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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.
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 .
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...
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]
An affine space need not be included into a linear space, but is isomorphic to an affine subspace of a linear space. All n -dimensional affine spaces over a given field are mutually isomorphic. In the words of John Baez , "an affine space is a vector space that's forgotten its origin".