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摘要：數(shù)形結(jié)合是數(shù)學(xué)解題中常用的思想方法,它使某些抽象的數(shù)學(xué)問題直觀化、生動(dòng)化給人以直觀感.本文論述了如何用數(shù)形結(jié)合方法來解答高中的一些數(shù)學(xué)題目，其重點(diǎn)在于論述如何把數(shù)與式的代數(shù)信息和點(diǎn)與形的幾何信息有機(jī)和諧地結(jié)合在一起；同時(shí)，本文不僅論述一種解題方法，還在于培養(yǎng)學(xué)生的數(shù)學(xué)基本功、解題思維、創(chuàng)造性與發(fā)散性思維等思想.本文從數(shù)向形的轉(zhuǎn)化與形向數(shù)的轉(zhuǎn)化兩方面來論述主題. 關(guān)鍵詞： 數(shù)形結(jié)合 思想方法
【Abstract】 : Several Shapes Combinations mathematical problem-solving methods used in, it makes some abstract mathematical problem visualization, of giving vivid visual sense. This paper discusses a method of combining the operation with figure how to answer some of the high school math questions its focus is on how to incorporate a number and type of algebra with information and points of geometry information organic harmonious combination; Meanwhile, the paper not only deals with a problem-solving approach, but also to nurture the basic skills of mathematics, problem-solving thinking, creativity and divergent thinking such thoughts. This paper to the shape of a few into shape and to the conversion of several discussed two topics. 【Keywords】: Several Shapes Combinations Thinking
數(shù)學(xué)研究的對象是現(xiàn)實(shí)世界的空間形式和數(shù)量關(guān)系，即“形”與“數(shù)”的相互結(jié)合，稱為數(shù)形結(jié)合.數(shù)形結(jié)合是使抽象思維和形象思維相互作用來實(shí)現(xiàn)數(shù)量關(guān)系與圖形性質(zhì)的相互轉(zhuǎn)化，是一種極富數(shù)學(xué)特點(diǎn)的信息轉(zhuǎn)換，它不僅使某些抽象的數(shù)學(xué)問題直觀化、生動(dòng)化、給人以直觀感，而且使許多復(fù)雜的數(shù)學(xué)問題迎刃而解，達(dá)到柳暗花明. 數(shù)形結(jié)合法就是根據(jù)數(shù)學(xué)問題的條件與結(jié)論之間的內(nèi)在聯(lián)系，既分析其代數(shù)含義，又揭示其幾何意義，它將數(shù)與式的代數(shù)信息和點(diǎn)與形的幾何信息互相轉(zhuǎn)換，最終使數(shù)量關(guān)系和空間形式巧妙、和諧有機(jī)結(jié)合在一起.著名數(shù)學(xué)家華羅庚曾說：“數(shù)無形時(shí)少直覺，形少數(shù)時(shí)難入微” [1].這足以說明“以形助數(shù)”和“以數(shù)輔形”的重要性所在，即進(jìn)一步強(qiáng)調(diào)了數(shù)形結(jié)合思想在數(shù)學(xué)解題中的地位與作用. 數(shù)形結(jié)合思想方法在解題中的應(yīng)用是非常廣泛的，縱觀多年來的高考試題，巧妙運(yùn)用數(shù)形結(jié)合的思想方法解題可起到事半功倍的效果.現(xiàn)將數(shù)形結(jié)合思想在數(shù)學(xué)解題中的應(yīng)用從以下兩方面進(jìn)行探討. |
