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升维与降格是最常见的思维方法。这“升”与“降”的一对矛盾的和谐统一,正是辩证法在数学中的生动体现。折叠——平面图形立体化;展开——立体图形平面化。这一折和一展,将我们的思维带入到更深刻的境地……当你在研究和讨论编一个折叠问题的时候,总是在考虑折叠前和折叠后这两个方面,着力去寻找那些不变的量和已经发生了变化的条件。而当你把一个立体图形展成一个平面图形的时候,你也总是那样的“展前顾后”,在前后的对比中抓住矛盾的主要方面,从而发现解决问题的捷径。是啊,折与展,互相依存,折与展,彼此联系。
Rising and demotion are the most common ways of thinking. The harmony and unification of this pair of “ups” and “downs” is a vivid manifestation of dialectics in mathematics. Folding - three-dimensional graphics; unfolded - three-dimensional graphics plane. This folding and exhibition has brought our thinking to a deeper level... When you are researching and discussing a folding problem, you always look at the two aspects before and after folding. Those constant quantities and conditions that have changed. When you develop a three-dimensional graphic into a flat graphic, you are always “premature” and grasp the main aspects of contradiction in the comparison before and after, so as to find a shortcut to solve the problem. Yes, ah, folding and exhibition, interdependence, folding and exhibition, and contact each other.