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'''Orazio Lomi Gentileschi''' was an [[Italy|Italian]] painter. He was born in [[1563]] in [[Pisa]] (in [[Tuscany]]) and he died in [[1639]] in [[London]]. He was the father of the painter [[Artemisia Gentileschi]].
In [[mathematics]], the '''root mean square''' or ''rms'' is a [[statistics|statistical]] measure of the magnitude of a varying quantity. It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the ''square root'' of the ''mean'' of the ''squares'' of the values.
He is generally named Orazio Lomi de Gentileschi; it appears that De Gentileschi was his correct surname, Lomi being the surname which his mother had borne during her first marriage. He was born at Pisa, and studied under his half-brother Aurelio Lomi, whom in course of time he surpassed. He afterwards went to [[Rome]], and was associated with the landscape-painter [[Agostino Tasi]], executing the figures for the landscape backgrounds of this artist in the [[Palazzo Rospigliosi]], and it is said in the great hall of the [[Quirinal Palace]], although by some authorities the figures in the last-named building are ascribed to [[Lanfranco]].
The rms for a collection of ''N'' values {''x''<sub>1</sub>, ''x''<sub>2</sub>, ... , ''x''<sub>N</sub>} is:
His best works are ''Saints Cecilia and Valerian'', in the [[Palazzo Borghese]], Rome; ''David after the death of Goliath'', in the Palazzo Doria, [[Genoa]]; and some works in the royal palace, [[Turin]], noticeable for vivid and uncommon coloring. At an advanced age Gentileschi went to [[England]] at the invitation of [[Charles I of England|Charles I]], and he was employed in the palace at [[Greenwich]]. [[Van dyck]] included him in his portraits of a hundred illustrious men. His works generally are strong in shadow and positive in color. He died in England in 1646.
:<math>
x_{\mathrm{rms}} =
\sqrt {{1 \over N} \sum_{i=1}^{N} x_i^2} =
\sqrt {{x_1^2 + x_2^2 + \cdots + x_N^2} \over N}
</math>
{{1911}}
and the corresponding formula for a continuous function f(''t'') defined over the interval T<sub>1</sub> ≤ ''t'' ≤ T<sub>2</sub> is:
{{Commons|Category:Orazio Gentileschi}}
:<math>
{{artist-stub}}
x_{\mathrm{rms}} = \sqrt {{1 \over {T_2 - T_1}} {\int_{T_1}^{T_2} {[f(t)]}^2\, dt}}.
</math>
[[Category:Italian painters|Gentileschi, Orazio]]
=== Uses ===
{{lived|b=1563|d=1639|key=Gentileschi, Orazio}}
The RMS value of a function is often used in [[physics]]. For example, we may wish to calculate the power ''P'' dissipated by an electrical conductor of resistance ''R''. It is easy to do the calculation when a constant current ''I'' flows through the conductor. It is simply,
:<math>(1)\qquad\qquad P = I^2 R</math>
But what if the current is a varying function I(''t'')? This is where the rms value comes in. It may be shown that the rms value of I(''t'') can be substituted for the constant current ''I'' in the above equation to give the mean power dissipation, thus:
:<math>(2)\qquad\qquad P = I_{rms}^2 R</math>
In the common case of [[alternating current]], when I(''t'') is a [[sinusoid]]al current, as is approximately true for mains power, the rms value is easy to calculate from equation (2) above. The result is:
:<math>I_{\mathrm{rms}} = {I_p \over {\sqrt 2}}</math>
where I<sub>p</sub> is the peak amplitude.
The RMS value can be calculated using equation (2) for any waveform, for example an audio or radio signal. This allows us to calculate the mean power delivered into a specified load. For this reason, listed voltages for power outlets (eg. 110V or 240V) are almost always quoted in RMS values, and not peak-to-peak values.
It is important to note that rms is a mean value and not an instantaneous measurement. Therefore expressions such as "peak RMS power", sometimes used in advertisements for audio amplifiers, are misleading. See also [[PMPO]].
==See also==
* [[Standard deviation]]
* [[Table of mathematical symbols]]
== External links ==
* [http://www.tpi-thevalueleader.com/rms.html RMS values and measurement]
* [http://www.hifi-writer.com/he/misc/rmspower.htm An explanation of why RMS is not usually equivalent to power]
[[Category:Statistics]]
[[de:Effektivwert]] [[sv:Effektivvärde]] [[nl:Root mean square]]
[[Category:Means]]
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