The riddle
What Did the Triangle Say to the Circle?
Counting corners
A triangle has three corners, each coming to a point. A circle has none, since its edge is one smooth curve. From where the triangle stands, a circle has no points at all, which is the first meaning of "pointless". The second meaning is the everyday one, without purpose, and the triangle intends it as an insult.
A fair reply
The circle has a comeback available. A circle is made of points, endlessly many, each the same distance from the center. What it lacks is corners, which geometers call vertices. So "pointless" is a fair description only if a point means a sharp corner.
Three corners, one total
The angles at the corners of any triangle add up to 180 degrees, whatever its shape, a result from Euclid's Elements. Triangles also resist being squashed out of shape without bending a side, which is why roof trusses and bridge frames are built from them.
Where the names come from
Triangle comes from Latin and means three-cornered, from tri, three, and angulus, a corner. Circle comes from the Latin circulus, a small ring. One name counts corners and the other describes a ring.
Drawing the scene
The joke is easiest to enjoy with a sketch. Draw a triangle on the left of a page and a circle on the right, and give each a face and a speech bubble. The triangle's three sharp corners are plain to see, and the smooth circle beside it has nothing for the insult to land on, which is the whole of the joke.