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- [[Koch Curve]] (Snowflake): A classic example of a fractal, this curve is constructed by repeatedly subdividing a triangle, resulting in a shape w ...ry. Each point on the Mandelbrot set corresponds to a value in the complex plane, and the set’s intricate boundary shows self-similar patterns at varying2 KB (302 words) - 10:17, 27 September 2024
- An elliptic curve is the set of points <math>(x,y)</math> satisfying some two variable third ...elian group structure on its points. This means that given 2 points on the curve, they can be added in a way that satisfies the normal laws of addition, lik5 KB (849 words) - 15:14, 18 May 2021
- ...n.) As is clear from their definition, the conic sections are all [[plane curve]]s, and every conic section can be described in [[Cartesian coordinates]] b * A [[circle]] is the conic section formed when the cutting plane is [[parallel]] to the [[base (geometry) | base]] of the cone or equivalent6 KB (1,003 words) - 15:47, 13 November 2024
- ...''D'', and let <math>\Gamma\subseteq D</math> be a [[simple closed Jordan curve]]. Then for any <math>z_0</math> in the interior of <math>\Gamma</math>, we ...>f</math> be an [[entire]] function (i.e. holomorphic on the whole complex plane). If <math>\lvert f(z)\rvert \le A</math> for all <math>z</math> for some2 KB (271 words) - 21:06, 12 April 2022
- The point <math>P = (1,2,3)</math> is reflected in the <math>xy</math>-plane, then its image <math>Q</math> is rotated <math>180^\circ</math> about the The [[graph]] below shows a portion of the [[curve]] defined by the quartic [[polynomial]] <math>P(x) = x^4 + ax^3 + bx^2 + cx13 KB (1,948 words) - 09:35, 16 June 2024
- ...e [[abelian group]] of [[point]]s over a [[number field]] of an [[elliptic curve]] <math>E</math> to the [[order]] of the [[root|zero]] of the associated <m ...elliptic curve there is a finite [[subset]] of the rational points on the curve, from which all further rational points may be generated.7 KB (1,102 words) - 16:23, 6 September 2008
- Now plot these in the coordinate plane and draw a line through them: ...h>p(x)</math>, is to find the zeros of <math>p(x)=0</math>. Then a smooth curve should be drawn through the zeros accounting for multiple roots and making3 KB (497 words) - 04:11, 8 June 2023
- ...nd a [[circle]], though it may refer to the distance around any [[smooth]] curve, while the term perimeter is typically reserved for [[polygon]]s and other1 KB (183 words) - 20:04, 3 July 2024
- |A point is doing Brownian motion in the plane. It is now at (x=1, y=1). With probability 1, it will reach the line (y=0). |Can you arrange ten points in the plane in such a way that they cannot be covered by a set of non-overlapping unit22 KB (3,358 words) - 14:17, 18 July 2017
- ...curve contained in the ball and having length less than 2. Prove that the curve is contained entirely within some hemisphere of the given ball. ...only one great circle through the two points, as three points determine a plane–a counterexample to this claim would then be readily found.'''2 KB (360 words) - 22:13, 18 July 2016
- ...,\,\,P_0,\,\,\,\,P_1,\,\,\,\,P_2,\,\,\,\,P_3,\,\,\,\,\ldots</cmath> in the plane with the following property: For any three distinct integers <math>a,b,</ma Consider an elliptic curve with a generator <math>g</math>, such that <math>g</math> is not a root of2 KB (451 words) - 18:09, 1 May 2014
- ...oints <math>P(-1,-2)</math> and <math>Q(4,2)</math> in the <math>xy</math>-plane; point <math>R(1,m)</math> is taken so that <math>PR+RQ</math> is a minimum ...rea bounded by the <math>x</math>-axis, the line <math>x=8</math>, and the curve defined by16 KB (2,662 words) - 14:41, 13 November 2024
- ...raph this in the Cartesian plane and find the area of the region below the curve and above the line <math>y=0</math>. ...perimeter of square). Notice that the desired area of the region below the curve we found earlier is the sum of a quarter circle with radius <math>\frac12</12 KB (1,981 words) - 17:33, 3 September 2023
- ...e nearest positive integer, what is the area of the region bounded by this curve? ...tions to the equation <math>(z+6)^8=81</math> are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled <math14 KB (2,118 words) - 14:36, 28 October 2021
- ...Theorem: “Any continuous simple closed curve in the plane, separates the plane into two disjoint regions, the inside and the outside”. This theorem impl2 KB (374 words) - 03:41, 19 January 2019
- There are <math>n\ge 2</math> line segments in the plane such that every two segments cross and no three segments meet at a point. G ...section points [color=#f00]red[/color]. Join the blue points with a smooth curve <math>\cal{C}</math> such that none of the line segments intersect <math>\c6 KB (1,094 words) - 13:31, 4 December 2024
- ...construction of the real numbers, convergence of sequences, subsets of the plane as metric spaces, limits, notions of [[continuity]], [[Derivative|different ...culus, integrals are introduced as the approximation of the area under the curve of a continuous functions by rectangles as the number of rectangles becomes9 KB (1,409 words) - 01:41, 30 May 2023
- ...er one revolution. Prove that there is a fixed point <math>P</math> in the plane such that the two points are always equidistant from <math>P.</math> ...t M of the figure F' describes a curve <math>\Gamma'</math> similar to the curve <math>\Gamma</math>.8 KB (1,485 words) - 21:55, 29 January 2021
- * Define a quadratic bezier curve function. ...s with <math>3</math> seats in each row. Eight passengers have boarded the plane and are distributed randomly among the seats. A married couple is next to b21 KB (2,950 words) - 11:55, 21 January 2025
- What is the area of the region in the coordinate plane defined by <math>[0, 6]</math> <math>\times</math> <math>[0, 6]</math> in the coordinate plane and hops to that point. She then randomly13 KB (1,959 words) - 12:42, 14 June 2024