This applet presents a dynamic construction for studying the properties of the centroid or geometric center https://en.wikipedia.org/wiki/Centroid.
The centroid or geometric center of figure is the arithmetic mean position of all n- points in the figure:
. Two special expressions are associated with centroid.
- From its definition: : The Addition of radius vectors of all points relative to the centroid is zero.
- 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 is the smallest. You can compare results with the Steiner's theorem in the case of unit point masses. https://en.wikipedia.org/wiki/Parallel_axis_theorem
Creation of this applet was inspired by alfinio https://www.geogebra.org/material/show/id/DZbG9HMZ— February 26, 2015 - 11:36 PM to prove and implement it for more general case.
Change the number of particles n in a system, the position of points P, B. Make sure that the formula is correct and try again.