Search results

  • ...thesis]] or the [[Axiom of Choice]]. It is a good example of a [[diagonal argument]], a method pioneered by the mathematician [[Georg Cantor]].
    4 KB (757 words) - 10:44, 8 March 2018
  • ...<math>BC</math>. Describe the [[locus]] of the [[intersection]]s of the [[diagonal]]s of all possible rectangles <math>DEFG</math>. ...ath>I</math> of the diagonals of <math>DEFG</math> is also the midpoint of diagonal <math>DF</math>, so
    2 KB (416 words) - 19:00, 21 September 2014
  • ...h> on <math>\ell_r</math>, i.e. <math>a_{r\sigma(j)}=0</math>, by the same argument we have <math>s(c_\sigma(j))\ge s(c_\sigma(r))</math>, hence <math>s(\ell_j If the main diagonal contains all zeroes, we can immediately deduce from the condition that the
    6 KB (1,192 words) - 13:14, 29 January 2021
  • ...licity). It follows that <math>y_{n}</math> is a linear combination of the diagonal elements of <math>D</math>, namely <math>r_1^n, r_2^n, \ldots, r_k^n</math> A note about this argument: all of the power series used here are defined formally, and so we do not a
    19 KB (3,412 words) - 13:57, 21 September 2022
  • Let three-in-a-row/column/diagonal be a "win" and let player <math>0</math> be the one that fills in <math>0</ If player X takes a diagonal, player Y cannot win. If either takes a row, all the columns are blocked, a
    6 KB (1,057 words) - 00:58, 8 January 2023
  • It is clear, that two such line segments may only intersect when they are diagonal and perpendicular to each other. But the prince has only one diagonal move at his disposal.
    1 KB (242 words) - 14:46, 9 January 2017
  • ...ons is equal to 10<math>w</math>:6<math>w</math> = 10:6. Through a similar argument, the areas between each set of vertical lines also maintains a ratio of 10: Motivation : Notice that a cross section of any diagonal plane not going through the top or bottom face of the cylinder is an ellips
    11 KB (1,849 words) - 16:34, 2 December 2024
  • The diagram is certainly not to scale, but the argument is sound (I believe) and involves re-ordering the construction as specified ...ts <math>BD, CE, AB</math> and <math>AC</math> and the parallelism of its diagonal and the base of the triangle formed by the perpendiculars from one vertex o
    4 KB (792 words) - 00:44, 19 November 2023
  • * in any diagonal, if the number of entries on the diagonal is a multiple of three, then one third of the entries are <math>I</math>, o ...ells <math>(i,j)</math> for which <math>i+j</math> is a constant, and the diagonal of this second type consists all cells <math>(i,j)</math> for which <math>i
    3 KB (573 words) - 13:37, 4 December 2024
  • ...th>. Solving we get <math>PA = 4</math>, <math>PC = 14</math>, giving us a diagonal of length <math>\sqrt{212}</math> and area <math>\boxed{106}</math>. Denote by <math>\theta</math> the argument of point <math>P</math> on the circle.
    22 KB (3,480 words) - 18:33, 1 August 2024
  • We think about which letter is in the diagonal with <math>20</math> of a letter. We find that it is <math>2(2 + 5 + 8 + 11 ...t{P}</math> diagonal of length <math>3</math> and an <math>\text{R}</math> diagonal of length <math>1.</math>
    13 KB (1,839 words) - 23:54, 2 November 2024
  • ...n. So, there are <math>13 - 1 = 12</math> ways to seat him. With a similar argument, the third man can be seated in <math>10</math> ways, the fourth man in <ma ...ls, and choosing <math>5</math> where there will be a single man. For each diagonal, the man can go on either side, and there are <math>\binom{14}{5}</math> wa
    11 KB (1,803 words) - 10:57, 30 October 2024
  • This triangles lies in parallel planes, which are normal to cube diagonal <math>AC'.</math> Find the maximum value <math>F_m = max (F(x))</math> and all argument values <math>x_0</math> such that <math>F_m = F(x_0)</math>.
    48 KB (8,214 words) - 07:59, 30 July 2024