List of centroids

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The following is a list of centroids of various two-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of . For an object of uniform composition (mass, density, etc.) the centroid of a body is also its centre of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines.

Centroids[edit]

For each two-dimensional shape below, the area and the centroid coordinates are given:

Shape Figure Area
Right-triangular area Centroid of a triangle.svg
Quarter-circular area[1] Centroid of a quarter circle.svg
Semicircular area[2] Centroid of a semicircle.svg
Quarter-elliptical area Centroid of a quarter ellipse.svg
Semielliptical area Centroid of a semiellipse.svg
Semiparabolic area

The area between the curve and the axis, from to

Half Parabolic Segment Centroid.png
Parabolic area The area between the curve and the line
Parabolic spandrel The area between the curve and the axis, from to
General spandrel The area between the curve and the axis, from to
Circular sector Centroid of a circular sector.svg
Circular segment Centroid of a circular segment.svg
Quarter-circular arc The points on the circle and in the first quadrant
Semicircular arc The points on the circle and above the axis
Arc of circle The points on the curve (in polar coordinates) , from to

See also[edit]

References[edit]

  1. ^ "Quarter Circle". eFunda. Retrieved 23 April 2016. 
  2. ^ "Circular Half". eFunda. Retrieved 23 April 2016. 

External links[edit]