Geometry – Pick Coordinate Too Early is a Sin

by allenlu2007

from MathTheBeautiful



Geometry + Algebra (or calculus) 是最好的 weapon.

但是引入特定座標系同時也是 sin.


vector calculus, tensor calculus, or differential geometry 就是引入座標系但是不指明座標系。


是否可解釋 Lagrangian mechanic and Hamiltonian mechanics that can use generalized coordinates?






Mean curvature = 0 is the key to minimum surface area!

不要太早選 coordinate system.

In differential geometry 就是要注意或是避免這個問題。使用 local coordinate

tensor calculus is the saver

or differential geometry – don’t pick the coordinate system, but use it.


Laplacian of mean curvature = 0?


Vector calculus or tensor calculus =>  powerful computation but keep geometric insight!