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helicoid

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helicoid
helicoid, a. and n. (ˈhɛlɪkɔɪd) Also 7 -oeid. [mod. ad. Gr. ἑλικοειδής of winding or spiral form, f. ἕλιξ helix + εἶδος shape: see -oid. Cf. F. hélicoïde (1704 in Hatz.-Darm.).] A. adj. 1. Having the form of a helix; screw-shaped; spiral. Chiefly in Zool. of shells, and in Bot. of forms of infloresc... Oxford English Dictionary
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Isotropic helicoid
An isotropic helicoid is a shape that is helical, so it rotates as it moves through a fluid, and yet is isotropic, so that its rotation and drag are the wikipedia.org
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Generalized helicoid
One gets a helicoid (closed right ruled generalized helicoid). (2) The line intersects the axis, but not orthogonally. , S. 47 mathcurve.com: circular generalized helicoid mathcurve.com: developable generalized helicoid mathcurve.com: ruled generalized helicoid K3Dsurf: wikipedia.org
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helicoidly
ˈhelicoidly, adv. [f. helicoid a. + -ly2.] In a helicoid manner, spirally.1849 Dana Geol. App. i. (1850) 720 A fusiform chamber helicoidly divided. Oxford English Dictionary
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Opens of helicoid and catenoid Helicoid (H) and Catenoid (C) are locally isometrics. It means that there is a locally diffeomorphims $\phi: U \subset H \longrightarrow V\subset C$ such that $\left<d\phi_{p}(w_{1}), d\...
Whether two surfaces are locally isometric is an intrinsic question: There is a local diffeomorphism that preserves the _first_ fundamental form. This says nothing about the extrinsic geometry, i.e., the Gauss map or the second fundamental form. Thus, we expect no relation between the lines of curva...
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Catenoid
Helicoid transformation Because they are members of the same associate family of surfaces, one can bend a catenoid into a portion of a helicoid without corresponds to a catenoid, and corresponds to a left-handed helicoid. wikipedia.org
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Calculate the area of ​the helicoid defined by the image of $\phi:D\subset \mathbb{R}\to \mathbb{R}^3$; $\phi (u, v) = (u (\cos v), u (\sin v), v)$ **Calculate the area of ​​the helicoid defined by the image of $\phi:...
Your surface area element $\mathrm d A$ is wrong. The area of a paramerized surface surface $\phi:D\to \mathbb{R}^3$ is defined as $$ A(\phi) = \int_{\phi(D)} \, \mathrm dA = \iint_D |\phi_u \times \phi_v| \, \mathrm du\, \mathrm dv. $$ We have $$ \mathrm d\phi = \begin{pmatrix}\phi_u & \phi_v\end{p...
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Is my proof of showing a helicoid and catenoid are isometric, correct? This is the question I have: Let $S$ denote the surface of revolution $$(x,y,z)=(\cos\theta \cosh v, \sin \theta \cosh v, v)$$ $0 < \theta < 2 \p...
Finding surface of revolution isometric to helicoid <
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Right conoid
Other right conoids include: Helicoid: Whitney umbrella: Wallis's conical edge: Plücker's conoid: hyperbolic paraboloid: (with x-axis and y-axis as See also Conoid Helicoid Whitney umbrella Ruled surface External links Right Conoid from MathWorld. wikipedia.org
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How to calculate a surface integral on a helicoid? I have to calculate $$\iint_S \sqrt{x^2+y^2} \,dx\,dy$$ where $S$ is a 3-D helicoidal surface defined by : \begin{align} x&=3v\cos(\theta)\\\ y&=3v\sin(\theta)\\\ z&...
You have the parametrization $r(v,\theta)=(3vcos(\theta),3vsin(\theta),2\theta)$. Now by simple calculation: $r_v=(3cos(\theta),3sin(\theta),0)$ $r_\theta=(-3vsin(\theta),3vcos(\theta),2)$ Now you need to calculate the cross product of the vectors $r_v\times r_\theta$. Also note that $\sqrt{x^2+y^2}...
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Translation surface (differential geometry)
Its parametric representation is (MCS) Helicoid as translation surface and midchord surface A helicoid is a special case of a generalized helicoid The helicoid with the parametric representation has a turn around shift (German: Ganghöhe) . wikipedia.org
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Minimal surfaces and gaussian and normal curvaturess If $M$ is the surface $$x(u^1,u^2) = (u^2\cos(u^1),u^2\sin(u^1), p\,u^1)$$ then I am trying to show that $M$ is minimal. $M$ is referred to as a helicoid. Also I a...
Note that $$x_{1}=\frac{\partial x}{\partial u^1}=(-u^2\sin(u^1),u^2\cos(u^1),p)$$ and $$x_{2}=\frac{\partial x}{\partial u^2}=(\cos(u^1),\sin(u^1),0).$$ This implies that the unit normal is given by $$x_1\times x_2=(-p\sin(u^1),p\cos(u^1),-u^2)$$ which implies that $$n=\frac{x_1\times x_2}{\|x_1\ti...
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螺旋曲面
描述 螺旋曲面曾在1774年及1776年分别由莱昂哈德·欧拉及Jean Baptiste Meusnier描述过，其英文Helicoid可以看出它和螺旋线（helix）之间的相关性：针对螺旋曲面上的每一点，都存在一个通过该点的螺旋线，且整条螺旋线都落在螺旋曲面上。 相关条目 直纹曲面 参考资料 外部连结 Interactive 3D Helicoid plotter using Processing (with code) WebGL-based Interactive 3D Helicoid 几何形状 极小曲面 曲面 wikipedia.org
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国际数学界是怎样识别人才的？
他发现了一种新的极小曲面，是平面，helicoid, catenoid 之后第一个有有限拓扑（有限同调群）的嵌入极小曲面——这里需要指出一下，他发现这个例子的时候并没有能够证明它是嵌入曲面。这种工作绝对可以中Annals的，可你看看他投了个什么杂志。。Bol. Soc. Bras. Mat. zhihu
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Two surfaces are not isometries of each other, but have the same Gaussian Curvature How can you show that two surfaces are not isometries of each other, but have the same Gaussian Curvature. For example, I see that: ...
Great question. Note that the reparametrization would have to leave the $s$-curves the same (so that the curvature functions match up). But this means we'd need to have the $E$s matching for the two surfaces, which we obviously don't.
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