以退求进是一种重要的数学思维模式,其含义正如华罗庚先生所言:“先足够地退到我们最容易看清楚问题的地方,认透了钻深了,然后再上去.”这种思维模式既包括直接后退模式,如降次法、消元法、化空间为平面法、特殊化法,又包括间接后退模式(即借助一定的方法进行后退),如类比法、 Retreat for progress is an important mathematical thinking mode. Its meaning is just what Mr. Hua Luogeng said: “First enough to retreat to the place where we can easily see the problem, we can think that we have drilled deeper, and then go up.” The mode of thinking includes not only the direct retreat mode, such as decrement method, elimination method, space-based plane method, specialization method, but also indirect retreat mode (that is, retreat with a certain method), such as analogy,