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Several countries define their local time by reference to Greenwich Mean Time. [19] [20] Some examples are: Belgium: Decrees of 1946 and 1947 set legal time as one hour ahead of GMT. [19] Ireland: "Standard Time" (Irish: Am Caighdeánach) is defined as being one hour in advance of GMT. [21] "Winter Time" (Am Geimhridh) is defined as being the ...
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 ...
The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean. [8] It is also used in the CPI calculation [9] and recently introduced "RPIJ" measure of inflation in the United Kingdom and in the European Union.
Another application of this theorem provides a geometrical proof of the AM–GM inequality in the case of two numbers. For the numbers p and q one constructs a half circle with diameter p + q. Now the altitude represents the geometric mean and the radius the arithmetic mean of the two numbers.
Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude. This measurement of time was used for everyday use during the 19th century before time zones were introduced beginning in the late 19th century; it still has some uses in astronomy and navigation.
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.
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To determine "longitude by chronometer," a navigator requires a chronometer set to the local time at the Prime Meridian. Local time at the Prime Meridian has historically been called Greenwich Mean Time (GMT), but now, due to international sensitivities, has been renamed as Coordinated Universal Time (UTC), and is known colloquially as "zulu time".