<!doctype html>
<html class="no-js" lang="en">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>
解题 - 语时lab
</title>
<link href="atom.xml" rel="alternate" title="语时lab" type="application/atom+xml">
<link rel="stylesheet" href="asset/css/foundation.min.css" />
<link rel="stylesheet" href="asset/css/docs.css" />
<script src="asset/js/vendor/modernizr.js"></script>
<script src="asset/js/vendor/jquery.js"></script>
<script src="asset/highlightjs/highlight.pack.js"></script>
<link href="asset/highlightjs/styles/github.css" media="screen, projection" rel="stylesheet" type="text/css">
<script>hljs.initHighlightingOnLoad();</script>
<script type="text/javascript">
function before_search(){
var searchVal = 'site:cshishaliu.github.io ' + document.getElementById('search_input').value;
document.getElementById('search_q').value = searchVal;
return true;
}
</script>
</head>
<body class="antialiased hide-extras">
<div class="marketing off-canvas-wrap" data-offcanvas>
<div class="inner-wrap">
<nav class="top-bar docs-bar hide-for-small" data-topbar>
<section class="top-bar-section">
<div class="row">
<div style="position: relative;width:100%;"><div style="position: absolute; width:100%;">
<ul id="main-menu" class="left">
<li id=""><a target="_self" href="index.html">Home</a></li>
<li id=""><a target="_self" href="book.html">Books</a></li>
<li id=""><a target="_self" href="links.html">Links</a></li>
<li id=""><a target="_self" href="archives.html">Archives</a></li>
<li id=""><a target="_self" href="about.html">About</a></li>
<li id=""><a target="_self" href="todo.html">Todo</a></li>
</ul>
<ul class="right" id="search-wrap">
<li>
<form target="_blank" onsubmit="return before_search();" action="https://google.com/search" method="get">
<input type="hidden" id="search_q" name="q" value="" />
<input tabindex="1" type="search" id="search_input" placeholder="Search"/>
</form>
</li>
</ul>
</div></div>
</div>
</section>
</nav>
<nav class="tab-bar show-for-small">
<a href="javascript:void(0)" class="left-off-canvas-toggle menu-icon">
<span> 语时lab</span>
</a>
</nav>
<aside class="left-off-canvas-menu">
<ul class="off-canvas-list">
<li><a target="_self" href="index.html">Home</a></li>
<li><a target="_self" href="book.html">Books</a></li>
<li><a target="_self" href="links.html">Links</a></li>
<li><a target="_self" href="archives.html">Archives</a></li>
<li><a target="_self" href="about.html">About</a></li>
<li><a target="_self" href="todo.html">Todo</a></li>
<li><label>Categories</label></li>
<li><a href="problemsolving.html">解题</a></li>
<li><a href="mathpost.html">数学随笔</a></li>
<li><a href="Dev.html">Dev</a></li>
<li><a href="Games.html">Games</a></li>
<li><a href="obsolete.html">obsolete</a></li>
<li><a href="misc.html">misc</a></li>
</ul>
</aside>
<a class="exit-off-canvas" href="#"></a>
<section id="main-content" role="main" class="scroll-container">
<script type="text/javascript">
$(function(){
$('#menu_item_index').addClass('is_active');
});
</script>
<div class="row">
<div class="large-8 medium-8 columns">
<div class="markdown-body home-categories">
<div class="article">
<a class="clearlink" href="15863333927200.html">
<h1>数列不等式 `lhc@jinan|20200407`</h1>
<div class="a-content">
<div class="a-content-text">
<p>已知数列 \(\{a_n\}\) 满足 \(a_1 = 1\), \(a_n a_{n+1} = n\), \(n = 1,2,3,\dots\). 求证: <br/>
\[<br/>
\frac1{a_1} + \frac1{a_2} + \frac1{a_3} + \dots + \frac1{a_n} \ge 2 \sqrt n - 1.<br/>
\]</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15863333927200.html">Read more</a>
<span class="date">2020/04/08</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15840603466913.html">
<h1>二元有理函数最值</h1>
<div class="a-content">
<div class="a-content-text">
<p>已知 \(x,y > 0\), 求 <br/>
\[<br/>
\frac{(2x+1) (y+1)}{2x^2 + 5y^2 + 7}<br/>
\]<br/>
的最大值.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15840603466913.html">Read more</a>
<span class="date">2020/03/13</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15490078791835.html">
<h1>两个数列不等式问题</h1>
<div class="a-content">
<div class="a-content-text">
<ol>
<li>已知实数 \(x_1, x_2, \dots, x_{10}\), \(\sum\limits_{k=1}^{10} k x_k = 1\). 求 \(\left( \sum\limits_{k=1}^{10} x_k \right)^2 + \sum\limits_{k=1}^{10} x_k^2\) 的最小值.</li>
<li>设 \(a_n = 1 + \dfrac12 + \dfrac13 + \dots + \dfrac1n\). 求证: 对 \(n\ge 2\) 有 \(a_n^2 < 2 \left( \dfrac{a_2}2 + \dfrac{a_3}3 + \dots \dfrac{a_n}n \right) + \dfrac{n+3}{2n+2}\).</li>
</ol>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15490078791835.html">Read more</a>
<span class="date">2019/02/01</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15421980305249.html">
<h1>CMO 2018 题 3</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 微博图床已挂, 本篇缺图, 需要找回</mark></p>
<p>\(\triangle ABC\) 中, \(AB < AC\), \(O\) 为外心, \(D\) 是 \(\angle BAC\) 平分线上一点, \(E\) 在 \(BC\) 上, 满足 \(OE \parallel AD\), \(DE \perp BC\). 在射线 \(EB\) 上取点 \(K\) 满足 \(EK = EA\), \(\triangle ADK\) 外接圆与 \(BC\) 交于另一点 \(P \ne K\), \(\triangle ADK\) 外接圆与 \(\triangle ABC\) 外接圆交于另一点 \(Q \ne A\). 求证: \(PQ\) 与 \(\triangle ABC\) 外接圆相切.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15421980305249.html">Read more</a>
<span class="date">2018/11/14</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15395877048195.html">
<h1>两个二次函数问题</h1>
<div class="a-content">
<div class="a-content-text">
<ol>
<li>已知二次函数 \(f(x) = a x^2 + b x + c\) 的图象过点 \((2,8)\), 且对一切实数 \(x\) 恒有 \(2x + 3 \le f(x) \le 2x^2 - 2x + 5\), 求 \(f(x)\).</li>
<li>在平面直角坐标系中, 不论 \(m\) 取何值时, 抛物线 \(y = mx^2 + (2m+1) x - (3m+2)\) 都不通过的直线 \(y = -x+1\) 上的点有哪些? (写出全部符合条件点的坐标)</li>
</ol>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15395877048195.html">Read more</a>
<span class="date">2018/10/15</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15348999728702.html">
<h1>伪装成函数方程的数论问题</h1>
<div class="a-content">
<div class="a-content-text">
<p>已知函数 \(f(x,y)\) 定义在正整数集上, 满足 \(\forall x,y \in \mathbb N^*\),</p>
<ol>
<li>\(f(x,x) = x\),</li>
<li>\(f(x,y) = f(y,x)\),</li>
<li>\((x+y) \cdot f(x,y) = y \cdot f(x, x+y)\).</li>
</ol>
<p>求证: \(f(x,y) = [x,y]\) (这里, \([x,y]\) 表示 \(x\) 与 \(y\) 的最小公倍数).</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15348999728702.html">Read more</a>
<span class="date">2018/08/22</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15337076183356.html">
<h1>二次根式化简</h1>
<div class="a-content">
<div class="a-content-text">
<p>计算:<br/>
\[<br/>
\dfrac{<br/>
1 + \sqrt{2-\sqrt2} + \sqrt{2-\sqrt3}<br/>
}{<br/>
\sqrt3 + \sqrt{2+\sqrt2} + \sqrt{2+\sqrt3}<br/>
}<br/>
\]</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15337076183356.html">Read more</a>
<span class="date">2018/08/08</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15331333919370.html">
<h1>liujihang 20180801</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 微博图床已挂, 本篇缺图, 需要找回</mark></p>
<p>无穷数列 \(P \colon a_1, a_2, \dots, a_n, \dots\) 满足 \(a_i \in \mathbb N^*\), 且 \(a_i \le a_{i+1}\) (\(i\in \mathbb N^*\)). 对于数列 \(P\), 记 \(T_k (P) = \min \{ n | a_n \ge k \}\) (\(k\in \mathbb N^*\)), 其中 \(\min \{ n | a_n \ge k \}\) 表示集合 \(\{ n | a_n \ge k \}\) 中最小的数.</p>
<ol>
<li>若数列 \(P\colon 1,3,4,7,\dots\), 写出 \(T_1(P), T_2(P), \dots, T_5(P)\);</li>
<li>若 \(T_k (P) = 2k-1\), 求数列 \(P\) 的前 \(n\) 项之和;</li>
<li>已知 \(a_{20} = 46\), 求 \(s = a_1 + a_2 + \dots + a_{20} + T_1 (P) + T_2 (P) + \dots + T_{46} (P)\) 的值.</li>
</ol>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15331333919370.html">Read more</a>
<span class="date">2018/08/01</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15327863271008.html">
<h1>不动点为复数值的递推数列问题</h1>
<div class="a-content">
<div class="a-content-text">
<p>正数数列 \(\{a_n\}\) 满足 \(S_n + 1 = \dfrac{S_n+4}{2a_n - S_n}\), 其中 \(S_n\) 是 \(\{a_n\}\) 的前 \(n\) 项和, 求 \(\{a_n\}\) 的通项公式.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15327863271008.html">Read more</a>
<span class="date">2018/07/28</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15288852882913.html">
<h1>三角不等式/极值问题</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 本题确认伪证了</mark></p>
<p>已知 \(A,B,C\) 为三角形三内角. 求 \(\dfrac{\cos^2 A}{1+\cos A} + \dfrac{\cos^2 B}{1+\cos B} + \dfrac{\cos^2 C}{1+\cos C}\) 的最小值.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15288852882913.html">Read more</a>
<span class="date">2018/06/13</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15265462412456.html">
<h1>一组高中联赛二试模拟/选拔题 `zhangboxin|20180516`</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 微博图床已挂, 本篇缺图, 需要找回</mark></p>
<p><mark>TODO: 本篇内容也还没完成</mark></p>
<p>这是二试难度的问题 (rdfz 20180516 高联选拔题)</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15265462412456.html">Read more</a>
<span class="date">2018/05/17</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15238569346799.html">
<h1>Poncelet 定理: 圆和抛物线 `zhangboxin|20180409`</h1>
<div class="a-content">
<div class="a-content-text">
<p>已知圆 \(C_1 \colon x^2+y^2 = 1\) 和抛物线 \(C_2 \colon y = x^2 - 2\). \(P,Q,R\) 是抛物线 \(C_2\) 上的三个不同的点, 且直线 \(PQ\) 和 \(PR\) 都是圆 \(C_1\) 的切线. 求证: \(QR\) 也是圆 \(C_1\) 的切线.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15238569346799.html">Read more</a>
<span class="date">2018/04/16</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15166882779923.html">
<h1>平面几何 `duyan|20180123|2`</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 微博图床已挂, 本篇缺图, 需要找回</mark></p>
<p>已知 \(H\) 为 \(\triangle ABC\) 的垂心, 过 \(H\) 的直线交 \(BC, AB\) 于 \(D,Z\), 过 \(H\) 且垂直于 \(ZH\) 的另一条直线交 \(BC, AC\) 于 \(E,X\), 点 \(Y\) 使得 \(DY \parallel AC, EY \parallel AB\). 求证: \(X,Y,Z\) 三点共线.</p>
<p><img src="https://ws2.sinaimg.cn/large/006tKfTcly1fnqjnu4ou9j30iu0h7js7.jpg" alt=""/></p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15166882779923.html">Read more</a>
<span class="date">2018/01/23</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15166821516457.html">
<h1>USAMO19xx #5, 高斯函数, 不等式, 第二数学归纳法</h1>
<div class="a-content">
<div class="a-content-text">
<p>证明不等式: <br/>
\[<br/>
[nx] \ge \dfrac{[x]}1 + \dfrac{[2x]}2 + \dfrac{[3x]}3 + \dots +\dfrac{[nx]}n<br/>
\]<br/>
其中, \(n \in \mathbb N^*\), \([x]\) 表示不大于 \(x\) 的最大整数.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15166821516457.html">Read more</a>
<span class="date">2018/01/23</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15166754034002.html">
<h1>一道难度其实不大的平面几何长度计算类证明题 `zhangboxin|20171218`</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 微博图床已挂, 本篇缺图, 需要找回</mark></p>
<p>在 \(\triangle ABC\) 中, \(\angle A = 4 \angle C\), \(\angle B = 2 \angle C\), 试证: \((BC+CA) \cdot AB = BC \cdot CA\).</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15166754034002.html">Read more</a>
<span class="date">2018/01/23</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15116623932028.html">
<h1>一个常规的递推数列不动点法问题及其引申 `zhangzhiyuan|20171125`</h1>
<div class="a-content">
<div class="a-content-text">
<p><mark>TODO: 本文暴露出了我曾经的数学基础的弱点, 需要修改</mark></p>
<p>数列 \(\{a_n\}\) 满足 \(a_1 = 2\), \(a_{n+1} = \dfrac{a_n}2 + \dfrac1{a_n}\), 求其通项公式.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15116623932028.html">Read more</a>
<span class="date">2017/11/26</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15111000681752.html">
<h1>lixinyi 20171119</h1>
<div class="a-content">
<div class="a-content-text">
<p>已知函数 \(f(x) = \sqrt{x^2+1}-ax\) (\(a \in \mathbb R\)).</p>
<p>(1) 当 \(a=1\) 时, 判断 \(f(x)\) 在 \(\mathbb R\) 上的点调性;<br/>
(2) 求实数 \(a\) 的取值范围, 使得函数 \(f(x)\) 在 \(\mathbb R^+\) 上是单调函数.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15111000681752.html">Read more</a>
<span class="date">2017/11/19</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15107317542032.html">
<h1>libinglun 20171112</h1>
<div class="a-content">
<div class="a-content-text">
<p>设 \(p\) 和 \(q\) 是两个质数, 求不能表示为 \(mp + nq\) (其中, \(m,n\) 是自然数) 的最大正整数 (用 \(p\) 和 \(q\) 表示).</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15107317542032.html">Read more</a>
<span class="date">2017/11/15</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15088927359289.html">
<h1>组合极值/组合构造问题 `kongyuqing|20171024`</h1>
<div class="a-content">
<div class="a-content-text">
<p>100 个数围成一圈, \(a_{3} > a_{2} + a_{1}\), \(a_{4} > a_{3} + a_{2}\), \(\dots\) , \(a_{100} > a_{99} + a_{98}\), \(a_{1} > a_{100} + a_{99}\), \(a_{2} > a_{1} + a_{100}\), 问其中最多有多少个正数?</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15088927359289.html">Read more</a>
<span class="date">2017/10/25</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15078172804643.html">
<h1>递推数列推出组合数的问题 `duyan@bj#4|20171012`</h1>
<div class="a-content">
<div class="a-content-text">
<p>已知 \(S_n\) 为数列 \(\{a_n\}\) 的前 \(n\) 项和, 规定 \(S_0 = 0\), 若对任意 \(n \in \mathbb N^*\), 均有 \(\dfrac{a_n}{2017} = - \dfrac{2017+S_{n-1}}{n}\), 则 \(\sum\limits_{n=1}^{2017} 2^n a_n = \) <code>______</code>.</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15078172804643.html">Read more</a>
<span class="date">2017/10/12</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="article">
<a class="clearlink" href="15075145910644.html">
<h1>三圆轮换对称不等式问题 `mawentao|20170914`</h1>
<div class="a-content">
<div class="a-content-text">
<p><code>问题</code> \(a,b,c \ge 0\), 求证:<br/>
\[<br/>
\begin{aligned}<br/>
&\sqrt{a^2 - ab + b^2} \cdot \sqrt{b^2 - bc + c^2} \\<br/>
&{}+ \sqrt{b^2 - bc + c^2} \cdot \sqrt{c^2 - ca + a^2} \\<br/>
&{}+ \sqrt{c^2 - ca + a^2} \cdot \sqrt{a^2 - ab + b^2}<br/>
\ge a^2 + b^2 + c^2<br/>
\end{aligned}<br/>
\]</p>
</div>
</div>
</a>
<div class="read-more clearfix">
<div class="more-left left">
<a href="15075145910644.html">Read more</a>
<span class="date">2017/10/09</span>
<span>posted in </span>
<span class="posted-in"><a href='problemsolving.html'>解题</a></span>
</div>
<div class="more-right right">
<span class="comments">
</span>
</div>
</div>
</div><!-- article -->
<div class="row">
<div class="large-6 columns">
<p class="text-left" style="padding-top:25px;">
</p>
</div>
<div class="large-6 columns">
<p class="text-right" style="padding-top:25px;">
</p>
</div>
</div>
</div>
</div><!-- large 8 -->
<div class="large-4 medium-4 columns">
<div class="hide-for-small">
<div id="sidebar" class="sidebar">
<div id="site-info" class="site-info">
<div class="site-a-logo"><img src="https://i.loli.net/2020/02/26/hjpG5rStAgRYm9P.jpg" /></div>
<h1>语时lab</h1>
<div class="site-des">Gnoloac 发文的地方</div>
<div class="social">
<a target="_blank" class="weibo" href="https://weibo.com/gnoloac" title="weibo">Weibo</a>
<a target="_blank" class="github" target="_blank" href="https://github.com/cshishaliu" title="GitHub">GitHub</a>
<a target="_blank" class="email" href="mailto:cshishaliu@163.com" title="Email">Email</a>
<a target="_blank" class="rss" href="atom.xml" title="RSS">RSS</a>
</div>
</div>
<div id="site-categories" class="side-item ">
<div class="side-header">
<h2>Categories</h2>
</div>
<div class="side-content">
<p class="cat-list">
<a href="problemsolving.html"><strong>解题</strong></a>
<a href="mathpost.html"><strong>数学随笔</strong></a>
<a href="Dev.html"><strong>Dev</strong></a>
<a href="Games.html"><strong>Games</strong></a>
<a href="obsolete.html"><strong>obsolete</strong></a>
<a href="misc.html"><strong>misc</strong></a>
</p>
</div>
</div>
<div id="site-categories" class="side-item">
<div class="side-header">
<h2>Recent Posts</h2>
</div>
<div class="side-content">
<ul class="posts-list">
<li class="post">
<a href="15864160277643.html">平面几何的全等和相似符号到底该怎么写</a>
</li>
<li class="post">
<a href="15863333927200.html">数列不等式 `lhc@jinan|20200407`</a>
</li>
<li class="post">
<a href="15863166036092.html">如何判断复合根式是否可以进一步化简</a>
</li>
<li class="post">
<a href="15859891289445.html">Simon Tatham's Portable Puzzle Collection</a>
</li>
<li class="post">
<a href="book.html">Books</a>
</li>
</ul>
</div>
</div>
</div><!-- sidebar -->
</div><!-- hide for small -->
</div><!-- large 4 -->
</div><!-- row -->
<div class="page-bottom clearfix">
<div class="row">
<p class="copyright">Copyright © 2015
Powered by <a target="_blank" href="http://www.mweb.im">MWeb</a>,
Theme used <a target="_blank" href="http://github.com">GitHub CSS</a>.</p>
</div>
</div>
</section>
</div>
</div>
<script src="asset/js/foundation.min.js"></script>
<script>
$(document).foundation();
function fixSidebarHeight(){
var w1 = $('.markdown-body').height();
var w2 = $('#sidebar').height();
if (w1 > w2) { $('#sidebar').height(w1); };
}
$(function(){
fixSidebarHeight();
})
$(window).load(function(){
fixSidebarHeight();
});
</script>
<script src="asset/chart/all-min.js"></script><script type="text/javascript">$(function(){ var mwebii=0; var mwebChartEleId = 'mweb-chart-ele-'; $('pre>code').each(function(){ mwebii++; var eleiid = mwebChartEleId+mwebii; if($(this).hasClass('language-sequence')){ var ele = $(this).addClass('nohighlight').parent(); $('<div id="'+eleiid+'"></div>').insertAfter(ele); ele.hide(); var diagram = Diagram.parse($(this).text()); diagram.drawSVG(eleiid,{theme: 'simple'}); }else if($(this).hasClass('language-flow')){ var ele = $(this).addClass('nohighlight').parent(); $('<div id="'+eleiid+'"></div>').insertAfter(ele); ele.hide(); var diagram = flowchart.parse($(this).text()); diagram.drawSVG(eleiid); } });});</script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-AMS_SVG-full"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({TeX: { equationNumbers: { autoNumber: "AMS" } }});</script>
</body>
</html>