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21 meters – height of High Force waterfall in England; 30.5 meters – length of the lion's mane jellyfish, the largest jellyfish in the world; 33 meters – length of a blue whale, [127] the largest animal on earth, living or extinct, in terms of mass; 39 meters – length of a Supersaurus, the longest-known dinosaur and longest vertebrate [128]
A metric space M is bounded if there is an r such that no pair of points in M is more than distance r apart. [b] The least such r is called the diameter of M. The space M is called precompact or totally bounded if for every r > 0 there is a finite cover of M by open balls of radius r. Every totally bounded space is bounded.
9 ft 8 in (2.95 m) Liverpool and Manchester Railway 1830 at opening day; later widened. 10 ft 8.5 in (3.26 m) United Kingdom (standard gauge plus 6 ft) 11 ft 0 in (3.35 m) New South Wales 1855 old standard (estimated) 12 ft 0 in (3.66 m) New South Wales 1910 new standard for 10 ft 6 in (3.20 m) wide carriages. Rounded in imperial.
A metric space is called complete if all Cauchy sequences converge. Every incomplete space is isometrically embedded, as a dense subset, into a complete space (the completion). Every compact metric space is complete; the real line is non-compact but complete; the open interval (0,1) is incomplete. Every Euclidean space is also a complete metric ...
For instance the same angle of 0.1 mrad will subtend 10 mm at 100 meters, 20 mm at 200 meters, etc., or similarly 0.39 inches at 100 m, 0.78 inches at 200 m, etc. Subtensions in mrad based optics are particularly useful together with target sizes and shooting distances in metric units .
It is also a measure of the space-filling capacity of a pattern and tells how a fractal scales differently, in a fractal (non-integer) dimension. [ 1 ] [ 2 ] [ 3 ] The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity ...
The Euclidean distance is the prototypical example of the distance in a metric space, [10] and obeys all the defining properties of a metric space: [11] It is symmetric, meaning that for all points and , (,) = (,). That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is ...
By multiplication, the best IAU 2009 estimate was A = c 0 τ A = 149 597 870 700 ± 3 m, [20] based on a comparison of Jet Propulsion Laboratory and IAA–RAS ephemerides. [21] [22] [23] In 2006, the BIPM reported a value of the astronomical unit as 1.495 978 706 91 (6) × 10 11 m. [8]
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