悠闲数学娱乐论坛(第2版) » Mathematica » 皮亚诺曲线怎么画

isee 发表于 2018-11-30 20:18

皮亚诺曲线怎么画

Rt

isee 发表于 2018-11-30 20:19

[url]https://blog.csdn.net/stereohomology/article/details/51105531[/url]

isee 发表于 2018-11-30 20:23

莫比乌斯环

[url]https://blog.csdn.net/Quant19861127/article/details/43156011?utm_source=blogxgwz1[/url]

色k 发表于 2018-11-30 20:34

完全看8懂……[img]https://qzonestyle.gtimg.cn/qzone/em/e246.gif[/img]

isee 发表于 2018-11-30 21:36

[b]回复 [url=http://kuing.orzweb.net/redirect.php?goto=findpost&pid=28986&ptid=5764]4#[/url] [i]色k[/i] [/b]


转载是专业搞代码的，我拿就用。。。要求不高，，，肯定是看不懂的，我。

hbghlyj 发表于 2022-2-11 23:38

[i=s] 本帖最后由 hbghlyj 于 2022-2-12 00:17 编辑 [/i]

[b]回复 [url=http://kuing.orzweb.net/redirect.php?goto=findpost&pid=28987&ptid=5764]5#[/url] [i]isee[/i] [/b]
如何理解Möbius环的参数方程$\huge\unicode{x1F62E}$
\begin{align*}x(u,v)&=\left(1+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\cos u\\y(u,v)&=\left(1+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\sin u\\z(u,v)&={\frac {v}{2}}\sin {\frac {u}{2}}\\\end{align*}for $0\leq u<2\pi$ and $-1\leq v\leq 1$. This produces a Möbius strip of width 1, whose center circle has radius 1, lies in the $xy$-plane and is centered at (0,0,0). The parameter $u$ runs around the strip while $v$ moves from one edge to the "other".
当$u=0$时得到的参数曲线$\left(1+\frac v2,0,0\right)$是从$\left(\frac12,0,0\right)$到$\left(\frac32,0,0\right)$的$x$轴上的一条线段.
当$u=2π$时得到的参数曲线$\left(1-\frac v2,0,0\right)$是从$\left(\frac32,0,0\right)$到$\left(\frac12,0,0\right)$的$x$轴上的一条线段.
所以说这是两条线段反向粘在一起了!
[img]https://plus.maths.org/issue26/features/mathart/Twist.gif[/img]
当$u=π$时得到的参数曲线$\left(-1,0,\frac v2\right)$是从$\left(-1,0,\frac12\right)$到$\left(-1,0,-\frac12\right)$的平行于$z$轴的一条线段.
当$v=0$时得到的参数曲线$\left(\cos u,\sin u,0\right)$是$xy$-平面上的圆.

hbghlyj 发表于 2022-2-11 23:40

切1刀变成一条普通纸带(两面,用粉色和蓝色标记)<br>
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hbghlyj 发表于 2022-2-11 23:42

[i=s] 本帖最后由 hbghlyj 于 2022-2-11 23:53 编辑 [/i]

切两刀变成1条普通纸带(两面,用粉色和蓝色标记),和1个Möbius环(紫色):<br><?xml version="1.0" encoding="UTF-8"?>
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hbghlyj 发表于 2022-2-12 00:12

[i=s] 本帖最后由 hbghlyj 于 2022-2-12 00:19 编辑 [/i]

[url=https://blog.csdn.net/weixin_35107023/article/details/112329780]这里[/url]有一个推导
[url=https://plus.maths.org/content/os/issue26/features/mathart/index]plus.maths.org[/url]

hbghlyj 发表于 2022-2-19 05:18

[i=s] 本帖最后由 hbghlyj 于 2022-2-19 05:25 编辑 [/i]

[url=https://sites.google.com/view/enigmaths/surfaces/mobius]这里[/url]有一个隐式方程$$\large{(-0.99(x(x^2+y^2-z^2+1)-2yz)-2.03(x^2+y^2))^2=(x^2+y^2)(1.01(x^2+y^2+z^2+1)-1.98(yz-x))^2}$$
[attach]11096[/attach]

hbghlyj 发表于 2022-2-24 10:40

[i=s] 本帖最后由 hbghlyj 于 2022-2-24 02:45 编辑 [/i]

[code]ContourPlot3D[x^2 y + y^3 + 2 x^2 z + 2 y^2 z + y z^2 == 0, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}][/code][attach]11113[/attach][code]ParametricPlot3D[{(-t Sin[θ/2]) Cos[θ], (-t Sin[θ/2]) Sin[θ],t Cos[θ/2]}, {t, -1, 1}, {θ, 0, 2 Pi}][/code][attach]11114[/attach]
z=1平面截线:$$x^{2}y+y^{3}+2x^{2}+2y^{2}+y=0$$
[url]https://math.stackexchange.com/questions/1601718/integrating-a-density-over-a-mobius-strip?rq=1[/url]

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