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- ...hm that finds the [[greatest common divisor]] (GCD) of two elements of a [[Euclidean domain]], the most common of which is the [[nonnegative]] [[integer]]s <mat Start with any two elements <math>a</math> and <math>b</math> of a [[Euclidean Domain]]6 KB (923 words) - 16:39, 30 September 2024
- ...t, although it should be intuitively clear because it is properties of the Euclidean metric which motivate the definition of a metric.813 bytes (132 words) - 16:49, 28 March 2009
- #REDIRECT [[Euclidean algorithm]]33 bytes (3 words) - 12:02, 20 February 2007
- ...n domain''' (or '''Euclidean ring''') is a type of [[ring]] in which the [[Euclidean algorithm]] can be used. Formally we say that a ring <math>R</math> is a Euclidean domain if:2 KB (357 words) - 14:28, 22 August 2009
- #REDIRECT [[Euclidean domain]]30 bytes (3 words) - 18:10, 19 February 2007
- #REDIRECT[[Euclidean domain]]29 bytes (3 words) - 18:11, 19 February 2007
- ...idean geometry''' is geometry that stemmed from the work of [[Euclid]]. In Euclidean geometry, there are 5 [[postulate]]s. The 5th is the parallel postulate. ...than the other postulates, and more wordy. This postulate is the basis of Euclidean geometry.805 bytes (121 words) - 17:10, 15 August 2023
- ...e [[Cartesian plane]], and so forth. In this representation, the study of Euclidean space is called [[coordinate geometry]]. ...{y}) = \sqrt{(x_1-y_1)^2 + \cdots + (x_n - y_n)^2}</math>. Similarly, the Euclidean space of dimension <math>n</math> is the unique (up to [[isomorphism]]) [[v1,018 bytes (164 words) - 11:46, 13 March 2010
- #REDIRECT:[[Euclidean algorithm]]33 bytes (3 words) - 10:39, 5 February 2022
Page text matches
- ...nch Class topics at MathILy-Er are likely to include voting theory and non-Euclidean geometry.)5 KB (706 words) - 22:49, 29 January 2024
- ...mazon.com/gp/product/0883858398?%2AVersion%2A=1&%2Aentries%2A=0&pldnSite=1 Euclidean Geometry in Mathematical Olympiads] by Evan Chen * [http://www.amazon.com/exec/obidos/ASIN/0883855224/artofproblems-20 Non-Euclidean Geometry] by [[H.S.M. Coxeter]].24 KB (3,198 words) - 19:44, 4 December 2024
- ...ttp://www.amazon.com/exec/obidos/ASIN/1930190859/artofproblems-20 Advanced Euclidean Geometry] by Alfred S. Posamentier.7 KB (901 words) - 13:11, 6 January 2022
- ...ch that <math>ax+by=1</math> (a special case of [[Bezout's Lemma]]). The [[Euclidean Algorithm]] can be used to compute the coefficients <math>x,y</math>.2 KB (245 words) - 17:45, 14 October 2024
- * [[Euclidean algorithm]]1,015 bytes (104 words) - 16:21, 1 September 2024
- ...a</math> in <math>\mathbb{R}^p</math> (the <math>p</math>-th dimensional [[Euclidean space]]), such that the vertices of the hypercube are at <math>(\pm a/2,\pm16 KB (2,660 words) - 22:42, 28 August 2024
- Let <math>A,B,C,D</math> be four points in the Euclidean plane. Taking an inversion centered at <math>D</math> (the point doesn't ma7 KB (1,198 words) - 08:36, 8 December 2024
- ...the intersections of the sides summing to 180 degrees. Triangles exist in Euclidean [[geometry]], and are the simplest possible polygon. In [[physics]], triang4 KB (631 words) - 20:16, 8 October 2024
- === Euclidean algorithm === The [[Euclidean algorithm]] is much faster and can be used to give the GCD of any two numbe2 KB (288 words) - 21:40, 26 January 2021
- ...hm that finds the [[greatest common divisor]] (GCD) of two elements of a [[Euclidean domain]], the most common of which is the [[nonnegative]] [[integer]]s <mat Start with any two elements <math>a</math> and <math>b</math> of a [[Euclidean Domain]]6 KB (923 words) - 16:39, 30 September 2024
- A '''circle''' is a geometric figure commonly used in Euclidean [[geometry]].9 KB (1,585 words) - 12:46, 2 September 2024
- ...ften refer to a vector as "a quantity with a direction and magnitude." For Euclidean geometers, a vector is essentially a directed line segment. In many situati11 KB (1,876 words) - 18:01, 29 August 2024
- * [[Euclidean algorithm]]553 bytes (76 words) - 19:01, 17 March 2023
- == Euclidean Geometry == {{main|Euclidean geometry}}3 KB (478 words) - 00:52, 25 August 2024
- ...ex number]]s. (We can think of this as <math>n</math>-dimensional "complex Euclidean" space.) Let <math>R=\mathbb{C}[X_1,\ldots,X_n]</math> be the [[polynomial2 KB (361 words) - 00:59, 24 January 2020
- ...elementary mathematics such as [[arithmetic]], [[elementary algebra]] or [[Euclidean geometry]]. It also arises and plays an important role in the more general7 KB (1,327 words) - 17:39, 28 September 2024
- (We know this last fraction is fully reduced by the [[Euclidean algorithm]] -- because <math>4 = 403 - 399</math>, <math>\gcd(403, 399) | 43 KB (581 words) - 20:19, 22 September 2024
- A ''line'' in the euclidean sense is defined as the shortest distance between two points. It is define674 bytes (106 words) - 17:40, 9 May 2024
- ...ind the GCD of <math>a_n</math> and <math>a_{n+1}</math>, we can use the [[Euclidean algorithm]]: ...ath> x-200</math> term share factors with the <math>2x+1</math>. Using the Euclidean Algorithm, <math>\gcd(x-200,2x+1)=\gcd(x-200,2x+1-2(x-200))=\gcd(x-200,401)5 KB (795 words) - 21:27, 19 December 2024
- ...+10 \mid n^3+100</math>, <math>\gcd(n^3+100,n+10)=n+10</math>. Using the [[Euclidean algorithm]], we have <math>\gcd(n^3+100,n+10)= \gcd(-10n^2+100,n+10)</math>2 KB (338 words) - 18:56, 15 October 2023