The centroid of a triangle with uniform density is indeed the center of gravity. This conclusion holds true when the density is uniformly distributed about the centroid. To prove this, one must compare the definitions of the center of mass and the centroid under the condition of constant density. The discussion clarifies that while the centroid serves as the center of gravity in specific cases, this is not universally applicable to all triangles.
PREREQUISITESStudents of physics and mathematics, educators teaching geometry, and professionals in engineering fields who require a solid understanding of centroids and centers of gravity in uniform density contexts.
In general, this isn't true. Indeed, it is true if the triangle in question has uniform density (or the density is uniformly distributed about the centroid).Suk-Sci said:How to prove that centroid is the centre of gravity of a triangle...