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直线既简单,又不简单.说直线简单是指确定直线的条件简单,如两点,一点一方向都可确定直线,进而直线方程的表达形式简单.说直线不简单,是说许多高深的数学知识都可以在直线上找到影子,直线是许多复杂数学知识“心理成像”[1]的载体.把貌似简单的东西弄清楚了,就可以更好地认知一些复杂的事物,以简识繁.1.线性化将复杂的问题简单化,以简驭繁是数学追求的目标.曲线变化多端,但只要在某点处可导,那么曲线在这点的附近就可近似看作一条切线,即局部线性化.
Straight line is simple, not simple. Straight line means that the conditions to determine a straight line is simple, such as two points, one by one can determine the direction of a straight line, and then straightforward equation expression is simple. Straight line is not simple, is that many deep Mathematical knowledge can be found in the shadow of a straight line, which is the carrier of many complex mathematical knowledge “psychological imaging ” [1] .Clear seemingly simple things, you can better understand some complex things to Simple and complicated .1. Linearization Simplify the complex problems to simplify the complex is the goal of mathematics. Curves vary, but as long as the point at a guide, then the curve in the vicinity of this point can be approximated as A tangent, that is, local linearization.