611000089782, 4.484505312930438, 4.351323289153505, 4.247598231617496, 4.1755259564793175, 4.136761196238791, 4.13224143554845, 4.162078239786235, 4.225543890675222, 4.321156902430798, 4.446844126378843, 4.600141117256812, 4.778391342128177, 4.9789154686393635, 5.199136906705688, 5.436662561807941, 5.689325527049847, NaN}
  16. Segment(J, K) → l
  17. Segment(J, L) → m
  18. Sequence(J + (i / n * (K - J)), i, 1, n) → l10, {(1.2478260869565216, 0.6747826086956522), (1.0556521739130433, 0.4895652173913044), (0.8634782608695651, 0.30434782608695654), (0.671304347826087, 0.11913043478260876), (0.47913043478260864, -0.06608695652173913), (0.28695652173913033, -0.2513043478260869), (0.09478260869565203, -0.4365217391304349), (-0.09739130434782606, -0.6217391304347825), (-0.28956521739130436, -0.8069565217391305), (-0.48173913043478267, -0.9921739130434782), (-0.6739130434782608, -1.1773913043478261), (-0.8660869565217393, -1.362608695652174), (-1.0582608695652174, -1.5478260869565217), (-1.250434782608696, -1.73304347826087), (-1.442608695652174, -1.9182608695652172), (-1.634782608695652, -2.103478260869565), (-1.8269565217391301, -2.288695652173913), (-2.0191304347826087, -2.473913043478261), (-2.2113043478260868, -2.659130434782609), (-2.4034782608695653, -2.8443478260869566), (-2.595652173913043, -3.029565217391304), (-2.7878260869565215, -3.214782608695652), (-2.98, -3.4)}
  19. Sequence(J + (i / n * (L - J)), i, 1, n) → l11, {(1.6391304347826086, 0.6765217391304348), (1.8382608695652174, 0.4930434782608696), (2.037391304347826, 0.3095652173913044), (2.236521739130435, 0.12608695652173918), (2.4356521739130432, -0.05739130434782602), (2.634782608695652, -0.24086956521739122), (2.833913043478261, -0.42434782608695654), (3.0330434782608693, -0.6078260869565216), (3.2321739130434786, -0.7913043478260869), (3.431304347826087, -0.974782608695652), (3.630434782608696, -1.1582608695652175), (3.829565217391304, -1.3417391304347825), (4.028695652173913, -1.5252173913043476), (4.227826086956522, -1.7086956521739132), (4.426956521739131, -1.8921739130434783), (4.626086956521739, -2.0756521739130434), (4.8252173913043475, -2.2591304347826084), (5.024347826086957, -2.442608695652174), (5.223478260869565, -2.626086956521739), (5.422608695652174, -2.809565217391304), (5.621739130434783, -2.9930434782608693), (5.820869565217391, -3.176521739130435), (6.02, -3.36)}
  20. Sequence(Segment[Element[l11, i], Element[l10, n - i]], i, 1, n) → l12, {5.894081232285386, 5.662892979724317, 5.446878921097513, 5.247913186842476, 5.0680040850839125, 4.909247167384485, 4.773753224536358, 4.6635503322386525, 4.580464311413041, 4.525988805685134, 4.501162714732612, 4.506476079384453, 4.541823122698945, 4.60651252640809, 4.699332696062259, 4.818658285753226, 4.962577688630172, 5.129021028498036, 5.315873010156791, 5.5210619235528515, 5.742622521248466, 5.9787349693432965, NaN}
  21. Polygon(M, N, O, P) → q1, m_1, n_1, o, p
  22. Point(f) → R
  23. Point(g) → S
  24. Point(h) → T
  25. Point(i) → U
  26. Point(j) → V
  27. Point(k) → W
  28. Point(l) → Z
  29. Point(m) → A_1

AI 绘图提示语参考

绘制一组平行的交叉网格图案。先画四条起始线段作为每组的基准边，再从每条边的起点到终点均匀取若干点，然后连接这些点形成对角线段，使同组的两条边之间产生交叉的网纹效果，共形成三组这样的图案。最后在最上方绘制一个四边形，并在每条基准线段上随机放置一个点。整体呈现类似圣诞贺卡窗格装饰的几何构造。
以上提示语为根据原始绘图命令整理而来，仅供参考。