In layman’s terms please, no geometry/engineering jargon.
In: Engineering
Because it’s the only self supporting shape.
Imagine the sides of a triangle are sticks which are connected so that they can pivot.
Now push, pull, and twist on that triangle. No matter what you do, it stays a triangle.
If you try that with any other shape, the sides can move and pivot relative to each other while still staying connected but still allow the shape to collapse.
It all comes down to how the forces are distributed. The easiest comparison is with a square. Shear forces (side-to-side) on a square put force into the sides, which then transfer that force into the joints at the corners. That lever action puts immense stress on the corners, so they are likely to break.
Triangles, however, distribute force much better. If you push sideways into the point of a triangle, the force will travel more or less straight down the sides and down into the ground. The joints aren’t doing the heavy lifting, so a triangular structure is a lot stronger.
A triangle is the shape with the fewest number of sides, and thus the most acute or “closed” internal angles, of any shape. 2-sided shapes dont exist, and squares/rectangles have a wider internal angle.
A shapes “strength” is derived from how much force is needed to “bend” each angle open. The more closed the angle starts, the more force it takes to “open” the angle.
Triangles have the most “closed” angles. Squares are number 2, pentagons number 3, etc.
It’s not that they’re the strongest shape – there is a very specific thing that they’re good at. A triangle cannot change shape without changing the length of its sides – this is uniquely true. Imagine a square – if you pulled on the corner then the square would stretch into a parallelogram as the corners bend even if the sides don’t change length.
Triangles can’t be stretched like that. Because of this, if you pull on the corner of a triangle, you will not create any bending force in the sides. Only squishing and stretching.
Let’s pause that for a moment. If I handed you a stick and asked you to break it, how would you go about it? You would bend it, right? You can’t pull a stick apart or crush it with your bare hands but you can *bend* it pretty easily. It’s way easier to bend a material than to stretch or squish it.
So triangles allow us to turn a force *at their corner* into just squishing and stretching, which is easier for materials to deal with. If the force is *not* at the corner then all bets are off.
We do have to go a little bit into geometry for this, but I promise, it’s not big. While you were studying geometry in school, you may have heard of the SSS postulate: if you have two triangles, and their sides have the same lengths, then they are the exact same shape.
This, right here, is pretty much it. If something has more than three sides, I can change the angles around to make more shapes: for example, I could turn a rectangle into a parallelogram, or flip some of the angles in a pentagon inside out, or any number of other things. And when you try to build things out of other shapes, you can see this as well: the angles can bend and distort the original shape, even if nothing is wrong with the beams that make up the sides of these shapes. But triangles are rigid: for any set of three side lengths, there is only one shape it can have. Angles and sides shouldn’t distort unless they snap completely.
This will probably require some drawing. Or match sticks or something to help visualize, but it’s actually a pretty simple geometrical reason: triangles are the shape with the highest load diffusion on their sides. Other answers kind of hit on this but not really so I’m going to try to help out a little more on the visualization of this. Take a triangle, draw it or something, then draw a line from one point to the middle of the opposite side. That is your force. Notice something here: that force is being applied to a point. This means the force will be distributed along the sides of that shape, and what’s at the other end of those sides? The other side. The only other side. So you can just….divide the force in half. Each side is sharing half the load. Try this again with a square. No matter how you orient this, you are applying force in a weird way. Take the example of the side. You push down on the side and now instead of having a pushing force being evenly distributed, you have a pulling force, trying to pull the bean apart. This is much weaker. Now on a point, you will see that the force is pushing the sides out, and then has to push the lower sides in. You can actually help this out pretty easily, of you just connect the middle two corners together to keep the shape from flattening! But notice what you just did? That’s right triangles. You can explore this with any shape you want really, and you’ll find that the strongest configuration for that shape is to divide it into triangles.
One property of a triangle is that for any three side of any length, there is only one possible set of angles that are possible. Triangles are the only shape for which this is true. To distort a triangle you have to distort the lengths of the side, which, in practical terms, means either breaking or bending them. Any other shape can distort without stressing the sides.
Triangle focus all the forces applied to it onto the material, most other shapes focus the forces onto the joints of the shape.
Joints are the weakest part of a shape
It’s a reverse-knife. A knife takes all of the force from your hand and puts it on a thin blade. You can also reverse this – take the force from a small area and spread it out wide. That’s what a triangle does.
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