https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=Vanille 2026-05-17T12:20:55Z User contributions MediaWiki 1.30.0 https://www.explainxkcd.com/wiki/index.php?title=2509:_Useful_Geometry_Formulas&diff=217355 2021-08-31T08:46:53Z

<p>Vanille: Start transcript; not sure if/how to describe the position of arrows with text</p> <hr /> <div>{{comic<br /> | number = 2509<br /> | date = August 30, 2021<br /> | title = Useful Geometry Formulas<br /> | image = useful_geometry_formulas.png<br /> | titletext = Geometry textbooks always try to trick you by adding decorative stripes and dotted lines.<br /> }}<br /> <br /> ==Explanation==<br /> {{incomplete|Created by an AREA OF A CIRCLE IN A SPHERE. Explain the formulas for each of the areas, and also the correct formula for the 3D object they seems to represent. Do NOT delete this tag too soon.}}<br /> This comic showcases area formulae for 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 a circle, the second an equation for a triangle with an elliptical base, the third an equation for a rectangle with an elliptical base and top, and the fourth a hexagon consisting of two right angled congruent corners and two congruent diagonal lines connecting them. In each case, only the outlines of each shape have any practical meaning.<br /> <br /> Such illustrations are commonly found in geometry textbooks, which need to depict three-dimensional figures on a two-dimensional page using dashed lines to indicate a line occluded by the solid. The joke is that the formulas are for the area of each two-dimensional shape as drawn, not for the surface area or volume of the illustrated 3D object (as would be shown in the geometry textbook). And that the text books just add the &quot;decorative&quot; stripes and dotted lines to trick the reader, as stated in the title text.<br /> <br /> In reading order they are a circle (illustrating a sphere), a triangle combined with a half-ellipse (illustrating a cone), a rectangle with two half-ellipses (illustrating a cylinder) and a convex 6-sided polygon with parallel sides and two right angle corners (illustrating a rectangular prism).<br /> <br /> ==Transcript==<br /> {{incomplete transcript|Do NOT delete this tag too soon.}}<br /> :[Four figures in two rows of two, each depicts a two-dimensional representation of a three-dimensional object, with some labeled dimensions represented as arrows and a formula underneath indicating its area]<br /> <br /> :Useful geometry formulas<br /> <br /> :[Top left; a sphere with its radius labeled r]<br /> A = πr²<br /> <br /> :[Top right; a cone with its height h. The ellipse in place of the base has semi-minor axis a and semi-major axis b]<br /> A = 1/2 πab + bh<br /> <br /> :[Bottom left; a cylinder with height h. The ellipses have semi-minor axis r and semi-major axis d]<br /> A = d(πr/2 + h)<br /> <br /> :[Bottom right; a prism with width b, height h, depth d. The base has an angle θ]<br /> A = bh + d(b sinθ + h cosθ)<br /> <br /> {{comic discussion}}<br /> <br /> [[Category:Math]]</div>

Vanille