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• Geometric inequality
  A '''geometric inequality''' is an [[inequality]] involving various measures ([[angle]]s, ...\le 1</math>. This means that given a perimeter <math>P</math> for a plane figure, the [[circle]] has the largest area. Conversely, of all plane figures with
  7 KB (1,300 words) - 01:11, 28 October 2024
• Circle
  A '''circle''' is a geometric figure commonly used in Euclidean [[geometry]]. ...in, the little green arcs in the diagram will become the blue line and the figure will approach the shape of a rectangle with length <math> r </math> and wid
  9 KB (1,510 words) - 19:56, 16 January 2025
• Isoperimetric Inequalities
  ...rimetric Inequalities''' are [[inequalities]] concerning the [[area]] of a figure with a given [[perimeter]]. They were worked on extensively by [[Lagrange]] ...leq 1</math>. This means that given a perimeter <math>P</math> for a plane figure, the circle has the largest area. Conversely, of all plane figures with are
  789 bytes (115 words) - 17:08, 29 December 2021
• Semiperimeter
  ...<math>\frac{P}{2}</math>, where <math>P</math> is the total perimeter of a figure. It is typically denoted <math>s</math>. In a triangle, it has uses in for The semiperimeter has many uses in geometric formulas. Perhaps the simplest is <math>A=rs</math>, where <math>A</math>
  740 bytes (113 words) - 15:19, 11 July 2024
• Rhombus
  A '''rhombus''' is a geometric figure that lies in a [[plane]]. It is defined as a [[quadrilateral]] all of whos * Its diagonals divide the figure into 4 congruent [[triangle]]s.
  3 KB (490 words) - 15:30, 22 February 2024
• Kite
  A '''kite''' is a geometric figure that lies in a plane. [[Quadrilateral]] <math>ABCD</math> is a kite if and
  784 bytes (122 words) - 13:09, 22 July 2024
• Trapezoid
  A '''trapezoid''' is a cool and pretty geometric figure that lies in a plane. It is also a type of [[quadrilateral]].
  1 KB (246 words) - 10:54, 2 January 2024
• Isosceles trapezoid
  An '''isosceles trapezoid''' is a geometric figure that lies in a [[plane]]. It is a specific type of [[trapezoid]] in which
  601 bytes (84 words) - 20:40, 13 February 2025
• 2003 AMC 12B Problems
  flower bed are as shown in the figure. She plants one flower per square foot in The second and fourth terms of a geometric sequence are 2 and 6. Which of the following is a possible first term?
  13 KB (1,987 words) - 18:53, 10 December 2022
• Perimeter
  ...rimeter''' of a geometric figure is the distance around the outside of the figure. Perimeter is often denoted by P. The perimeter of a [[circle]] is called i
  896 bytes (137 words) - 18:57, 2 September 2024
• 1989 AIME Problems/Problem 3
  ...number]]s. To figure out which rational number, we sum an [[infinite]] [[geometric series]], <math>0.d25d25d25\ldots = \sum_{n = 1}^\infty \frac{d25}{1000^n}
  4 KB (584 words) - 14:38, 11 August 2024
• 1999 AIME Problems/Problem 11
  We factor the <math>\frac{1}{2i}</math> and split into two geometric series to get <math>\frac{1}{2i}\left(\frac{-\frac{1}{x^{35}}(x^{35}-1)}{x- ...at <math>x^{36}=-1</math>, so <math>-\frac{1}{x^{35}}=x</math>, so our two geometric series are actually the same. We combine the terms and simplify to get <mat
  5 KB (816 words) - 13:39, 29 June 2024
• 2000 AIME I Problems/Problem 6
  ...math>x</math> and <math>y</math> is exactly <math>2</math> more than the [[geometric mean]] of <math>x</math> and <math>y</math>? Since the arithmetic mean is 2 more than the geometric mean, <math>\frac{x+y}{2} = 2 + \sqrt{xy}</math>. We can multiply by 2 to g
  6 KB (970 words) - 10:17, 11 January 2025
• Congruent (geometry)
  '''Congruency''' is a property of multiple geometric figures. ...p of the other, with all parts lining up perfectly with no parts on either figure left over. In plain language, two objects are congruent if they have the s
  10 KB (1,655 words) - 16:56, 17 September 2024
• 2004 AMC 10A Problems
  In the figure, <math>\angle EAB</math> and <math>\angle ABC</math> are right angles. <mat ...rogression. What is the smallest possible value for the third term of the geometric progression?
  15 KB (2,092 words) - 20:32, 15 April 2024
• LaTeX:Pictures
  ...ictures and diagrams into LaTeX documents. If you're dealing strictly with geometric diagrams, consider reading about [[Asymptote: About|Asymptote]], a graphics ...you are using LaTeX to produce PDF documents, you can make images such as geometric diagrams in your documents. The machine that we'll use to include images is
  9 KB (1,437 words) - 19:36, 7 December 2024
• 1951 AHSME Problems
  The limit of the sum of an infinite number of terms in a geometric progression is <math> \frac {a}{1- r}</math> where <math> a</math> denotes Which of the following methods of proving a geometric figure a locus is not correct?
  23 KB (3,646 words) - 21:53, 21 June 2024
• 1959 AHSME Problems
  If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification: By adding the same constant to <math>20,50,100</math> a geometric progression results. The common ratio is:
  22 KB (3,348 words) - 12:53, 22 July 2024
• 1966 AHSME Problems
  If the arithmetic mean of two numbers is <math>6</math> and their geometric mean is <math>10</math>, then an equation with the given two numbers as roo ...of sides numbered <math>k</math> and <math>k+2</math> until they meet. (A figure is shown for the case <math>n=5</math>).
  19 KB (3,160 words) - 11:36, 29 July 2024
• 2009 AMC 12A Problems
  ...th>F_3</math> has <math>13</math> diamonds. How many diamonds are there in figure <math>F_{20}</math>? ...<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) - 13:13, 12 August 2020

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