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Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.
Boggle gives you 3 minutes to find as many words (3 letters or more) as you can in a grid of 16 letters. You can also try the grid of 16 letters. Letters must be adjacent and longer words score better. See if you can get into the grid Hall of Fame !
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In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field.
Formally, given a vector field v, a vector potential is a vector field A such that
If a vector field v admits a vector potential A, then from the equality
which implies that v must be a solenoidal vector field.
An interesting question is then if any solenoidal vector field admits a vector potential. The answer is yes, if the vector field satisfies certain conditions.
Then, A is a vector potential for v, that is,
The vector potential admitted by a solenoidal field is not unique. If A is a vector potential for v, then so is
where m is any continuously differentiable scalar function. This follows from the fact that the curl of the gradient is zero.
This nonuniqueness leads to a degree of freedom in the formulation of electrodynamics, or gauge freedom, and requires choosing a gauge.