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[摘要]數(shù)形結(jié)合思想是數(shù)學(xué)中一個(gè)重要的數(shù)學(xué)思想，利用這個(gè)思想我們在解題時(shí)可以把抽象問題轉(zhuǎn)化成具體問題，使抽象思維和形象思維緊密地結(jié)合起來，即把抽象的數(shù)學(xué)語言與直觀的圖形結(jié)合起來，把數(shù)與形相互為用。本文通過對高考數(shù)學(xué)試題的分析，使中學(xué)生在解決數(shù)學(xué)問題的過程中體會(huì)數(shù)形結(jié)合的基本思想以及在利用此思想解題時(shí)應(yīng)注意的問題并靈活的加以運(yùn)用，尋求到最佳的解題方法。 [關(guān)鍵詞] 數(shù)學(xué)思想 數(shù)形結(jié)合 解題方法 幾何圖形
[Abstract] combining the operation with figure mathematical thinking is an important mathematical thinking, We use this idea in problem solving abstract problems can be translated into specific issues, so that the image abstract thinking and thinking closely combined, which is an abstract mathematical language and visual graphics combine, with a few mutual shape for the end. Based on the Math papers detailed analysis of the topic. secondary school students solve math problems in the process of combining the operation with figure understand the basic thinking and the use of this thinking they should pay attention to problem solving and the flexibility to be used to find the best way to solve problems. [Key words]Mathematics thought Number shape union Problem solving method Geometric figure
華羅庚先生曾說過：“數(shù)缺形時(shí)少直覺，形缺數(shù)時(shí)難入微，數(shù)形結(jié)合百般好，隔離分家萬事非”?？梢姅?shù)形結(jié)合的重要性。用數(shù)形結(jié)合思想解題，就是利用代數(shù)的方法來研究圖形的形狀、大小及圖形間的關(guān)系或運(yùn)用圖形的性質(zhì)簡化繁瑣的代數(shù)運(yùn)算和邏輯推理，在運(yùn)用此方法時(shí)，要充分挖掘基本量的內(nèi)涵。例如點(diǎn)在曲線上，則點(diǎn)的坐標(biāo)為此曲線方程的根，絕對值和復(fù)數(shù)的模的幾何意義等。用數(shù)形結(jié)合思想解題是高中數(shù)學(xué)中一個(gè)重要的方法，下面就結(jié)合近幾年的高考試題，從數(shù)形結(jié)合思想所包含的兩個(gè)方面來探索數(shù)形結(jié)合思想在高中數(shù)學(xué)中的應(yīng)用。 |
