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The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object X {\displaystyle X} in n {\displaystyle n} - dimensional space is the intersection of all hyperplanes that divide X {\displaystyle X} into two parts of equal moment about the hyperplane.
Draw a line joining the centroids. The centroid of the shape must lie on this line . Divide the shape into two other rectangles, as shown in fig 3. Find the centroids of these two rectangles by drawing the diagonals. Draw a line joining the centroids. The centroid of the L-shape must lie on this line .
In geometry, the Euler line, named after Leonhard Euler (/ ˈ ɔɪ l ər / OY-lər), is a line determined from any triangle that is not equilateral.It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
The three medians intersect in a single point, the triangle's centroid or geometric barycenter. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field. [30]
The three medians of a triangle intersect at the triangle's centroid (the point on which the triangle would balance if it were made of a thin sheet of uniform-density metal). The nine-point center of a triangle lies at the midpoint between the circumcenter and the orthocenter. These points are all on the Euler line.
A regular n-gon has a solid construction if and only if n=2 a 3 b m where a and b are some non-negative integers and m is a product of zero or more distinct Pierpont primes (primes of the form 2 r 3 s +1). Therefore, regular n-gon admits a solid, but not planar, construction if and only if n is in the sequence
For triangles (n = 3), the centroids of the vertices and of the solid shape are the same, but, in general, this is not true for n > 3. The centroid of the vertex set of a polygon with n vertices has the coordinates = =,