陶哲轩的数学题
据说，陶哲轩（Terrence Tao）是40岁以下最聪明的美国科学家。陶哲轩，1975年7月15日在澳大利亚出生，是家中长子。现任教于美国加州大学洛杉矶分校（UCLA）数学系，24岁时便被聘为正教授。研究涉及质数或素数形式，在压缩感知方面的突破性研究令工程师可以开发出用于核磁共振成像、天文仪器和数码相机领域的更尖端、更有效的成像技术。
据测试，陶哲轩的智商介于220至230之间，如此高的智商百万人中才会有一个。陶哲轩20岁获得普林斯顿大学博士学位，后来获得"菲尔兹奖"，这一奖项被誉为"数学界的诺贝尔奖"。
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他最近在Blog（此链接被屏蔽）上出了一道数学题，翻译如下：
Suppose you are trying to get from one end A of a terminal to the other end B. (For simplicity, assume the terminal is a one-dimensional line segment.) Some portions of the terminal have moving walkways (in both directions); other portions do not. Your walking speed is a constant v, but while on a walkway, it is boosted by the speed u of the walkway for a net speed of v+u. (Obviously, given a choice, one would only take those walkways that are going in the direction one wishes to travel in.) Your objective is to get from A to B in the shortest time possible.
在机场中，你想从A点前往B点。（为了将问题简化，假设机场是一条线性通道。）一些区域有电动扶梯（双向的），另一些区域没有。你的步行速度恒定为v，电动扶梯的运行速度为u，因此在扶梯上，你的实际速度为v+u。（显然，你不会搭乘与你前进方向不一致的扶梯。）你的目标是尽可能快地从A点到达B点。
1. Suppose you need to pause for some period of time, say to tie your shoe. Is it more efficient to do so while on a walkway, or off the walkway? Assume the period of time required is the same in both cases.
1. 假定你需要暂停片刻，比如系鞋带。请问你应该在电动扶梯上系，还是在没有上电动扶梯时系？假定两种情况下，系鞋带的时间相同。
2. Suppose you have a limited amount of energy available to run and increase your speed to a higher quantity v' (or v'+u, if you are on a walkway). Is it more efficient to run while on a walkway, or off the walkway? Assume that the energy expenditure is the same in both cases.
2. 假定你有有限数量的多余能量，用来奔跑。在跑动时，你的速度提高到v'（如果在电动扶梯上，就相应为v'+u）。请问你应该在电动扶梯上跑，还是在没有上电动扶梯时跑？假定两种情况下，你可供奔跑的能量相同。
3. Do the answers to the above questions change if one takes into account the various effects of special relativity? (This is of course an academic question rather than a practical one. But presumably it should be the time in the airport frame that one wants to minimise, not time in one's personal frame.)
3. 在狭义相对论的情况下，上述答案是否发生改变？
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第三个问题，我根本不懂，就不考虑了。
前两个问题，我一开始用直觉判断，后来发现想不清楚，只好老老实实拿出草稿纸，用方程式计算。刚才算出来的答案好像是，都应该在电动扶梯上完成。作者没有公布答案，不知道我算得对不对。
（来源：Greg Mankiw's Blog）
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