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Izu–Bonin–Mariana Arc, Mariana Trench, Pacific Ocean 11,034 36,197 6.86 2 Tonga Trench: Pacific Ocean 10,882 35,702 6.76 3 Emden Deep: Philippine Trench, Pacific Ocean 10,545 34,580 6.54 4 Kuril–Kamchatka Trench: Pacific Ocean 10,542 34,449 6.52 5 Kermadec Trench: Pacific Ocean 10,047 32,963 6.24 6 Izu–Ogasawara Trench: Pacific Ocean ...
Many of these problems are easily solvable provided that other geometric transformations are allowed; for example, neusis construction can be used to solve the former two problems. In terms of algebra , a length is constructible if and only if it represents a constructible number , and an angle is constructible if and only if its cosine is a ...
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
The Ancient Tradition of Geometric Problems studies the three classical problems of circle-squaring, cube-doubling, and angle trisection throughout the history of Greek mathematics, [1] [2] also considering several other problems studied by the Greeks in which a geometric object with certain properties is to be constructed, in many cases through transformations to other construction problems. [2]
In British and Canadian military argot it equates to a range of terms including slit trench, or fire trench (a trench deep enough for a soldier to stand in), a sangar (sandbagged fire position above ground) or shell scrape (a shallow depression that affords protection in the prone position), or simply—but less accurately—as a "trench".
"Can a ball be decomposed into a finite number of point sets and reassembled into two balls identical to the original?" The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different ...