Why equilateral triangle is a strong shape?

Answer 1

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Strong is a subjective term. I'm not quite sure how to apply "strong" to a basic geometric shape but I think I know where you are going with this...

Since it only takes three stationary points to define a plane, a triangle is the simplest shape made of straight lines which can define a plane. Triangles are rigid. I suppose since all sides of an equilateral triangle are the same length, they are all equally weak: the longer a span is between two points, the inherently weaker it is. Isosceles and scalene triangles always have two sides longer than the third, making those two sides weaker.

In construction, triangle shapes are used in braces and gussets for rigidity, and in joist and truss construction to provide a lightweight alternative to a solid beam without sacrificing load transference capabilities. A tetrahedron is the simplest three dimensional shape made up of triangles.

Comparatively, a circle is defined by two points, the center point and a perimeter point in motion around the center point (think of drawing a circle with a compass.) A circle is "stronger" than a triangle because it has no lines suspended between two points.

Spheres can withstand more external pressure than any other shape, hence, they are used in deep ocean craft.

JCS