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Difference between revisions of "Varignon theorem"

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One of the fundamental theorems in the theory of sliding vectors (cf. [[Vector|Vector]]). According to Varignon's theorem, if a system of sliding vectors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096330/v0963301.png" /> can be reduced to a single resultant <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096330/v0963302.png" />, the moment of the resultant about some point 0 (or axis <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096330/v0963303.png" />) is equal to the sum of the moments of the vectors constituting the system about this point (or axis):
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One of the fundamental theorems in the theory of sliding vectors (cf. [[Vector]]). According to Varignon's theorem, if a system of sliding vectors $F_{\nu}$ can be reduced to a single resultant $F$, the moment of the resultant about some point 0 (or axis $I$) is equal to the sum of the moments of the vectors constituting the system about this point (or axis):
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$$
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\mathrm{mom}_0 F = \sum_{\nu} \mathrm{mom}_0 F_{\nu}\,;\ \ \ \mathrm{mom}_I F = \sum_{\nu} \mathrm{mom}_I F_{\nu} \ .
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$$
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096330/v0963304.png" /></td> </tr></table>
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Established in 1687 by P. Varignon for a convergent system of forces. The theorem is extensively employed in geometrical statics, kinematics of rigid bodies and strength of materials.
  
Established in 1687 by P. Varignon for a convergent system of forces. The theorem is extensively employed in geometrical statics, kinematics of rigid bodies and strength of materials.
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Latest revision as of 19:11, 26 December 2017

One of the fundamental theorems in the theory of sliding vectors (cf. Vector). According to Varignon's theorem, if a system of sliding vectors $F_{\nu}$ can be reduced to a single resultant $F$, the moment of the resultant about some point 0 (or axis $I$) is equal to the sum of the moments of the vectors constituting the system about this point (or axis): $$ \mathrm{mom}_0 F = \sum_{\nu} \mathrm{mom}_0 F_{\nu}\,;\ \ \ \mathrm{mom}_I F = \sum_{\nu} \mathrm{mom}_I F_{\nu} \ . $$

Established in 1687 by P. Varignon for a convergent system of forces. The theorem is extensively employed in geometrical statics, kinematics of rigid bodies and strength of materials.

How to Cite This Entry:
Varignon theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Varignon_theorem&oldid=42610
This article was adapted from an original article by V.V. Rumyantsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article