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3D亚伯：轮廓=旋转体截面

3D亚伯：轮廓=旋转体截面
几何画板及绘图内容加载中，请稍等……
2019-03-28 23:36
函数解析几何立体几何函数图像
所属专题 GeoGebra 3D & AR: Geometry Resources & Challenges
①本范例演示了如何通过亚伯拉罕·林肯的轮廓生成旋转体表面，并展示其截面特性；②涉及核心数学概念包括旋转体、截面、函数、解析几何；③作图要点：利用GeoGebra命令如Corner（角点）、Midpoint（中点）、Rotate（旋转）、Function（函数）、Surface（表面）、Point（点）、OrthogonalLine（垂线）、Line（直线）、Distance（距离）、Translate（平移）等构建图形；④适合高中及以上学生学习立体几何、函数图像及旋转体知识。

GeoGebra 命令及参数

  1. Corner(pic1, 4) → C
  2. Corner(pic1, 3) → D
  3. Midpoint(A, D) → E
  4. Rotate(pic1, π / 2, E) → pic1'
  5. Function({1.5248963794530292, 5.051539539125208, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.992057427589251, 1.9872981250795718, 1.982538822569893, 1.977779520060214, 1.968260915040856, 1.958742310021498, 1.94922370500214, 1.9397050999827818, 1.930186494963424, 1.920667889944066, 1.8778341673569547, 1.8635562598279176, 1.8492783522988807, 1.8350004447698436, 1.8135835834762881, 1.7921667221827324, 1.7826481171633743, 1.7731295121440163, 1.7636109071246584, 1.7540923021053005, 1.7445736970859425, 1.7350550920665844, 1.7302957895569053, 1.7255364870472263, 1.7207771845375472, 1.7160178820278682, 1.7112585795181892, 1.7064992770085101, 1.701739974498831, 1.6969806719891523, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.6922213694794732, 1.701739974498831, 1.7112585795181892, 1.7207771845375472, 1.730295789556905, 1.7398143945762632, 1.7493329995956213, 1.7588516046149794, 1.7683702096343374, 1.7778888146536953, 1.7874074196730534, 1.7969260246924115, 1.8064446297117696, 1.8112039322214486, 1.8159632347311276, 1.8207225372408065, 1.8254818397504853, 1.8302411422601645, 1.8350004447698436, 1.8397597472795226, 1.8445190497892014, 1.8492783522988807, 1.8587969573182388, 1.8683155623375967, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8778341673569547, 1.8825934698666338, 1.8873527723763128, 1.8921120748859919, 1.896871377395671, 1.9016306799053497, 1.9063899824150288, 1.9111492849247078, 1.9159085874343866, 1.920667889944066, 1.930186494963424, 1.9397050999827818, 1.94922370500214, 1.958742310021498, 1.968260915040856, 1.977779520060214, 1.9991963813537696, 2.0206132426473253, 2.042030103940881, 2.0634469652344363, 2.084863826527992, 2.1062806878215476, 2.1157992928409057, 2.1253178978602634, 2.1348365028796215, 2.1491144104086586, 2.1633923179376957, 2.177670225466733, 2.182429527976412, 2.187188830486091, 2.19194813299577, 2.201466738015128, 2.2109853430344857, 2.2205039480538438, 2.225263250563523, 2.230022553073202, 2.234781855582881, 2.23954115809256, 2.244300460602239, 2.249059763111918, 2.249059763111918, 2.249059763111918, 2.249059763111918, 2.249059763111918, 2.23954115809256, 2.230022553073202, 2.2205039480538438, 2.177670225466733, 2.172910922957054, 2.1681516204473748, 2.1633923179376957, 2.14197545664414, 2.1205585953505843, 2.099141734057029, 2.0777248727634734, 2.034891150176362, 1.992057427589251, 1.94922370500214, 1.9063899824150288, 1.8635562598279176, 1.8540376548085595, 1.8445190497892014, 1.8350004447698436, 1.8135835834762881, 1.7921667221827324, 1.7874074196730534, 1.7826481171633743, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7778888146536953, 1.7874074196730534, 1.7969260246924115, 1.8064446297117696, 1.8112039322214486, 1.8159632347311276, 1.8207225372408065, 1.8254818397504853, 1.8302411422601645, 1.8350004447698436, 1.8397597472795226, 1.8445190497892014, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8492783522988807, 1.8445190497892014, 1.8397597472795226, 1.8350004447698436, 1.8302411422601645, 1.8254818397504853, 1.8207225372408065, 1.8159632347311276, 1.8112039322214486, 1.8064446297117696, 1.7921667221827324, 1.7778888146536955, 1.7636109071246584, 1.742194045831103, 1.7207771845375472, 1.6993603232439916, 1.677943461950436, 1.668424856931078, 1.65890625191172, 1.649387646892362, 1.606553924305251, 1.5637202017181397, 1.5208864791310286, 1.4780527565439174, 1.4352190339568063, 1.3923853113696951, 1.349551588782584, 1.3067178661954728, 1.2638841436083617, 1.2067725134922136, 1.1853556521986581, 1.1639387909051024, 1.1544201858857444, 1.1449015808663863, 1.1353829758470284, 1.1258643708276703, 1.1163457658083122, 1.1068271607889542, 1.1020678582792751, 1.0973085557695963, 1.0925492532599173, 1.0925492532599173, 1.0925492532599173}) → f
  6. Surface(f, n, Line[E, H]) → b
  7. Point(f) → J
  8. Rotate(b, π / 2, J, Plane[J, E, I]) → b'
  9. Rotate(pic1', ((-π)) / 2, J) → pic1''
  10. Rotate(f, ((-π)) / 2, J) → f_2
  11. OrthogonalLine(J, z = 0) → h
  12. Rotate(f, n, Line[E, H]) → f_1
  13. Rotate(f_1, π / 2, J, Plane[J, E, I]) → a
  14. Line(J, J + (0, 0, 1)) → j
  15. Line(N, O) → k
  16. Line(E, H) → l
  17. Rotate(Line[E, H], π / 2, J, Plane[J, E, I]) → m
  18. Distance(J, m) → c
  19. Translate(J, Vector[((-c), 0, 0)]) → J'