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曹娟兰 2020-10-17 21:46

完美数与形的结合,可以使抽象问题直观化

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马福全 2020-10-17 12:19

<p><span style="color: rgb(51, 51, 51); font-family: 微软雅黑; font-size: 12px; background-color: rgb(255, 255, 255);">数形结合可以使抽象问题直观化,有利于抽象思维和形象思维的协调发展,可以优化解决问题的方法</span></p>

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马正虎 2020-10-17 12:11

<p>数形结合的思想重点考查以形释数,同时考查以数解形,题型会渗透到解答题,题量会加大.数形结合常用于解方程、解不等式、求函数值域、解复数和三角问题中,充分发挥形的形象性、直观性、数的深刻性、精确性,弥补形的表面性,数的抽象性,从而起到优化解题途径的作用。</p>

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刘春年 2020-10-17 12:08

<p><span style="color: rgb(51, 51, 51); font-family: 微软雅黑; font-size: 12px; background-color: rgb(255, 255, 255);">“以形助数”和“以数辅形”</span></p>

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郭淑兰 2020-10-17 12:05

<p class="reader-word-layer reader-word-s1-18" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.73px; background-color: rgb(255, 255, 255); width: 3337px; height: 167px; line-height: 167px; top: 4156px; left: 1429px; z-index: 32;">数形结合思想可以使抽象的数学问题直观化、</p><p class="reader-word-layer reader-word-s1-5" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.79px; background-color: rgb(255, 255, 255); width: 2002px; height: 167px; line-height: 167px; top: 4156px; left: 4726px; z-index: 33;">使繁难的数学问题简捷化,</p><p class="reader-word-layer reader-word-s1-13" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.74px; background-color: rgb(255, 255, 255); width: 1335px; height: 167px; line-height: 167px; top: 4156px; left: 6691px; z-index: 34;">使得原本需要通过</p><p class="reader-word-layer reader-word-s1-7" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.77px; background-color: rgb(255, 255, 255); width: 1668px; height: 167px; line-height: 167px; top: 4403px; left: 1429px; z-index: 35;">抽象思维解决的问题,</p><p class="reader-word-layer reader-word-s1-19" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.8px; background-color: rgb(255, 255, 255); width: 2335px; height: 167px; line-height: 167px; top: 4403px; left: 3060px; z-index: 36;">有时借助形象思维就能够解决,</p><p class="reader-word-layer reader-word-s1-8" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.81px; background-color: rgb(255, 255, 255); width: 2669px; height: 167px; line-height: 167px; top: 4403px; left: 5357px; z-index: 37;">有利于抽象思维和形象思维的协调发</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 3652px; height: 167px; line-height: 167px; top: 4651px; left: 1429px; z-index: 38; letter-spacing: -1.6px;">展和优化解决问题的方法。数学家华罗庚曾说过:</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 2817px; height: 167px; line-height: 167px; top: 4651px; left: 4978px; z-index: 39; letter-spacing: -1.89px;">“数缺形时少直觉,形少数时难入微。</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 316px; height: 167px; line-height: 167px; top: 4651px; left: 7710px; z-index: 40; letter-spacing: -18.05px;">”这</p><p class="reader-word-layer reader-word-s1-7" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.77px; background-color: rgb(255, 255, 255); width: 4671px; height: 167px; line-height: 167px; top: 4899px; left: 1429px; z-index: 41;">句话深刻地揭示了数形之间的辩证关系以及数形结合的重要性</p><p class="reader-word-layer reader-word-s1-18" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.73px; background-color: rgb(255, 255, 255); width: 3337px; height: 167px; line-height: 167px; top: 4156px; left: 1429px; z-index: 32;">数形结合思想可以使抽象的数学问题直观化、</p><p class="reader-word-layer reader-word-s1-5" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.79px; background-color: rgb(255, 255, 255); width: 2002px; height: 167px; line-height: 167px; top: 4156px; left: 4726px; z-index: 33;">使繁难的数学问题简捷化,</p><p class="reader-word-layer reader-word-s1-13" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.74px; background-color: rgb(255, 255, 255); width: 1335px; height: 167px; line-height: 167px; top: 4156px; left: 6691px; z-index: 34;">使得原本需要通过</p><p class="reader-word-layer reader-word-s1-7" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.77px; background-color: rgb(255, 255, 255); width: 1668px; height: 167px; line-height: 167px; top: 4403px; left: 1429px; z-index: 35;">抽象思维解决的问题,</p><p class="reader-word-layer reader-word-s1-19" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.8px; background-color: rgb(255, 255, 255); width: 2335px; height: 167px; line-height: 167px; top: 4403px; left: 3060px; z-index: 36;">有时借助形象思维就能够解决,</p><p class="reader-word-layer reader-word-s1-8" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.81px; background-color: rgb(255, 255, 255); width: 2669px; height: 167px; line-height: 167px; top: 4403px; left: 5357px; z-index: 37;">有利于抽象思维和形象思维的协调发</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 3652px; height: 167px; line-height: 167px; top: 4651px; left: 1429px; z-index: 38; letter-spacing: -1.6px;">展和优化解决问题的方法。数学家华罗庚曾说过:</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 2817px; height: 167px; line-height: 167px; top: 4651px; left: 4978px; z-index: 39; letter-spacing: -1.89px;">“数缺形时少直觉,形少数时难入微。</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 316px; height: 167px; line-height: 167px; top: 4651px; left: 7710px; z-index: 40; letter-spacing: -18.05px;">”这</p><p class="reader-word-layer reader-word-s1-7" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.77px; background-color: rgb(255, 255, 255); width: 4671px; height: 167px; line-height: 167px; top: 4899px; left: 1429px; z-index: 41;">句话深刻地揭示了数形之间的辩证关系以及数形结合的重要性</p><p>数形结合可以使抽象问题直观化,有利于抽象思维和形象思维的协调发展,可以优化解决问题的方法</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 3652px; height: 167px; line-height: 167px; top: 4651px; left: 1429px; z-index: 38; letter-spacing: -1.6px;">数学家华罗庚曾说过:</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 2817px; height: 167px; line-height: 167px; top: 4651px; left: 4978px; z-index: 39; letter-spacing: -1.89px;">“数缺形时少直觉,形少数时难入微。</p><p class="reader-word-layer reader-word-s1-3" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; background-color: rgb(255, 255, 255); width: 316px; height: 167px; line-height: 167px; top: 4651px; left: 7710px; z-index: 40; letter-spacing: -18.05px;">”这</p><p class="reader-word-layer reader-word-s1-7" style="margin-top: -760px; margin-bottom: 0px; padding: 0px; position: absolute; word-break: keep-all; -webkit-font-smoothing: antialiased; text-shadow: rgba(0, 0, 0, 0.004) 1px 1px 1px; font-size: 167px; font-family: 宋体, &quot;115d924b77232f60ddcca14b0020001&quot;, 宋体; letter-spacing: -0.77px; background-color: rgb(255, 255, 255); width: 4671px; height: 167px; line-height: 167px; top: 4899px; left: 1429px; z-index: 41;">句话深刻地揭示了数形之间的辩证关系以及数形结合的重要性。</p><p><br/></p>

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刘春年 2020-10-17 11:56

<p>数形结合是一个数学思想方法,包含“以形助数”和“以数辅形”两个方面,其应用大致可以分为两种情形:或者是借助形的生动和直观性来阐明数之间的联系,即以形作为手段,数为目的,比如应用函数的图像来直观地说明函数的性质;或者是借助于数的精确性和规范严密性来阐明形的某些属性,即以数作为手段,形作为目的,如应用曲线的方程来精确地阐明曲线的几何性质。</p><p>--------------------------------------------------------</p><p><br/></p>

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