Here’s a great Geometry activity relating to triangles and points of concurrency (incenter, orthocenter, circumcenter, centroid). I stole this from a friend in Utah.

Cut out some cardboard shapes. Take a shape (start with a circle) and rest it on top of something stable (like a soup can or paper cup). Pour salt on top until you get a nice pile of salt and the three-dimensional pile of salt doesn’t change anymore. (Use something to catch all the salt so you don’t make a mess.) For a circle, you’ll get a cone. For a triangle, you’ll get this.

Neat, huh? Now to all you Geometry fans out there, what are those lines formed by the ridges of the pyramid and where is that apex? Is it the incenter, circumcenter, centroid or some other point of concurrency?

It’s a very fun activity that makes these ideas relating to triangle centers become more tangible. Also very fun is trying to predict what kind of three-dimensional shape will result when you pour salt over other shapes, like a star or semicircle or the letter E, etc..