2509: Useful Geometry Formulas - Revision history

Firestar233: math terminology error

2024-03-25T00:48:43Z

math terminology error

Lettherebedarklight: /* Explanation */ grammar

2023-11-10T07:06:55Z

‎Explanation: grammar

Xurkitree10: /* Transcript */

2023-04-20T03:47:26Z

‎Transcript

Xurkitree10: /* Explanation */

2022-12-30T16:11:14Z

‎Explanation

Davidy22: Reverted edits by [[Special:Contributions/Davidy22, the racist homosexual, is known to visit Norwegian gay bars with his boyfriend Kynde. He has cheated on Kynde at least twice with Vandalbane (a big guy for you). They all have micropenises.|Davidy22,...

2022-06-02T06:20:14Z

Reverted edits by [[Special:Contributions/Davidy22, the racist homosexual, is known to visit Norwegian gay bars with his boyfriend Kynde. He has cheated on Kynde at least twice with Vandalbane (a big guy for you). They all have micropenises.|Davidy22,...

Davidy22, the racist homosexual, is known to visit Norwegian gay bars with his boyfriend Kynde. He has cheated on Kynde at least twice with Vandalbane (a big guy for you). They all have micropenises. at 05:42, 2 June 2022

2022-06-02T05:42:22Z

172.70.110.209: Undo revision 270820 by Explain xkcd server admin (talk)

2022-05-20T22:22:35Z

Undo revision 270820 by Explain xkcd server admin (talk)

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Explain xkcd server admin at 21:26, 20 May 2022

2022-05-20T21:26:20Z

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Jacky720: rv

2022-05-04T23:53:12Z

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Ex Kay Cee Dee at 23:53, 4 May 2022

2022-05-04T23:53:09Z

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 This illustration is commonly used to depict a 3D cylinder or right circular prism.  In this case, the upper ellipse represents the "visible" part of the top circular surface, with its "depth" shorter than its "width" due to foreshortening, and the lower part of the lower ellipse represents the "front" edge of the lower surface; the dotted half of the lower ellipse represents the occluded "back" edge of the lower surface.
-To add to the confusion, the upper ellipse has its major axis labeled 'd' which usually denotes the diameter of a circular surface, while the lower ellipse has its semimajor axis labeled 'r' which similarly denotes a radius, even though the ellipses drawn have neither diameter nor radius.  The 'h' denoting height is also used for both rectangles and solid objects.  While 'd' in this case is required for the area calculation of the 2D shape, in textbooks only 'r' may be marked and the arrow may be offset at a diagonal rather than in line with any figurative axis, to imply its applicability to any angle of radius.
+To add to the confusion, the upper ellipse has its major axis labeled 'd' which usually denotes the diameter of a circular surface, while the lower ellipse has its semiminor axis labeled 'r' which similarly denotes a radius, even though the ellipses drawn have neither diameter nor radius.  The 'h' denoting height is also used for both rectangles and solid objects.  While 'd' in this case is required for the area calculation of the 2D shape, in textbooks only 'r' may be marked and the arrow may be offset at a diagonal rather than in line with any figurative axis, to imply its applicability to any angle of radius.
 The non-overlapping parts of the 2D shape are composed of the rectangle formed by the major axes of the two ellipses and the vertical lines, plus half of the top ellipse and half of the bottom ellipse.  The area of the rectangle is dh, and the area of an ellipse with semimajor axis d/2 and semiminor axis r is πrd/2.  The total area is A = d(πr/2 + h), which is captioned below the figure.

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 This illustration is commonly used to depict a rectangular prism, with 'b' denoting the 'breadth', 'd' the 'depth' and 'h' the 'height'.  However, the labeled angle θ, which is necessary for the area calculation of the 2D shape, would not normally be used in a diagram of a rectangular prism, as all angles are assumed to be right angles.  A rhomboidal prism could be accurately described by this diagram with the assumption that the 'base' parallelogram is perpendicular to the 'front' and that the only non-right angle is θ.  In that case 'd' would not accurately describe the depth of the solid, which would be d sin θ.
-The area of the 2D shape is comprised of the rectangle at the lower left, the parallelogram above it, and the parallelogram on the right.  The area of the rectangle representing the front face of the prism is bh. The area of the upper parallelogram is db&nbsp;sin&nbsp;θ. The area of the right parallelogram is dh&nbsp;cos&nbsp;θ.  The equation for this area is  A = bh + d(b sinθ + h cosθ) as is given below the figure.
+The area of the 2D shape comprises the rectangle at the lower left, the parallelogram above it, and the parallelogram on the right.  The area of the rectangle representing the front face of the prism is bh. The area of the upper parallelogram is db&nbsp;sin&nbsp;θ. The area of the right parallelogram is dh&nbsp;cos&nbsp;θ.  The equation for this area is  A = bh + d(b sinθ + h cosθ) as is given below the figure.
 The surface area of the prism would be 2bh&nbsp;+&nbsp;2db sin θ&nbsp;+&nbsp;2dh. The volume is bdh sin θ. Assuming a 3D shape, θ can be artificially altered by the projection; the assumption could be made that θ is 90 degrees, and sin θ is 1 (and therefore can be eliminated from the formulas), but since θ is marked, such an assumption might not be valid.

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 ==Transcript==
 :[Four figures in two rows of two, each being a common two-dimensional representation of a three-dimensional object, with solid lines in front and dotted lines behind. Each figure has some labeled dimensions represented with arrows and a formula underneath indicating its area. Above the four figures is a header:]
 :Useful geometry formulas

← Older revision		Revision as of 16:11, 30 December 2022
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	==Explanation==		==Explanation==
−	{{incomplete\|Created by a STRIPED AND DOTTED TEXTBOOK ILLUSTRATOR. Explain the formulas for each of the areas, and also the correct formula for the 3D object they seem to represent. Consider whether to add a table with the formula given and the correct formula for the 3D shape. Do NOT delete this tag too soon.}}
	This comic showcases area formulas for the areas of four two-dimensional geometric shapes which each have extra dotted and/or solid lines making them look like illustrations for 3-dimensional objects. The first, a simple equation for the area of a circle, the second an equation for the area of a triangle with a semi-elliptic base, the third an equation for the area of a rectangle with an elliptical base and top, and the fourth an equation for the area of a hexagon consisting of two opposing right-angled corners and two parallel diagonal lines connecting their sides. In each case, only the area formed by the outline of each shape is calculated.		This comic showcases area formulas for the areas of four two-dimensional geometric shapes which each have extra dotted and/or solid lines making them look like illustrations for 3-dimensional objects. The first, a simple equation for the area of a circle, the second an equation for the area of a triangle with a semi-elliptic base, the third an equation for the area of a rectangle with an elliptical base and top, and the fourth an equation for the area of a hexagon consisting of two opposing right-angled corners and two parallel diagonal lines connecting their sides. In each case, only the area formed by the outline of each shape is calculated.

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 | number    = 2509
 | date      = August 30, 2021
-| title     = Useful [[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR 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SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAK[[File:Alligator with open mouth.jpg|thumb|left|ALLIGATOR SOYJAK]]ALLIGATOR SOYJAKGeometry Formulas
+| title     = Useful Geometry Formulas
 | image     = useful_geometry_formulas.png
 | titletext = Geometry textbooks always try to trick you by adding decorative stripes and dotted lines.