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1d
answered Is a principal bundle automorphism locally given by a left action?
1d
answered (Co)Tangent bundle of Cone manifold
1d
revised cross product of vector and direction
added 147 characters in body
1d
answered The Euclidean Metric on $\mathbf R^3$ Induces an Index-Lowering Isomorphism $b:\mathfrak X(\mathbf R^3)\to \Omega^1(\mathbf R^3)$.
1d
comment cross product of vector and direction
Actually this is circular, because the $Z$ direction is chosen exactly so that $\vec z = \vec x \times \vec y$ (it uses a cross product!), which implies what you say.
1d
answered cross product of vector and direction
1d
comment Definition of the vector cross product
The wedge product is a little more natural than the cross product, but less intuitive. The wedge product of two vectors gives you the directed area spanned by the two. The cross product gives you a vector normal to that area, whose length is equal to the area. Clearly the latter is possible only in 3 dimensions. This "being normal to" is the geometric way of visualizing Hodge duality.
1d
revised Is 'a' differentiable in f when f is a product of a differentiable and non-differentiable function?
added 661 characters in body
1d
answered Is 'a' differentiable in f when f is a product of a differentiable and non-differentiable function?
1d
comment Difference between infinitesimal motion and finite motion
Are you sure it's not the opposite, infinitesimal motions commute, finite motions don't?
1d
answered Definition of the vector cross product
Jul
1
comment Embedding of a smooth manifold
Yeah, I think so.
Jul
1
revised Embedding of a smooth manifold
added 1 character in body
Jul
1
comment Embedding of a smooth manifold
Sure, sorry, edited.
Jul
1
answered Embedding of a smooth manifold
Jul
1
asked Sets of compositions of homomorphisms
Jul
1
comment Proof composition of analytic functions is analytic
If you are allowed to pass to the complex plane, it becomes an easy question of holomorphy.
Jul
1
comment To what extent were mathematicians in previous centuries aware of the lack of rigour in their methods?
I would also say that, since mathematics has gone a long way since the pre-modern era, today it is much harder just to "have an intuition", or at least, to have an intuition which everyone shares. Math has become quite too hard for that. So rigor is becoming more important to convince the others of your ideas.
Jul
1
revised Intuitive reason for Fourier Series Convergence
deleted 1 character in body
Jul
1
answered Stoke's Theorem Application on Cylinder