7812032 的博客

日志

关于我

华三火

文章分类

·默认分类（944）

【原创】数学篇（W）——又一个三角形中的几何不等式猜想

2014-09-26 06:08:07| 分类：默认分类 | 标签： |举报 |字号大中小订阅

下载LOFTER 我的照片书 |

在三角形ABC中，以ma等，wa等，ra等，s分表其中线，角平分线，旁切圆半径和半周，∑表循环和，则猜想有

(∑ma)^2≥2*s^2*[∑ra/(wa+ra)]≥(∑wa)^2 (*)

成立，又

(*)式可改写成等价形式

2*[(∑wa)/(∑a)]^2≤∑ra/(wa+ra)≤2*[(∑ma)/(∑a)]^2 (**)

注 (*)式实质给出了∑ma与∑wa的一个优美的隔离.

评论这张

转发至微博

阅读(110)| 评论(0)

历史上的今天

this.p={  m:2,
              b:2,
              loftPermalink:'',
              id:'fks_087070084087089075081086095066072087083068083085083067086094',
              blogTitle:'【原创】数学篇（W）——又一个三角形中的几何不等式猜想',
              blogAbstract:'<font face=\"黑体\"   \><span style=\"line-height: 42px;\"   \><font size=\"5\"   \>  <b\>在</b\></font\><font size=\"5\"   style=\"font-weight: bold;\"   \>三角形ABC中，以m</font\><font size=\"3\"   style=\"font-weight: bold;\"   \>a</font\><font size=\"5\"   style=\"font-weight: bold;\"   \>等，w</font\><font size=\"3\"   style=\"font-weight: bold;\"   \>a</font\><font size=\"5\"   style=\"font-weight: bold;\"   \>等，r</font\><font size=\"3\"   style=\"font-weight: bold;\"   \>a</font\><font size=\"5\"   \><b\>等，s分表其中线，角平分线，旁切圆半径和半周，∑表循环和，则猜想有</b\></font\></span\></font\><wbr\><div\><font face=\"黑体\"   \><span style=\"line-height: 42px;\"   \><b\><font size=\"5\"   \>      (∑m</font\><font size=\"3\"   \>a</font\><font size=\"5\"   \>)^2≥2*s^2*[∑r</font\><font size=\"3\"   \>a</font\><font size=\"5\"   \>/(w</font\><font size=\"3\"   \>a</font\><font size=\"5\"   \>+r</font\></b\></span\></font\></div\>',
              blogTag:'',
              blogUrl:'blog/static/12773502820148236349280',
              isPublished:1,
              istop:false,
              type:0,
              modifyTime:1411777531264,
              publishTime:1411682887959,
              permalink:'blog/static/12773502820148236349280',
              commentCount:0,
              mainCommentCount:0,
              recommendCount:0,
              bsrk:-100,
              publisherId:0,
              recomBlogHome:false,
              currentRecomBlog:false,
              attachmentsFileIds:[],
              vote:{},
              groupInfo:{},
              friendstatus:'none',
              followstatus:'unFollow',
              pubSucc:'',
              visitorProvince:'',
              visitorCity:'',
              visitorNewUser:false,
              postAddInfo:{},
              mset:'000',
              mcon:'',
              srk:-100,
              remindgoodnightblog:false,
              isBlackVisitor:false,
              isShowYodaoAd:false,
              hostIntro:'',
              hmcon:'1',
              selfRecomBlogCount:'0',
              lofter_single:'<iframe width="140" height="560" style="overflow:hidden;" src="http://www.lofter.com/mailEntry.do?blogad=1&blog" frameBorder="0"></iframe>'
            }

{list a as x}
    {if !!x}
    <div class="iblock nbw-fce nbw-f40">
      <a class="fc03 noul" target="_blank" hidefocus="true" href="http://blog.163.com/${x.visitorName}/">
      {if x.visitorName==visitor.userName}
      <img alt="${x.visitorNickname|escape}" onerror="this.src=location.f40" class="cwd bdwa bdc0" src="${fn1(x.visitorName)}&r=${visitor.imageUpdateTime}"/>
      {else}
      <img alt="${x.visitorNickname|escape}" onerror="this.src=location.f40" class="cwd bdwa bdc0" src="${fn1(x.visitorName)}"/>
      {/if}
      </a>
      <div class="cwd vname thide">
        {if x.moveFrom=='wap'}
          <a class="noul pnt" target="_blank" href="http://blog.163.com/services/wapblog.html?frompersonalbloghome"><span title="来自网易手机博客" class="iblock wapIcon"> </span></a>
        {elseif x.moveFrom=='iphone'}
          <a class="noul pnt" target="_blank"><span title="来自iPhone客户端" class="iblock iphoneIcon"> </span></a>
        {elseif x.moveFrom=='android'}
          <a class="noul pnt" target="_blank"><span title="来自Android客户端" class="iblock androidIcon"> </span></a>
        {elseif x.moveFrom=='mobile'}
          <a class="noul pnt" target="_blank" href="http://blog.163.com/services/emsblog.html?frompersonalbloghome"><span title="来自网易短信写博" class="iblock wapIcon"> </span></a>
        {/if}
        <a class="fc03 m2a"  target="_blank" hidefocus="true" href="http://blog.163.com/${x.visitorName}/">
          ${fn(x.visitorNickname,8)|escape}
        </a>
      </div>
    </div>
    {/if}
    {/list}

<#--最新日志，群博日志--> <#--推荐日志-->

<p class="fc06">推荐过这篇日志的人：</p>
    <div>
      {list a as x}
      {if !!x}
      <div class="iblock nbw-fce nbw-f40">
        <a class="fc03 noul" target="_blank" hidefocus="true" href="http://blog.163.com/${x.recommenderName}/">
        <img alt="${x.recommenderNickname|escape}" onerror="this.src=location.f40" class="cwd bdwa bdc0" src="${fn1(x.recommenderName)}"/>
        </a>
        <div class="cwd thide">
          <a class="fc03 m2a" target="_blank" hidefocus="true" href="http://blog.163.com/${x.recommenderName}/">
            ${fn(x.recommenderNickname,6)|escape}
          </a>
        </div>
      </div>
      {/if}
      {/list}
    </div>
    {if !!b&&b.length>0}
    <p  class="fc06">他们还推荐了：</p>
    <ul>
    {list b as y}
      {if !!y}
        <li class="rrb"><span class="iblock">·</span><a class="fc03 m2a" target="_blank" href="http://blog.163.com/${y.recommendBlogPermalink}/?from=blog/static/12773502820148236349280">${y.recommendBlogTitle|escape}</a></li>
      {/if}
    {/list}
    </ul>
    {/if}

<#--引用记录--> <#--博主推荐--> <#--随机阅读--> <#--首页推荐--> <#--历史上的今天--> <#--被推荐日志--> <#--上一篇，下一篇--> <#-- 热度 -->

{list a as x}
    {if !!x}
    <div class="hotItem iblock nbw-fce nbw-f40">
      <a class="fc03 noul" target="_blank" hidefocus="true" href="http://blog.163.com/${x.publisherUsername}/">
      {if x.publisherUsername==visitor.userName}
      <img alt="${x.publisherNickname|escape}" onerror="this.src=location.f40" class="cwd bdwa bdc0" src="${fn1(x.publisherUsername)}&r=${visitor.imageUpdateTime}"/>
      {else}
      <img alt="${x.publisherNickname|escape}" onerror="this.src=location.f40" class="cwd bdwa bdc0" src="${fn1(x.publisherUsername)}"/>
      {/if}
      </a>
      <div class="cwd vname thide">
        <a class="fc03 m2a"  target="_blank" hidefocus="true" href="http://blog.163.com/${x.publisherUsername}/">
          ${fn(x.publisherNickname,8)|escape}
        </a>
      </div>
      <a class="f-myLikeIcons hottype {if x.type==1} js-liketype{elseif x.type==2} js-reblogtype{elseif x.type==3} js-sharetype{else}{/if}" target="_blank" hidefocus="true" href="http://blog.163.com/${x.publisherUsername}/"> </a>
    </div>
    {/if}
    {/list}

<#-- 网易新闻广告 --> <#--右边模块结构--> <#--评论模块结构--> <#--引用模块结构--> <#--博主发起的投票-->

页脚

我的照片书 - 手机博客 - 下载LOFTER APP - 订阅此博客

7812032 的博客

导航

日志

【原创】数学篇（W）——又一个三角形中的几何不等式猜想

历史上的今天

最近读者

热度

评论

页脚