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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 ...


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 ...


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 :)


As pointed out by lemon, two angles are enough to specify a direction in a three dimensional coordinate system, but another is needed to specify a complete coordinate transformation. You can think of a rotation transformation in three dimensions as a mapping between two different coordinate systems. Two angles are needed to specify the relative pointing ...


You have ignored outside influences. Something as simple as asteroids striking the outside of the sphere would push it out of concentric balance and cause a drift toward eccentricity, eventually leading to a contact between the star and the shere (or more likely a vaporization of part of the sphere well before a contact). There would need to be active ...


You are differentiating with respect to $t$, and by the chain rule $${d \over dt}(f(x)) = {df \over dx}{dx \over dt}={df \over dx} \dot{x}$$ You have just missed the $\dot x$ part resulting from proper application of the chain rule!

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