Artificial intelligent assistant

tractrix

answer Answers

ProphetesAI is thinking...

MindMap

Sources

1
tractrix
‖ tractrix Geom. (ˈtræktrɪks) Pl. ˈtractrices (-ɪsiːz). [mod.L. (Huygens) fem. of tractor: see tractor, and cf. directrix.] A curve such that the intercept on the tangent between its point of contact and a fixed straight line is constant; so called as being traced by the centre of gyration of a rigi... Oxford English Dictionary
prophetes.ai 0.0 3.0 0.0
2
Antaeotricha tractrix
Antaeotricha tractrix is a moth in the family Depressariidae. It was described by Edward Meyrick in 1925. It is found in Brazil. References Moths described in 1925 tractrix Moths of South America wikipedia.org
en.wikipedia.org 0.0 1.5 0.0
3
Syntractrix
A syntractrix is a curve of the form It is the locus of a point on the tangent of a tractrix at a constant distance from the point of tangency, as the wikipedia.org
en.wikipedia.org 0.0 0.90000004 0.0
4
tractatrix
‖ tractatrix (trækˈteɪtrɪks) Pl. -trices (-trɪsiːz). [L. tractātrix (Martial, in sense 1), fem. of tractātor shampooer, also one who treats of a subject: see tractator.] 1. A female shampooer. rare—1.1874 M. Collins Frances II. 117 That stout Miss Susanetta, with her shrill voice, and her hands of t... Oxford English Dictionary
prophetes.ai 0.0 0.6 0.0
5
syntractrix
‖ syntractrix Geom. (sɪnˈtræktrɪks) [mod.L., f. syn-1 + tractrix.] The locus of a point on the tangent to a tractrix at a constant distance from its intersection with the axis. Also synˈtractory [tractory n. 3].1820 G. Peacock Examples Diff. Calc. i. xxiii. 175 Syntractory. 1852 G. Salmon Higher Pla... Oxford English Dictionary
prophetes.ai 0.0 0.6 0.0
6
Evolute of a Catenary Ref of evolute of catenary Evolute of a Tractrix is a Catenary. What is the evolute of a Catenary? Sketched by Leonardo DaVinci Page 3, Fig 2. EDIT1: and also on Page 23, Fig 8. DaVinci_Last...
I actually disagree with the mathworld answer. If you take the simplest case ($a=1$), the catenary is $\alpha(t)=(t,\cosh t)$. The general formula for the evolute of a plane curve is $$\beta(t) = \alpha(t) + \frac1{\kappa(t)}N(t),$$ where $N$ is the principal normal. For the catenary, we calculate t...
prophetes.ai 0.0 0.3 0.0
7
Pseudosphere
Tractroid The same surface can be also described as the result of revolving a tractrix about its asymptote. The precise mapping is where is the parametrization of the tractrix above. wikipedia.org
en.wikipedia.org 0.0 0.3 0.0
8
Tractrix tangent segment (from Baby Do-Carmo) I need some help with question 4 in section 1.3 in Baby Do-Carmo textbook in DG. The question asks: Let $\alpha(t):(0,\pi)\rightarrow R^2 $ be given by: $$ \alpha(t)= (\c...
You can find the tangent line of a curve at a point $\alpha(t)=(\alpha_1(t),\alpha_2(t))$ by the formula $$ \det\begin{pmatrix} X-\alpha_1(t) & \alpha_1'(t) \\\ Y-\alpha_2(t) & \alpha_2'(t)\end{pmatrix} $$ (for the sake of completeness, with your curve it is the locus of $(X,Y)$ such that $-\sin t \...
prophetes.ai 0.0 0.3 0.0
9
1692 in science
Mathematics The tractrix, sometimes called a tractory or equitangential curve, is first studied by Christiaan Huygens, who gives it its name. wikipedia.org
en.wikipedia.org 0.0 0.3 0.0
10
Prove that the evolute of the tractrix $x=a(\cos t+\log \tan\frac{t}{2}),y=a\sin t$ is the catenary $y=a\cosh (\frac{x}{a})$ Prove that the evolute of the tractrix $x=a(\cos t+\log \tan\frac{t}{2}),y=a\sin t$ is the c...
I'm going to use this parametric equation for a tractrix: $x(t)=a(t-\tanh t)$, $y(t)= a \text{ sech } x $ The general formula for an evolute is $$X[x
prophetes.ai 0.0 0.3 0.0
11
Dini's surface
is named after Ulisse Dini and described by the following parametric equations: Another description is a generalized helicoid constructed from the tractrix wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
12
tractory
tractory, a. and n. rare. (ˈtræktərɪ) [ad. L. tractōri-us of or for drawing, f. tract-, ppl. stem of trahĕre to draw: see -ory.] † A. adj. Serving for traction; tractive. Obs.1684 tr. Bonet's Merc. Compit. x. 368 He shews the various uses of his..tractorie Machine which he invented. B. n. † 1. Old n... Oxford English Dictionary
prophetes.ai 0.0 0.0 0.0
13
Pursuit curve
See also Logarithmic spiral Tractrix Circles of Apollonius#Apollonius pursuit problem Pursuit–evasion References External links Mathworld, with a slightly wikipedia.org
en.wikipedia.org 0.0 0.0 0.0
14
曳物线
曳物线（英语：tractrix）是几何学中的一个曲线。力学意义下，曳物线是指连接一个线段的质点受垂直于初始静止状态时线段方向的牵引力作用下的运动轨迹，其笛卡尔坐标系下的最常用的参数方程形式为 其中tanh, cosh 分别为双曲正切函数和双曲余弦函数， 为线段长，. 历史 曳物线的英文“tractrix”来源于拉丁语 trahere，其意为“牵拉、拖拽”。 wikipedia.org
zh.wikipedia.org 0.0 0.0 0.0
15
Hilbert theorem and constant negative curvature surfaces Let us consider the tractroid (pseudosphere) obtained by rotation from the tractrix curve. The surface is not defined on the "big rim", so it is not a complete ...
It's compact, but obviously not _complete_. (Wait, are you including the truncating surfaces in the result? Then it fails to be differentiable at the edges, so it doesn't have a Gaussian curvature there, much less a constant negative one).
prophetes.ai 0.0 0.0 0.0