Difference between revisions of "Barycenter Command"

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<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {1, 1, 1, 1}]</code> yields point ''A(0,0)''}}
 
<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {1, 1, 1, 1}]</code> yields point ''A(0,0)''}}
 
:{{example|1=  
 
:{{example|1=  
<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {2, 1, 1, 1}</code> yields point ''B(0.4,0)''. The ''x''-coordinate of this point was determined by '' <math> \frac{1}{ 2+1+1+1 }*(2*2+1*0+1*(-2)+1*0)</math>''}}
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<code>Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {2, 1, 1, 1}</code> yields point ''B(0.4,0)''. The ''x''-coordinate of this point was determined by '' <math> \frac{1}{ 2+1+1+1 }*(2*2+1*0+1*(-2)+1*0)</math> = <math>\frac{1}{ 5 }*2</math> = 0.4''}}

Revision as of 08:42, 10 July 2012


Barycenter[ <List of Points>, <List of Weights> ]
Set the center of a system of points in the list, defined as the average of their positions, weighted by their value, using the proper formula.
Example: Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {1, 1, 1, 1}] yields point A(0,0)
Example: Barycenter[{(2, 0), (0, 2), (-2, 0), (0, -2)}, {2, 1, 1, 1} yields point B(0.4,0). The x-coordinate of this point was determined by \frac{1}{ 2+1+1+1 }*(2*2+1*0+1*(-2)+1*0) = \frac{1}{ 5 }*2 = 0.4
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