On the Division of the Plane by Lines
On the Division of the Plane by Lines
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DOI：
10.1080/00029890.1978.11994663
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发表时间：
1978-10
影响因子：
0.5
通讯作者：
J. Wetzel
中科院分区：
文献类型：
--
作者：
J. Wetzel
1.在数学中，偶尔会发生这样的情况，即一个结果正确的“真实”原因与构成其证明的论点完全无关。在证明中使用的推理受到严格的限制：论点必须仔细组织，逻辑上正确，并且完整。每一种可能性都必须加以研究。直觉是更自由的：直觉的洞察力可能是支离破碎的、不完整的；严谨和逻辑是无关紧要的；甚至不正确的洞察力有时也可能有用。虽然对结果证明的良好理解通常有助于对结果的全面理解，但良好的直觉洞察力可能有助于更多。事实上，恰当的直觉可以让原本神秘的结果看起来几乎显而易见。
1. It occasionally happens in mathematics that the" real" reasons for the correctness of a result are quite unrelated to the arguments that comprise its proof. The reasoning used in proofs is severely restricted: the arguments must be carefully organized, logically correct, and complete. Every possibility has to be examined. The intuition is freer: intuitive insights may be fragmented, incomplete; rigor and logic are irrelevant; and even incorrect insights may sometimes be useful. While a good understanding of the proof of a result usually contributes to the full comprehension of the result, good intuitive insights may contribute even more. Indeed, appropriate intuitions can make an otherwise mysterious result seem virtually obvious.