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248 Gm (1.7 au) – diameter of Enif, a small red supergiant star in the constellation Pegasus [180] 280 Gm (1.9 au) – diameter of Deneb, a blue supergiant and the brightest star in the Cygnus constellation [181] 511 Gm (3.4 au) – average diameter of Mira, a pulsating red giant and the progenitor of the Mira variables.
Proof without words of the AM–GM inequality: PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. Visual proof that (x + y) 2 ≥ 4xy. Taking square roots and dividing by two gives the AM ...
GM gigamolar 10 −12 M pM picomolar 10 12 M TM teramolar 10 −15 M fM femtomolar 10 15 M PM petamolar 10 −18 M aM attomolar 10 18 M EM examolar 10 −21 M zM zeptomolar 10 21 M ZM zettamolar 10 −24 M yM yoctomolar 10 24 M YM yottamolar 10 −27 M rM rontomolar 10 27 M RM ronnamolar 10 −30 M qM quectomolar 10 30 M QM quettamolar
Proof without words of the inequality of arithmetic and geometric means, drawn by CMG Lee. PR is a diameter of a circle centred on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, right triangle PGR can be split into two similar triangles PQG and GQR; GQ / a = b / GQ, hence GQ = √(ab), the geometric mean ...
The outhouse is a unit of area used in nuclear physics equal to 10 −6 barns (100 am 2 = 10 −34 m 2). The barn (b) is a unit of area used in nuclear physics equal to one hundred femtometres squared (100 fm 2 = 10 −28 m 2). The are (a) is a unit of area equal to 100 m 2. The decare (daa) is a unit of area equal to 1000 m 2.
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