| 飞越北极 直通北美——2000年全国大学生数学建模竞赛C题 |
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| 引用本文： | 向红军,王金华,何艳.飞越北极 直通北美——2000年全国大学生数学建模竞赛C题[J].湘南学院学报,2001,22(2):40-45,54. |
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| 作者姓名： | 向红军 王金华 何艳 |
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| 作者单位： | 郴州师范高等专科学校,数学系,湖南,郴州,423000 |
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| 摘 要： | 对“飞越北极 ,北京至底特律的飞行时间可节省 4小时”问题 ,从数学的角度分别给出了 :(1)地球是球体 ,(2 )地球是椭球体两种情况下的合理解释 .对问题 1,主要利用了空间解析几何的有关知识求得可节省时间约 3.95 5 5小时 ;对问题 2 ,主要运用了微分几何的有关知识 ,求得曲线的最短弧长 ,得到了从北京飞越北极到底特律可节省时间约 3.96 0 2小时 ;并且对模型进行了评价 .
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| 关 键 词： | 北极 最短距离 空间直角坐标系 模型 |
| 文章编号： | 1008-2042(2001)02-0040-06 |
| 修稿时间： | 2000年12月19日 |
Flying Across the North Polar Regions to North America--Question C in the National College Students' Mathematics Contest in Modeling of the Year 2000 |
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| XIANG Hong-jun,WANG Jin-hua,HE Yan.Flying Across the North Polar Regions to North America--Question C in the National College Students'''' Mathematics Contest in Modeling of the Year 2000[J].Journal of Xiangnan University,2001,22(2):40-45,54. |
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| Authors: | XIANG Hong-jun WANG Jin-hua HE Yan |
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| Abstract: | Two explanations are given from the angle of mathematics about “It saves nearly 4 hours across the North Polar Regions to North America form Beijing to Detroit” under the following two cases: (1) The earth is a globe; (2) The earth is an ellipsoid. In(1), space analytical geometry theory is applied to obtain a Conclusion that the time saved is about 3.9555 hours; In(2), differential geometry is applied to abtain the shortest curve length, and the result is that the time saved is about 3.9602 hours. Evaluation of the model is also given. |
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| Keywords: | the North polar regions the short cut the space right angel coordinate system model |
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