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鉴于许多爱好数学的年轻朋友都对非欧几何怀有神秘感,笔者斗胆试陈拙识.本文究竟是确能解惑还是只可增疑,企盼读者依实感不吝明示.学无止境,与读者们共勉.1.欧几里得几何的公理系统数学学科由于极其注重理论的严谨性,所以每逢采用新术语,都给出定义,即以先行的术语确切地解释它;每逢引进新命题,都给出证明,即从先行的命题演绎地推出它.然而学科的论述总有个开端,对于那里使用的新术语和新命题,上述常规显然失效.
Because many young friends who love math are mysterious to non-Euclidean geometry, I dare to try my best to understand this article.Whether this article can really solve or only increase suspicion? We encourage each other.1 The axiology system of Euclidean geometry With its emphasis on theoretical rigor, the mathematical discipline gives a definition every time a new term is adopted, ie an exact explanation of it in a preemptive terminology; whenever a new proposition is introduced , Is proof that deductive deduction from the proposition of the introduction of it.However, the discourse of the discipline there is always a beginning, the new terms and new propositions used there, the apparent failure of the above.