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  • ...nging Problems in Geometry] -- A good book for students who already have a solid handle on elementary geometry. ...cal-Library/dp/0883856247/ref=sr_1_1?ie=UTF8&s=books&qid=1199807249&sr=1-1 Geometric Transformations III] by I. M. Yaglom.
    24 KB (3,198 words) - 19:44, 4 December 2024
  • ...points and a plane through any three points, there is a three-dimensional "solid" or 3-plane through any four points. Thus in an n-dimensional space, one ca [[Category:Geometric Inequalities]]
    3 KB (602 words) - 08:01, 7 June 2023
  • A solid rectangular block is formed by gluing together <math> N </math> congruent 1 ...n\ge1, </math> the terms <math> a_{2n-1}, a_{2n}, a_{2n+1} </math> are in geometric progression, and the terms <math> a_{2n}, a_{2n+1}, </math> and <math> a_{2
    9 KB (1,410 words) - 04:05, 20 February 2019
  • Compute the sum of all twenty-one terms of the geometric series ...and <math>n</math> are positive integers such that <math>m < n</math>, the geometric mean of <math>m</math> and <math>n</math> is greater than <math>2007</math>
    30 KB (4,794 words) - 22:00, 8 May 2024
  • A '''pyramid''' is a 3-dimensional [[geometric solid]]. It consists of a [[base]] that is a [[polygon]] and a [[point]] not on ...with their bases joined form an [[octahedron]], which is another Platonic solid.
    2 KB (329 words) - 20:05, 20 August 2021
  • A '''regular tetrahedron''' is a 3-dimensional [[geometric solid]]. It is also a special type of [[pyramid]]. It consists of a [[base]] tha
    1 KB (178 words) - 10:32, 29 March 2012
  • ...ic progression. Find the sum of the lengths in cm of all the edges of this solid.
    71 KB (11,749 words) - 11:39, 20 November 2024
  • .../math>, and the third is left unchanged. The volume of the new rectangular solid is <math>5</math> less than that of the cube. What was the volume of the cu ...<math>a + ar_2 + ar_2^2 + ar_2^3 + \cdots</math> be two different infinite geometric series of positive numbers with the same first term. The sum of the first
    13 KB (2,105 words) - 12:13, 12 August 2020
  • ...<math>b</math>, and <math>2009</math>, with <math>a<b<2009</math>, form a geometric sequence with an integer ratio. What is <math>a</math>? .../math>, and the third is left unchanged. The volume of the new rectangular solid is <math>5</math> less than that of the cube. What was the volume of the cu
    14 KB (2,126 words) - 16:46, 13 June 2024
  • ...serted between <math>8</math> and <math>5832</math>, the fifth term in the geometric series is: The volume of a rectangular solid each of whose side, front, and bottom faces are <math> 12\text{ in}^{2} </m
    22 KB (3,306 words) - 18:50, 3 May 2023
  • ...metric progression. The sums of the lengths in cm of all the edges of this solid is
    17 KB (2,488 words) - 02:26, 20 March 2024
  • ...metric progression. The sums of the lengths in cm of all the edges of this solid is As the dimensions are in geometric progression, let them be <math>\frac{b}{r}</math>, <math>b</math>, and <mat
    3 KB (396 words) - 00:37, 20 March 2024
  • For <math>-1<r<1</math>, let <math>S(r)</math> denote the sum of the geometric series <cmath>12+12r+12r^2+12r^3+\cdots .</cmath> Let <math>a</math> betwe A ''regular icosahedron'' is a <math>20</math>-faced solid where each face is an equilateral triangle and five triangles meet at every
    8 KB (1,360 words) - 00:05, 29 November 2024
  • ...had the least. The three numbers of peanuts that each person had formed a geometric progression. Alex eats <math>5</math> of his peanuts, Betty eats <math>9</m ..._2, b_3,...</math> are an increasing arithmetic sequence and an increasing geometric sequence, respectively. Let <math>c_n=a_n+b_n</math>. There is an integer <
    8 KB (1,312 words) - 20:16, 3 March 2021
  • The volume of a certain rectangular solid is <math>216\text{ cm}^3</math>, its total surface area is <math>288\text{ ...ic progression. Find the sum of the lengths in cm of all the edges of this solid.
    1 KB (176 words) - 16:08, 15 March 2021
  • ...ioned into <math>5</math> regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch ar ...tic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. The first three terms of the resulting four-
    18 KB (2,662 words) - 18:03, 3 November 2024
  • Pólya proposed a method in which the researcher replaces the geometric problem of finding the optimum with a mechanical or optical model and appli ...So the point <math>M</math> of the contact with the sphere (or any convex solid) must be at the center of mass of the polygon <math>BCD.</math>
    12 KB (2,104 words) - 13:11, 24 February 2024