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- The Archytas curve may be constructed as the intersection of a (right circular) cylinder and a ...e ''x'' with ''r'' + ''x''. This would correspond to a shift of the entire curve along the ''x'' direction. ...14 KB (2,478 words) - 07:56, 21 May 2021
- Let <math>\gamma\colon [a,b]\to \mathbb C</math> be a continuous curve. It is called rectifiable if its length ...polygonal chain <math>P</math> can be used to approximate the length of a curve <math>\gamma</math>. ...6 KB (987 words) - 15:01, 13 December 2024
- ...s. Instead of an interval,[[Complex Analysis/rectifiable curve|rectifiable curve]] serves as the integration domain. The integral is taken over complex-valu == Definition - Rectifiable Curve == ...13 KB (2,166 words) - 06:07, 7 March 2025
- + It is often used to fit a curve - It must be used to fit a curve ...950 bytes (176 words) - 08:23, 1 December 2016
Page text matches
- ...= \{\gamma(t): t \in [a,b]\} </math></center> is called the "trace" of the curve. * A curve is called differentiable, <math>C^k</math>, etc., if the defining mapping h ...2 KB (329 words) - 13:24, 7 January 2025
- + It is often used to fit a curve - It must be used to fit a curve ...950 bytes (176 words) - 08:23, 1 December 2016
- ...ter/|parameter]] <math>t</math> such that the parametric equations for the curve satisfy the [[../GeodesicEquation/|geodesic equation]]. Put another way, if one picks a parameterization of a geodesic curve by an arbitrary parameter <math>s</math> and sets <math>u^\mu = dx^\mu / ds ...1 KB (237 words) - 03:10, 13 September 2020
- ...d]] around some [[closed curve]] ''C'' (arbitrary but must be closed). The curve ''C'' in turn bounds both a [[surface]] ''S'' which the [[electric current] ...etic field|magnetic B-field]] (in [[Tesla (unit)|tesla]], T) around closed curve ''C'' is proportional to the total current ''I''<sub>enc</sub> passing thro ...2 KB (354 words) - 22:28, 11 September 2016
- Given a plane curve <math>\gamma</math>, its ''catacaustic'' (Greek <math>\varkappa\alpha\tau\a ...from the origin is a congruent spiral. The catacaustic of the exponential curve, <math>y = e^x</math>, reflecting the vertical rays, <math>x = t</math>, is ...735 bytes (113 words) - 04:02, 1 July 2015
- ...''logistic curve''' is a common "S" shape ([[w:en:sigmoid function|sigmoid curve]]), with equation:<ref>Wikipedia contributors (February 5, 2020). [[:w:Spec *<math>M</math> = the curve's capacity of the growth, and ...2 KB (297 words) - 12:12, 30 May 2023
- == Tangent vector to a curve == ...n (curve) of the parameter <math>t</math>. The unit tangent vector to the curve traced by the function <math>\mathbf{x}</math> is given by ...7 KB (1,183 words) - 22:32, 25 July 2017
- ...<math>df(x_1)/dx\,</math>. Therefore, the equation of the tangent to the curve at <math>(x_1, f(x_1))\,</math> is Recall that the root of <math>f(x)\,</math> is the point where the curve of the function meets the <math>x\,</math>-axis. Therefore, we can repeat ...2 KB (349 words) - 01:14, 26 July 2017
- ...hly tangent to the closed curved over the arbitrary two dimensional closed curve <math>{\mathcal C}</math> equals the integral of the difference of the part bounded inside the curve or otherwise the outside of the curve values of the field make virtually no contributions to the integral over th ...4 KB (788 words) - 10:45, 28 May 2024
- ...w ... this thing is an ''integral''. It should measure the area between a curve and the ''x''-axis. It should distribute over summation and scalar multipl ...ssure us that length-measure is a reasonable formalization of area under a curve. ...2 KB (303 words) - 05:27, 31 December 2023
- ...of mass]] places itself as low as possible, determine the equation of the curve formed by a flexible homogeneous wire or a thin chain with length <math>l</ where both the path integrals are taken along some curve <math>c</math>.\, Using a Lagrange multiplier <math>\lambda</math>, the tas ...3 KB (491 words) - 03:25, 13 September 2020
- ...nd derivative <math>f''</math> is positive. In the picture below, the sine curve is concave up on the interval\, <math>(-\pi,\,0)</math>. ...ecreases, and <math>f''</math> is negative. In the picture below, the sine curve is concave down on the interval\, <math>(0,\,\pi)</math>. ...3 KB (559 words) - 03:35, 13 September 2020
- represents a curve called ''clothoid'' . The curve has the shape of a "<math>\sim</math>" ...3 KB (524 words) - 16:49, 6 March 2022
- ...g that the field is sufficiently smooth that its gradient exists along the curve i.e. ...over the curve by the finite sum by dividing densely the space around the curve <math>\mathcal C</math> ...7 KB (1,278 words) - 18:20, 16 December 2022
- Let <math>\gamma\colon [a,b]\to \mathbb C</math> be a continuous curve. It is called rectifiable if its length ...polygonal chain <math>P</math> can be used to approximate the length of a curve <math>\gamma</math>. ...6 KB (987 words) - 15:01, 13 December 2024
- Let's derive the equation \,<math>y = y(x)</math>\, of this curve, called the ''catenary'' , in its plane with <math>x</math>-axis horizontal In any point \,<math>(x,\,y)</math>\, of the wire, the tangent line of the curve forms an angle <math>\varphi</math> with the positive direction of <math>x< ...3 KB (558 words) - 03:15, 13 September 2020
- ...he geodesic by writing the equation for the length <math>l_v</math> of a ''curve'' -- which is defined as a [[../Bijective/|function]] <math>f: (R) \to \S_C ...zation of [[../CosmologicalConstant/|energy]] as well as the length of the curve. ...3 KB (516 words) - 15:28, 12 September 2020
- ...s]] [[w:en:Mathematical object|object]] in a two-dimensional plane (i.e. a curve in the plane) or in a higher-dimensional space. </math> is a curve in the <math display="inline"> ...12 KB (1,851 words) - 13:29, 7 January 2025
- Let us consider three simple examples: The Shortest Line, The Curve of Quickest Descent, and The Minimum Surface of Revolution. ...rtest Line}. Let it be required to find the equation of the shortest plane curve joining two given points. ...14 KB (2,416 words) - 03:35, 13 September 2020
- ...th> (where <math>L</math> denotes the [[Complex_Analysis/Curve|length of a curve]]) [[Complex_Analysis/Rectifiable_Curve|rectifiable curve or length of a curve]] ...5 KB (748 words) - 19:14, 12 December 2024