  We present three reasons for rewriting the Einstein equation. The new version
is physically equivalent but geometrically more clear. 1. We write $4 \pi$
instead of $8 \pi$ at the r.h.s, and we explain how this factor enters as
surface area of the unit 2--sphere. 2. We define the Riemann curvature tensor
and its contractions (including the Einstein tensor at the l.h.s.) with one
half of its usual value. This compensates not only for the change made at the
r.h.s., but it gives the result that the curvature scalar of the unit 2--sphere
equals one, i.e., in two dimensions, now the Gaussian curvature and the Ricci
scalar coincide. 3. For the commutator $[u,v]$ of the vector fields $u$ and $v$
we prefer to write (because of the analogy with the antisymmetrization of
tensors) $$[u,v]\ = \ \frac{1}{2} \, ( \, u\, v \ - \ v \, u \,)$$ which is one
half of the usual value. Then, the curvature operator defined by $$ \nabla_{[u}
\ \nabla_{v]} \quad - \quad \nabla_{[u,\,v]}$$ (where $\nabla $ denotes the
covariant derivative) is consistent with point 2, i.e., it equals one half of
the usual value.
