Question

Part 1: What is the centroid of a triangle?
Part 2: Where can the centroid be found in relation to the triangle

Answer 1

http://www.netcomuk.co.uk/~jenolive/centroid.html

Answer 2

centroid is the point where the medians intersect.

Answer 3

\[(x _{1}+x _{2}+x _{3}/3), (y _{1}+y _{2}+y _{3}/3)\]

Answer 4

would it be right to say, centroid is center of a body and in this case it's the center of the triangle?

Answer 5

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three triangle medians (Johnson 1929, p. 249; Wells 1991, p. 150)

Answer 6

@Ishaan94: Centre of a polygon is the point inside the polygon which is equidistant from all sides, but centroid is not equidistant but incenter is, so ...

Answer 7

EarthCitizen, your formula is not correct.

Answer 8

\[ \left( \large \frac{x _{1}+x _{2}+x _{3}}3 , \frac{y _{1}+y _{2}+y _{3}}3 \right) \]

Answer 9

yeah i know, center of mass but is center of mass same as center of the body, when we say geometric center what do we mean by it?

oh okay, but does the center needs to be equidistant from all the sides, sides for vertices

Answer 10

like in physics we calculate center of mass (centroid) to represent a body, not incenter

Answer 11

centre is generally defined as equidistant from something.

Answer 12

I don't know why are you try to get a analogy of a planer figure with cenre of gravity ..

Answer 13

hmm we usually calculate center of mass in 2D space only, I mean nearly all interaction takes place in 2D space (in our current curriculum, physics)

i think centroid should be the center of a body, how will you define center of a unsymmetrical body?

Answer 14

Geometric center of a three dimensional solid may (made) be equal to the center of mass but they are conceptually different.

Answer 15

I can't think of anything else other than approximation for asymmetrical planer figures.