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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.
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 ...
A simple application of dimensional analysis to mathematics is in computing the form of the volume of an n-ball (the solid ball in n dimensions), or the area of its surface, the n-sphere: being an n-dimensional figure, the volume scales as x n, while the surface area, being (n − 1)-dimensional, scales as x n−1.
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 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).
The Army Physical Fitness Test (APFT) was a test designed to measure the muscular strength, endurance, and cardiovascular respiratory fitness of soldiers in the United States Army. The test contained three events: push-ups, sit-ups, and a two-mile run with a soldier scoring from 0 to 100 points in each event based on performance. A minimum ...
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]
[9] [10] [11] In 1938, Beno Gutenberg and Charles Richter analyzed a more extensive set of data and estimated the thickness of the outer core as 1,950 km (1,210 mi) with a steep but continuous 300 km (190 mi) thick transition to the inner core, implying a radius between 1,230 and 1,530 km (760 and 950 mi) for the inner core.