The Sturdy Triangle

Let’s start with a triangle. This is the most robust geometrical shape of all! Believe it or not, if you compare it with a rectangle you’ll be amazed:

triangle 1

Fasten 4 cardboard strips (with paper fastener) to form a rectangle. Now fasten just 3 to form a triangle. Move both around: the rectangle sways from side to side while the triangle doesn’t. Why? The vertices (that is the intersection between two edges) of a triangle are fixed, but not the rectangle’s ones. Why again? Because you can form (that is shape) a unique triangle if you get 3 sticks of determined lengths. A rectangle works differently. Press it and it becomes a parallelogram, press it more and it becomes a different parallelogram, and you can go on without changing its edges’ lengths. The rectangle can be deformed (it changes its original shape) infinitely.

catsNow take a look around you. You’re surrounded by hidden triangles: up in the ceiling, down within the floor, across rivers and highways. Next time in the shopping mall look up at the ceiling to see the heavy metallic beams that span the hypermarket. If the beams are uncovered you can see triangles inside them. Adding rods to the beam in order to form smaller and smaller triangles is known as triangulation. This is a process used since ancient times to stabilize roof structures, bridge structures and even sailing ships.

How would you triangulate a wooden roof? Divide the triangle in two other triangles, then divide one of the resulting triangles into smaller ones and so on. If the roof needs to span a wider distance between walls, keep forming more triangles to make the roof more rigid. The same idea of sturdy triangles lies in fan-like folding papers that become more rigid than the unfolded ones (you surely experimented this at school).

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