# Carnot's theorem

In

Euclidean geometry ,**Carnot's theorem**, named afterLazare Carnot (1753–1823), is as follows. Let "ABC" be an arbitrarytriangle . Then the sum of thesigned distance s from thecircumcenter "D" to the sides of triangle "ABC" is:"DF" + "DG" + "DH" = "R" + "r",

where "r" is the

inradius and "R" is thecircumradius . Here the sign of thedistances is taken negative if and only if theline segment "DX" ("X" = "F", "G", "H") lies completely outside the triangle. In the picture "DF" is negative and both "DG" and "DH" are positive.Carnot's theorem is used in a proof of the

Japanese theorem for concyclic polygons .**External links***

* [*http://www.cut-the-knot.org/proofs/carnot.shtml Carnot's Theorem*] atcut-the-knot

* [*http://www.cut-the-knot.org/pythagoras/Carnot.shtml Yet another Carnot's Theorem with multiple applications*] atcut-the-knot

* [*http://demonstrations.wolfram.com/CarnotsTheorem/ Carnot's Theorem*] by Chris Boucher.The Wolfram Demonstrations Project .

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Carnot-Clausiussches Theorem**— Carnot Clausiussches Theorem, s. Clausiusscher Grundsatz … Lexikon der gesamten Technik**Carnot's theorem**— /ˈkanoʊz ˌθɪərəm/ (say kahnohz .thearruhm) noun Physics a theorem which proposes that no engine operating between two temperatures can be more efficient than a Carnot engine operating between the same two temperatures. {See Carnot cycle} … Australian English dictionary**carnot's theorem**— noun or carnot s principle Usage: usually capitalized C Etymology: translation of French principe de Carnot, after N.L.S. Carnot, its formulator : a principle in thermodynamics: an engine working in a reversible cycle is at least as efficient as… … Useful english dictionary**Carnot's theorem**— Thermodynam. the principle that no engine operating between two given temperatures can be more efficient than a Carnot engine operating between the same temperatures. * * * … Universalium**Carnot's theorem (thermodynamics)**— Carnot s theorem, also called Carnot s rule is a principle which sets a limit on the maximum amount of efficiency any possible engine can obtain, which thus solely depends on the difference between the hot and cold temperature reservoirs. Carnot… … Wikipedia**Carnot**— is the name of a celebrated French family in politics and science with the following members:*Lazare Nicolas Marguerite Carnot (1753 1823), mathematician and politician. *Nicolas Léonard Sadi Carnot (1796 1832), mathematician and eldest son of… … Wikipedia**Carnot heat engine**— A Carnot heat engine [In French, Carnot uses machine à feu , which Thurston translates as heat engine or steam engine . In a footnote, Carnot distinguishes the steam engine ( machine à vapeur ) from the heat engine in general. (Carnot, 1824, p. 5 … Wikipedia**Carnot cycle**— The Carnot cycle is a particular thermodynamic cycle, modeled on the hypothetical Carnot heat engine, proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded upon by Benoit Paul Émile Clapeyron in the 1830s and 40s. Every thermodynamic… … Wikipedia**carnot's principle**— noun see carnot s theorem … Useful english dictionary**Carnot theorem**— Karno teorema statusas T sritis fizika atitikmenys: angl. Carnot theorem vok. Carnot Satz, m rus. теорема Карно, f pranc. théorème de Carnot, m … Fizikos terminų žodynas