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I've often heard in engineering that, "there is no shape stronger than a triangle." I also recall that arches are also very strong shapes, which can be crudely described as a perpendicularly-symmetrical half-an-ellipse; Which can be simplified to half a circle.

If there were no conventional complications with designing structures to utilize circles; Which shape is stronger?

Given a simple two-dimension-like application such as simple bridges or trusses as an example, of obvious visualizations.

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The short answer is, if you are making a bridge, triangles are, because the way they distribute weight when they are in a group makes them stronger. A single arch is stronger, but when you use lots of triangles when building a bridge it becomes stronger than using one arch. That is why we use triangles for most of our construction. There are tons of places online that talk about this. Below are some links: https://www.physicsforums.com/threads/physics-of-triangles.443267/ https://answers.yahoo.com/question/index?qid=20070712062525AAXy6Cm http://www.answers.com/Q/What_shape_is_stronger_an_arch_or_a_triangle

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  • $\begingroup$ and to add, if you're making a tank, then a circular wall will be more efficient than any other shape. depends of if the pressure is from the outside in (then you want a triangle) or from the inside out (then you want a circle). $\endgroup$ – robert bristow-johnson Apr 14 '15 at 18:52
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I'm glad that my head is spheroid instead of pyramidal: then the circle is favored.

The eggs have an extremely strong shape: then the circle is favored.

The insects are extremely strong and they favor the round shape.

The engineering/construction by humans are easier with rectilinear elements and the triangular shape are favored.

If I were an explorer of new continents (I'm recalling the conquest of the west of america and the confrontation with the natives(Indians)) I'd put the wagons in a circle to strengthen the defense. The circle is again favored.

/_ A corner of a triangle _\ is easier attacked from the two exterior sides, i.e. there are three weaker regions in the triangle (compared to the central region) .

In the circle there are no weaker regions and the limiting perimeter is minimal irt the protected area/volume.
The towers of the castles are more often than not with a circular pattern. This surface shape offers more options of reflection of any non perpendicular stroke.

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Triangular support(or triangle here) is unparalleled in terms of strength they provide to support load because all the hold mass is properly distributed across the support. You may disagree when g=0 :)

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