Why Triangles Hold Up Bridges

Of all polygons, only the triangle is rigid — you cannot deform it without changing the length of a side. The math behind this is elegant: three side lengths define exactly one triangle (up to reflection), so a triangle of fixed bars has only one possible shape. Pull or push on it and the angles stay locked.

That single property is why a steel truss can span a river on a frame far lighter than a solid beam. Engineer Buckminster Fuller pushed the idea to its limit with the geodesic dome, wrapping a sphere in thousands of small triangles so the structure carries enormous loads with almost no internal supports.