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The surface area and the volume of the truncated icosahedron of edge length are: [2] = (+ +) = +. The sphericity of a polyhedron describes how closely a polyhedron resembles a sphere. It can be defined as the ratio of the surface area of a sphere with the same volume to the polyhedron's surface area, from which the value is between 0 and 1.
Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
Volume; system unit code (alternative) symbol or abbrev. notes sample default conversion combinations SI: cubic kilometre: km3 km 3: US spelling: cubic kilometer: 1.0 km 3 (0.24 cu mi) cubic hectometre: hm3 hm 3: US spelling: cubic hectometer: 1.0 hm 3 (35,000,000 cu ft) cubic decametre: dam3 dam 3: US spelling: cubic dekameter: 1.0 dam 3 ...
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.
The factor–label method can convert only unit quantities for which the units are in a linear relationship intersecting at 0 (ratio scale in Stevens's typology). Most conversions fit this paradigm. An example for which it cannot be used is the conversion between the Celsius scale and the Kelvin scale (or the Fahrenheit scale). Between degrees ...
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If the edge length of a regular dodecahedron is , the radius of a circumscribed sphere (one that touches the regular dodecahedron at all vertices), the radius of an inscribed sphere (tangent to each of the regular dodecahedron's faces), and the midradius (one that touches the middle of each edge) are: [21] =, =, =. Given a regular dodecahedron ...