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<!DOCTYPE html><html lang="zh-CN" data-theme="light"><head><meta charset="UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width,initial-scale=1"><title>czp001的小站 - 却道天凉好个秋！</title><meta name="author" content="czp001"><meta name="copyright" content="czp001"><meta name="format-detection" content="telephone=no"><meta name="theme-color" content="#ffffff"><meta name="description" content="中二少年">
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class="article-meta__categories" href="/categories/Mathematica/">Mathematica</a></span><span class="article-meta tags"><span class="article-meta__separator">|</span><i class="fas fa-tag"></i><a class="article-meta__tags" href="/tags/%E7%BB%98%E5%9B%BE/">绘图</a><span class="article-meta__link">•</span><a class="article-meta__tags" href="/tags/Mathematica/">Mathematica</a></span></div><div class="content">
画一个大苹果🍎
参数方程如下
{x=cos(u)(cos(v)+1)+0.085cos(5u)y=(1+cos(u))sin(u)z=−0.7log(1−vπ)+6sin(v)+2cos(v) \begin{cases}
x=\cos (u) (\cos (v)+1)+0.085 \cos (5 u) \\
y = (1 + \cos (u)) \sin(u)\\
z=-0.7 \log \left(1-\frac{v}{\pi }\right)+6 \sin (v)+2 \cos (v)
\end{cases}
⎩⎨⎧x=cos(u)(cos(v)+1)+0.085cos(5u)y=(1+cos(u))sin(u)z=−0.7log(1−πv)+6sin(v)+2cos(v)
u,v∈[−π,π]u,v\in [-\pi ,\pi ]
u,v∈[−π,π]
Mathematica代码
12345ParametricPlot3D[{(1 + Cos[v]) Cos[u] + 0.08 ...</div></div></div><div class="recent-post-item"><div class="post_cover right_radius"><a href="/2022/09/28/%E5%A4%A7%E9%BB%84%E9%B8%AD%E6%96%B9%E7%A8%8B/" title="大黄鸭方程"> <img class="post_bg" src= "/pic/loading.gif" data-lazy-src="/pic/math_cover9.jpg" onerror="this.onerror=null;this.src='/pic/404.webp'" alt="大黄鸭方程"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/09/28/%E5%A4%A7%E9%BB%84%E9%B8%AD%E6%96%B9%E7%A8%8B/" title="大黄鸭方程">大黄鸭方程</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2022-09-28T15:01:46.000Z" title="发表于 2022-09-28 23:01:46">2022-09-28</time></span><span class="article-meta"><span class="article-meta__separator">|</span><i class="fas fa-inbox"></i><a class="article-meta__categories" href="/categories/Mathematica/">Mathematica</a></span><span class="article-meta tags"><span class="article-meta__separator">|</span><i class="fas fa-tag"></i><a class="article-meta__tags" href="/tags/%E7%BB%98%E5%9B%BE/">绘图</a><span class="article-meta__link">•</span><a class="article-meta__tags" href="/tags/Mathematica/">Mathematica</a></span></div><div class="content">
今天来整一个大黄鸭！！！🦆
模特在此
需要动鼠标转一下坐标轴，否则鸭头会朝下，不好看
123SphericalPlot3D[Log[x] + Sin[y], {x, 0, 2 \[Pi]}, {y, 0, 2 \[Pi]}, Boxed -> False, PlotStyle -> Yellow, Mesh -> None, PlotPoints -> 30, Axes -> True, SphericalRegion -> True, AxesLabel -> {"x", "y", "z"}]
调整之后是这样子。这鸭子爱说话，嘴变长了😄
俯视，还挺圆润🦆
</div></div></div><div class="recent-post-item"><div class="post_cover left_radius"><a href="/2022/09/18/Python%E7%88%AC%E8%99%AB%E4%B8%8B%E8%BD%BDB%E7%AB%99UP%E4%B8%BB%E8%A7%86%E9%A2%91%E5%B0%81%E9%9D%A2/" title="Python爬虫下载B站UP主视频封面"> <img class="post_bg" src= "/pic/loading.gif" data-lazy-src="/pic/math_cover9.jpg" onerror="this.onerror=null;this.src='/pic/404.webp'" alt="Python爬虫下载B站UP主视频封面"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/09/18/Python%E7%88%AC%E8%99%AB%E4%B8%8B%E8%BD%BDB%E7%AB%99UP%E4%B8%BB%E8%A7%86%E9%A2%91%E5%B0%81%E9%9D%A2/" title="Python爬虫下载B站UP主视频封面">Python爬虫下载B站UP主视频封面</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2022-09-18T13:14:13.000Z" title="发表于 2022-09-18 21:14:13">2022-09-18</time></span><span class="article-meta"><span class="article-meta__separator">|</span><i class="fas fa-inbox"></i><a class="article-meta__categories" href="/categories/Python/">Python</a></span><span class="article-meta tags"><span class="article-meta__separator">|</span><i class="fas fa-tag"></i><a class="article-meta__tags" href="/tags/Python/">Python</a><span class="article-meta__link">•</span><a class="article-meta__tags" href="/tags/%E7%88%AC%E8%99%AB/">爬虫</a></span></div><div class="content">
有时候感觉B站视频的封面很好看，想要保存，但在网页中右键→检查，然后定位元素一张一张手动保存很麻烦。这时可以写一个Python爬虫程序进行批量下载
挑一个想要下载的UP主
我来随便选一个，嘿嘿就她了漫罗拉，来到她的首页，首页的网址最后的数字314480501是UP主的UID,这是个重要参数，后面会用到。点击投稿栏目会看到所有的视频。
定位我们需要的请求地址
我们需要的地址就是浏览器地址栏上这个简单的地址吗？https://space.bilibili.com/314480501/video,右键检查找到这个请求，看看返回了什么，在返回的html里搜索几个视频标题，搜索不到标题。
这说明这些视频信息可能是是动态加载的，我们把筛选切换到Fetch/XHR重新查看这些过滤后的请求。经过一番检查发现有一个search?开头的请求是我们要找的，请求地址是https://api.bilibili.com/x/space/arc/search?mid=314480501&ps=30&tid=0&pn=1&keyword=&order=pubdate& ...</div></div></div><div class="recent-post-item"><div class="post_cover right_radius"><a href="/2022/08/23/%E7%88%B1%E5%BF%83%E6%96%B9%E7%A8%8B/" title="爱心方程"> <img class="post_bg" src= "/pic/loading.gif" data-lazy-src="/pic/math_cover1.webp" onerror="this.onerror=null;this.src='/pic/404.webp'" alt="爱心方程"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/08/23/%E7%88%B1%E5%BF%83%E6%96%B9%E7%A8%8B/" title="爱心方程">爱心方程</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2022-08-23T14:10:20.000Z" title="发表于 2022-08-23 22:10:20">2022-08-23</time></span><span class="article-meta"><span class="article-meta__separator">|</span><i class="fas fa-inbox"></i><a class="article-meta__categories" href="/categories/Mathematica/">Mathematica</a></span><span class="article-meta tags"><span class="article-meta__separator">|</span><i class="fas fa-tag"></i><a class="article-meta__tags" href="/tags/%E7%BB%98%E5%9B%BE/">绘图</a><span class="article-meta__link">•</span><a class="article-meta__tags" href="/tags/Mathematica/">Mathematica</a></span></div><div class="content">
说起❤爱心方程，大家最熟悉的应该是笛卡尔的心形线。方程千变万化，爱心方程也有很多种，我搜集了一些，有的也做了一些变化，一起来看看吧！
笛卡尔心形线
这是大家最熟悉的一种了，图中 a=3a=3a=3
ρ=a(1−cos(θ)),θ∈[0,2π]\rho =a (1-\cos (\theta )),\theta \in [0,2 \pi ]
ρ=a(1−cos(θ)),θ∈[0,2π]
1PolarPlot[3 (1 - Cos[\[Theta]]), {\[Theta], 0, 2 \[Pi]}]
带绝对值的二次方程
xxx不带绝对值的话，是一个倾斜的椭圆，加了之后图形关于yyy轴对称了，下半部分还削掉了两块
x2−y∣x∣+y2−1=0x^2-y \left| x\right|+y^2-1=0
x2−y∣x∣+y2−1=0
1ContourPlot[x^2 - Abs[x]*y + y^2 - 1 == 0, {x, -2, 2}, {y, 2, -2}]
加点变化
1234ContourPlot[{x^ ...</div></div></div><div class="recent-post-item"><div class="post_cover left_radius"><a href="/2022/08/18/%E7%9F%B3%E5%A2%A8%E7%83%AF%E5%88%86%E5%AD%90%E7%BB%93%E6%9E%84/" title="石墨烯分子结构"> <img class="post_bg" src= "/pic/loading.gif" data-lazy-src="/pic/math_cover3.webp" onerror="this.onerror=null;this.src='/pic/404.webp'" alt="石墨烯分子结构"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/08/18/%E7%9F%B3%E5%A2%A8%E7%83%AF%E5%88%86%E5%AD%90%E7%BB%93%E6%9E%84/" title="石墨烯分子结构">石墨烯分子结构</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2022-08-18T15:03:08.000Z" title="发表于 2022-08-18 23:03:08">2022-08-18</time></span><span class="article-meta"><span class="article-meta__separator">|</span><i class="fas fa-inbox"></i><a class="article-meta__categories" href="/categories/Mathematica/">Mathematica</a></span><span class="article-meta tags"><span class="article-meta__separator">|</span><i class="fas fa-tag"></i><a class="article-meta__tags" href="/tags/%E7%BB%98%E5%9B%BE/">绘图</a><span class="article-meta__link">•</span><a class="article-meta__tags" href="/tags/Mathematica/">Mathematica</a></span></div><div class="content">
慢慢开始更新吧，今天收到一个问题：画一个平面石墨烯的分子结构。
画法还是很自然的，先画一个正六边形，然后把点换成小球，把边换成管子，在Mathematica里可以用Ball和Tube函数，然后用Translate函数把这个图形单元做平移变换。
代码如下,unitHexagon是六边形单元，可以指定边和点的颜色
12345678910unitHexagon[colorhexa_, coloratom_] := {colorhexa, Tube[Table[{Cos[n Pi/3], Sin[n Pi/3], 0}, {n, 7}], 0.1], coloratom, Ball[#, 0.3] & /@ Table[{Cos[n Pi/3], Sin[n Pi/3], 0}, {n, 6}]};pts[x_, y_] := Block[{j, k}, Flatten[Table[{{3 (j + 1/2), Sqrt[ ...</div></div></div><div class="recent-post-item"><div class="post_cover right_radius"><a href="/2022/04/16/%E6%96%B0%E6%96%87%E7%AB%A0%E6%B5%8B%E8%AF%95/" title="新文章测试"> <img class="post_bg" src= "/pic/loading.gif" data-lazy-src="/pic/math_cover9.jpg" onerror="this.onerror=null;this.src='/pic/404.webp'" alt="新文章测试"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/04/16/%E6%96%B0%E6%96%87%E7%AB%A0%E6%B5%8B%E8%AF%95/" title="新文章测试">新文章测试</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">发表于</span><time datetime="2022-04-15T18:34:12.000Z" title="发表于 2022-04-16 02:34:12">2022-04-16</time></span><span class="article-meta"><span class="article-meta__separator">|</span><i class="fas fa-inbox"></i><a class="article-meta__categories" href="/categories/%E6%B5%8B%E8%AF%95/">测试</a></span><span class="article-meta tags"><span class="article-meta__separator">|</span><i class="fas fa-tag"></i><a class="article-meta__tags" href="/tags/%E6%B5%8B%E8%AF%95/">测试</a></span></div><div class="content">测试文章
测试abcd
分割线
数学表达式
求tan(x)\tan (x)tan(x),可以用
tan(x)=sin(x)cos(x)\tan (x)=\frac{\sin (x)}{\cos (x)}
tan(x)=cos(x)sin(x)
或者这个
tan(x)=∑x=1∞(−1)n−122n(22n−1)B2nx2n−1(2n)!\tan (x)=\sum _{x=1}^{\infty } \frac{(-1)^{n-1} 2^{2 n} \left(2^{2 n}-1\right) B_{2 n} x^{2 n-1}}{(2 n)!}
tan(x)=x=1∑∞(2n)!(−1)n−122n(22n−1)B2nx2n−1
其中B2nB_{2 n}B2n为伯努利数。B2nB_{2 n}B2n和1cos(x)\frac{1}{\cos (x)}cos(x)1都用多项式求逆来做。
24=0.52c+2d+24=a\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
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