Editing Euclidean geometry (section)

==Other general applications==
Because of Euclidean geometry's fundamental status in mathematics, it is impractical to give more than a representative sampling of applications here.

<gallery perrow="3">
File:us land survey officer.jpg|A surveyor uses a [[Dumpy level|level]]
File:Ambersweet oranges.jpg|[[Sphere packing]] applies to a stack of [[orange (fruit)|orange]]s.
File:Parabola with focus and arbitrary line.svg|A parabolic mirror brings parallel rays of light to a focus.
</gallery>

As suggested by the etymology of the word, one of the earliest reasons for interest in and also one of the most common current uses of geometry is [[surveying]].<ref>Ball, p.&nbsp;5.</ref> In addition it has been used in [[classical mechanics]] and the [[Visual perception#Cognitive and computational approaches|cognitive and computational approaches to visual perception of objects]]. Certain practical results from Euclidean geometry (such as the right-angle property of the 3-4-5 triangle) were used long before they were proved formally.<ref>Eves, vol. 1, p.&nbsp;5; Mlodinow, p.&nbsp;7.</ref> The fundamental types of measurements in Euclidean geometry are distances and angles, both of which can be measured directly by a surveyor. Historically, distances were often measured by chains, such as [[Gunter's chain]], and angles using graduated circles and, later, the [[theodolite]].

An application of Euclidean solid geometry is the [[packing problem|determination of packing arrangements]], such as the problem of finding the most efficient [[sphere packing|packing of spheres]] in n dimensions. This problem has applications in [[error detection and correction]].

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File:Damascus Khan asad Pacha cropped.jpg|Geometry is used in art and architecture.
File:Water tower cropped.jpg|The water tower consists of a cone, a cylinder, and a hemisphere. Its volume can be calculated using solid geometry.
File:Origami crane cropped.jpg|Geometry can be used to design origami.
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Geometry is used extensively in [[architecture]].

Geometry can be used to design [[origami]]. Some [[Compass and straightedge constructions#Impossible constructions|classical construction problems of geometry]] are impossible using [[compass and straightedge]], but can be [[mathematics of paper folding|solved using origami]].<ref>{{cite web |url=http://origametry.net/omfiles/geoconst.html |title=Origami and Geometric Constructions |first=Tom|last=Hull |author-link=Tom Hull (mathematician)|access-date=2025-04-08 }}</ref>