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  • ...<math>(bk,-ak)</math> for all integers <math>k</math>. If they are not, we simply divide them by their greatest common divisor. ...tions to the Pell equation when <math>D</math> is not a perfect square are connected to the continued [[fraction]] expansion of <math>\sqrt D</math>. If <math>a
    9 KB (1,434 words) - 00:15, 4 July 2024
  • Let ''f'' be [[holomorphic]] on a [[simply connected]] [[domain]] ''D'', and let <math>\Gamma\subseteq D</math> be a [[simple cl
    2 KB (271 words) - 21:06, 12 April 2022
  • ...ote: Basics|Variables and Data Types]] for the difference) in Asymptote is simply a piecewise cubic function of a parameter <math>t</math>, parameterized as ...in an curve that can be twisted. Keep in mind that if only two things are connected with <tt>..</tt>, the curve will be a straight line.
    7 KB (1,205 words) - 20:38, 26 March 2024
  • ...llows you to make tricky diagrams such as ones which include various items connected by arrows or lines. Take a look at the [http://www.tug.org/applications/Xy- <li>Simply put your .sty file in the same folder as your source files. Unfortunately,
    10 KB (1,656 words) - 08:33, 21 September 2024
  • ...h'' is a graph in which there is an edge joining every pair of vertices is connected. The complete graph on <math>n</math> vertices is denoted <math>K_n</math> ...very vertex is isolated. When drawn in the usual fashion, a null graph is simply a collection of scattered points (the vertices) with no edges connecting th
    8 KB (1,428 words) - 09:26, 27 August 2020
  • ...he four vertices of the triangles that aren’t vertices of the square are connected to form a larger square. Find the area of this larger square. ...area can be calculated by the product of its diagonals divided by two, we simply find the length of the diagonals, which is
    1 KB (237 words) - 22:47, 2 September 2024
  • ...here, or, more simply, that only a ''n'' manifold with no holes was simply connected. All cases of this conjecture had been proven up to this point except the c ...ids. These equations establish that the acceleration of fluid particles is simply the product of changes in pressure and dissipative viscous forces (similar
    13 KB (1,969 words) - 16:57, 22 February 2024
  • Suppose <math>\,G\,</math> is a connected graph with <math>\,k\,</math> edges. Prove that it is possible to label the .../math>. Similarly, if <math>v_n</math> has more than one edge, it must be connected to a vertex <math>v_{n+1}</math> which is either one of the <math>v_i</math
    4 KB (668 words) - 16:45, 30 January 2021
  • function in some [[simply connected]] region <math>R \subset \mathbb{C}</math>,
    7 KB (1,284 words) - 23:12, 3 April 2009
  • ...e]] in 1961. More rigorously, the conjecture is expressed as "Every simply connected, compact three-manifold (without boundary) is homeomorphic to the three-sph
    690 bytes (107 words) - 14:12, 31 March 2017
  • Five towns are connected by a system of roads. There is exactly one road connecting each pair of tow ...and <math>2^3</math> ways to assign the remaining <math>3</math> roads not connected to either of these towns. Therefore, the answer is <math>2^{{5\choose2}}-(5
    16 KB (2,867 words) - 16:51, 6 January 2024
  • ...termost vertex of <math>S</math> to the vertices that <math>S</math> isn't connected to. Note that the line that hits the hypotenuse must create a right angle, ...espect to <math>x</math>. <math>f(0) = \dfrac{12}{5}</math>, because it is simply the length of the hypotenuse's altitude. Similarly, <math>f(\dfrac{12}{7})
    17 KB (2,623 words) - 23:41, 30 October 2024
  • ...lines, thus making additional <math>m*(n-1)+1</math> bounded regions; when connected to point #2 on <math>\ell_B</math>, it crosses <math>m*(n-2)</math> lines, ...sider the complement, where new lines don't intersect other line segments. Simply observing, we see that the only line segments that don't intersect with the
    12 KB (2,025 words) - 13:56, 25 January 2024
  • ...which is why the theorem is also called Kirchhoff's Matrix Tree Theorem or simply Kirchhoff's Theorem. ...s an arbitrary column, and <math>\sim</math> denotes that two vertices are connected. Next, define the degree matrix as
    1 KB (264 words) - 10:26, 3 March 2022
  • ...he successors to this great cause, and each life taken, each life that was connected to a family, a community, is irrelevant, because thousands of similar lives This is the default type of movement and the one used when a player states simply that a model moved somewhere. The unit chosen moves up to half its speed in
    36 KB (5,897 words) - 18:28, 3 September 2024
  • ...ale in 1961. More rigorously, the conjecture is expressed as "Every simply connected, compact three-manifold (without boundary) is homeomorphic to the three-sph
    929 bytes (138 words) - 20:44, 29 September 2024
  • ...ath> is the total number of vertices as we are given that all vertices are connected to either <math>3</math> or <math>4</math> edges. Therefore, <math>A+B=14.< ...>3t + 3f = 42</cmath><cmath>f = 6</cmath><cmath>t = 8</cmath>Our answer is simply just <math>t</math>, which is <math>\boxed{\textbf{(D) }8}</math> ~musicalp
    6 KB (1,026 words) - 06:34, 5 November 2024
  • ...of <math>6</math> in <math>\text{mod 125}</math>, which, by inspection, is simply <math>21</math>. Hence, Now, if the center of <math>2</math> tangent circles are connected, the line segment will pass through the point of tangency. In this case, if
    64 KB (10,960 words) - 01:00, 26 December 2024