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1

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 ...


2

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 ...


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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 :)


5

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 ...


0

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 ...


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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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