Is the Center of Mass Also the Midpoint of a Triangle?

[sparkzbarca]

I blieve the mid point in space of arbitrary triangle formed by points A,B,C

is the point at which the line

A -> midpoint(B,C)
B -> midpoint (A,C)
C ->midpoint (A,B)

meet
(i also think C is redundant, that where A to mid and B to mid cross is basically the mid point of
the whole triangle)

Is my math right?

I can't seem to get a clear answer on google

this is for taking a computer model of a shape and finding the midpoint of one face of the model.
(the faces of course are made by connecting points into triangles)
As such it needs to be for an arbitrary triangle (not right angle only for example)

 

[Curious3141]

What's your definition of the "midpoint" of a triangle? You seem to mean the centroid, but did you know there are three other concepts that could equally validly be called the "midpoint" of a triangle?

See: http://www.mathopenref.com/triangleincenter.html (read that bit about "summary of triangle centres")

If you meant the centroid, yes, that's the way of constructing it, and only 2 of those lines are necessary to define it (the third line will intersect at the same point). The centroid is the most relevant to physical problems like finding the centre of mass of a triangular lamina, so if this is what you're doing, then you're on the right track.

 

[micromass]

What's your definition of the "midpoint" of a triangle? You seem to mean the centroid, but did you know there are three other concepts that could equally validly be called the "midpoint" of a triangle?

I don't really want to hijack this thread, but there are 5427 possible notions of the center of a triangle
See http://faculty.evansville.edu/ck6/encyclopedia/ETC.html

 

[Curious3141]

I don't really want to hijack this thread, but there are 5427 possible notions of the center of a triangle
See http://faculty.evansville.edu/ck6/encyclopedia/ETC.html

Whoa. You mathematician types obviously have nothing but time on your hands...or in your case, flippers, since you're a walrus.

 

[Janno]

Oops

"I can't seem to get a clear answer on google".

Well, I tried for myself, using "midpoint of triangle" for searching.

Lots of results.

 

[lavinia]

If you imagine the triangle as a piece of perfectly uniform cardboard, then the mid point you are speaking of is the center of mass of the triangle.

Suspend the triangle by a vertex in a gravitational field and let it hang freely . A plumb line dropped from the vertex will pass through the center of mass (center of gravity) for other wise the center of mass would exert a torque on the vertex. Since this is true starting from any vertex, the three plumb lines must intersect at the center of mass.

You are right that you only need two of these lines to find this point.

Can you show that this three sides are intersected at their midpoints?