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• Geometry
  ...metry''' is the field of [[mathematics]] dealing with figures in a given [[space]]. It is one of the two oldest branches of mathematics, along with [[arithm * The notion of [[dimension]]s is fundamental to geometry. [[N-space]] is a term related to this concept.
  3 KB (393 words) - 07:59, 25 September 2020
• Volume
  The '''volume''' of an object is a [[measure]] of the [[amount]] of [[space]] that it occupies. Note that volume only applies to three-[[dimension]]al ...defined by an upper bound of <math>f(x,y,z)</math> in the Cartesian three-space can be found using a triple [[integral]]: <math>\int_{a_z}^{b_z}\int_{a_y}^
  3 KB (523 words) - 20:24, 17 August 2023
• 2007 iTest Problems
  The space diagonal (interior diagonal) of a cube has length 6. Find the <math>\textit ...math>R</math> be the region consisting of points <math>(x,y)</math> of the Cartesian plane satisfying both
  33 KB (5,177 words) - 21:05, 4 February 2023
• Linear equation
  ...uation with the corresponding number of variables can be graphed as an n-1-space - this concept is the idea behind [[analytic geometry]] as envisioned by Fe
  1 KB (257 words) - 13:39, 14 July 2021
• Relation
  ...A</math> and a set <math>B</math> is formally defined as a subset of the [[Cartesian product]] <math>A \times B</math>. If <math>a \in A</math> and <math>b \in ...rak{R}</math> over the sets <math>A_1,\ldots,A_n</math> is a subset of the Cartesian product <math>A_1 \times A_2 \times \ldots \times A_n</math>. If <math>a_i
  2 KB (445 words) - 08:16, 21 August 2009
• Direct product
  is the [[Cartesian product]] of the sets <math>A_i</math>, with coordinatewise relations. ...form direct products of [[group]]s, [[ring]]s, [[module]]s, [[topological space |topologies]], [[partially ordered set]]s, and other structures. However,
  2 KB (280 words) - 12:32, 6 June 2008
• 2001 USAMO Problems/Problem 4
  Let <math>P</math> be the origin in vector space, and let <math>a, b, c</math> denote the position vectors of <math>A, B, C< Without loss of generality, assume that in a Cartesian coordinate system, <math>A</math> is at the point <math>(0, 0)</math> and <
  8 KB (1,470 words) - 22:24, 18 June 2022
• 1962 IMO Problems/Problem 7
  Let's consider a regular tetrahedron in the cartesian space with center at <math>(0,0,0)</math> with <math>r_c</math> as the circumradi
  11 KB (1,928 words) - 20:52, 21 November 2023
• Euclidean space
  ...ian plane]], and so forth. In this representation, the study of Euclidean space is called [[coordinate geometry]]. ...of dimension <math>n</math> is the unique (up to [[isomorphism]]) [[vector space]] of dimension <math>n</math> over <math>\mathbb{R}</math> (under [[pointwi
  1,018 bytes (164 words) - 12:46, 13 March 2010
• Connected set
  In [[topology]], a space <math>X</math> is '''connected''' if it cannot be '''separated''', that is ...nnected subspaces of <math>X</math> are one-point sets. Examples of such a space include the [[discrete topology]] and the [[lower-limit topology]].
  3 KB (497 words) - 16:27, 15 March 2010
• 2012 AMC 10B Problems/Problem 23
  ...eight of the structure if the tetrahedron was still on would simply be the space diagonal of the cube, <math>\sqrt{3}</math>, so we just subtract <math>\fra ...e cube's space diagonal should be <math>\frac{2}{3}</math> of the original space diagonal. Hence, the length is <math>\boxed{\textbf{(D)} \: \frac{2\sqrt{3}
  5 KB (851 words) - 11:25, 21 April 2024
• 2013 AMC 12B Problems/Problem 17
  Draw the sphere and the plane represented by the two equations in Cartesian space, with the <math>z</math>-axis representing <math>c</math>. The intersection
  7 KB (1,225 words) - 14:59, 8 August 2021
• Coordinate system
  Cartesian coordinate system Wikipedia: A Cartesian coordinate system is a coordinate system that specifies each point uniquely
  4 KB (591 words) - 01:23, 25 January 2016
• 2017 AMC 12A Problems
  The region consisting of all points in three-dimensional space within <math>3</math> units of line segment <math>\overline{AB}</math> has A square is drawn in the Cartesian coordinate plane with vertices at <math>(2, 2)</math>, <math>(-2, 2)</math>
  15 KB (2,418 words) - 16:58, 7 November 2022
• 2023 AIME II Problems/Problem 14
  Now, we realize that the 3D space inside the cube without water is a frustum, with <math>P</math> on its smal We introduce a Cartesian coordinate system to the diagram.
  10 KB (1,574 words) - 16:42, 8 March 2024