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求翻译达人人工翻译论文摘要,中译英,谢谢!

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求翻译达人人工翻译论文摘要,中译英,谢谢!
本文运用五色定理,通过解方程组得到平面图的面色数.具体分析了球面和环面上平面图面色数的计算,并将方程组的应用进行推广.
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this paper use the five-color theorem ,obtained the face chromatic number of plan view by solving equations.Besides,it concretely analysized the calculation of face chromatic number of plan view on the surface of the sphere and the ring ,and promoted the application of equations.