This applet presents a dynamic construction for studying the properties of the [color=#ff00ff]centroid[/color] or  [color=#ff00ff]geometric center[/color] [url=https://en.wikipedia.org/wiki/Centroid]https://en.wikipedia.org/wiki/Centroid[/url] .[br][color=#333333]The centroid or Geometric Center [/color]of figure is the arithmetic mean position [math]\vec{P_i}[/math] of all n- points in the figure:[br] [math]\vec{C_m}=\frac{\sum\vec{P_i}}{n},i=1,...,n[/math]. Two special expressions are associated with centroid.[br] - From its definition: [math]\sum\left(\vec{C_m}-\vec{P_i}\right)=0[/math] : The Addition of radius vectors of all points relative to the centroid is zero.[br] - Difference of the two sums: over the squared distances for all points from B and from the centroid is equal to the n times squared distance between centroid and B. It follows, that the sum of the squared distances for all points from the centroid [math]C_m[/math] is the smallest. You can compare results with the Steiner's theorem in the case of unit point masses. [url=https://en.wikipedia.org/wiki/Parallel_axis_theorem]https://en.wikipedia.org/wiki/Parallel_axis_theorem[/url] [br] Creation of this applet was inspired by alfinio [url=https://www.geogebra.org/material/show/id/DZbG9HMZ— February 26, 2015 - 11:36 PM]https://www.geogebra.org/material/show/id/DZbG9HMZ— February 26, 2015 - 11:36 PM[/url] to prove and implement it for more general case.[br] Change the number of particles n in a system, the position of points P[math]_i[/math], B. Make sure that the formula is correct and try again.[br]