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dreit
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I have always heard that triangles are the strongest geometric shapes. Can anyone explain why this is so?
Triangles are strong because they are the only polygon in which the angles at the corners cannot change without an associated change in the length of an edge.
? which bit of the statement are you doubting? Or is he being sloppy in some detail?Studiot said:Are you sure? I suggest you draw a few.
Studiot said:Are you sure? I suggest you draw a few.
Triangles are strong because they are the only polygon in which the angles at the corners cannot change without an associated change in the length of an edge.
Studiot said:Nobody said the polygons have to be regular,
so I have drawn one regular and one irregular example of where the angle changes substantially, from A to B, without change in the length of any side.
Dr Lots-o'watts said:What about arches and domes?
Studiot said:Nobody said the polygons have to be regular, so I have drawn one regular and one irregular example of where the angle changes substantially, from A to B, without change in the length of any side.
The first case is simple shear, the second is inversion of two sides.
sophiecentaur said:@schipp
Over to you. It must be something to do with angles too. Like, if you change one angle, at least one side must change length. Is that better?
Studiot said:I don't follow the relevance of the (nice) photos of the Quebec bridges?
Archosaur said:I see the triangle debate is settled, no?
As far as domes/arches go, the strongest shape is the "catenary". It is the shape a piece of string makes when it is suspended between two points. (note: it's NOT a parabola, or any conic section, for that matter). Flip that curve upside down and you have the best possible load bearing arch. Why is that? Because at every point on the curve, force is directed directly along the curve. There is no sheer stress, only compression.
http://en.wikipedia.org/wiki/Catenary"
Triangles are considered the strongest shape due to their inherent structural stability. The three sides of a triangle distribute forces evenly, making it difficult to deform or collapse. This is known as the principle of triangulation.
The shape of a triangle allows for the distribution of weight and forces evenly across its three sides. This results in a stronger and more stable structure compared to other shapes, such as squares or circles.
The center of gravity of a triangle is located at the intersection of its three medians, which are lines connecting each vertex to the midpoint of the opposite side. This point is where the weight of the triangle is evenly distributed, making it more stable and less likely to topple over.
The angle of a triangle plays a significant role in its strength. Triangles with acute angles are stronger than those with obtuse angles. This is because acute triangles have shorter sides, resulting in less bending and stress on the structure.
Yes, triangles are used in many real-life applications to create strong and stable structures. Some examples include bridges, cranes, and even the Eiffel Tower. The use of triangles in these structures allows for weight distribution and prevents buckling or collapsing under heavy loads.