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A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
The N class was a branch line steam locomotive that ran on the Victorian Railways (VR) from 1925 to 1966. A development of the successful K class 2-8-0, it was the first VR locomotive class designed for possible conversion from 5 ft 3 in (1,600 mm) to 4 ft 8 + 1 ⁄ 2 in (1,435 mm) standard gauge.
Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the ...
The surface area of a polyhedron is the sum of areas of its faces, for definitions of polyhedra for which the area of a face is well-defined. The geodesic distance between any two points on the surface of a polyhedron measures the length of the shortest curve that connects the two points, remaining within the surface.
The first 57 locomotives were built with domeless boilers with straight throatplates and a low degree of superheat (14 elements in two rows), the boilers of the remaining 13 (5007–5019) were provided with a three-row version (21 elements) [13] having greater total surface area and giving less obstruction to gas flow. [12]
The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality). The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R).
It is a direct consequence of the area inequality [38]: p.114 where K is the area of a convex quadrilateral with perimeter L. Equality holds if and only if the quadrilateral is a square. The dual theorem states that of all quadrilaterals with a given area, the square has the shortest perimeter.
1 μm – the side of a square of area 10 −12 m 2; 1 μm – edge of cube of volume 10 −18 m 3 (1 fL) 1–10 μm – diameter of a typical bacterium [citation needed] 1 μm – length of a lysosome; 1–2 μm – anthrax spore [85] 2 μm – length of an average E. coli bacteria; 3–4 μm – size of a typical yeast cell [86]