Take the tour ×  The proofs without words post has some great
entries. I'm interested in a similar concept: examples where a
problem in math or physics is accompanied by a geometric figure
that illuminates some key relationship in a way that formulas
might not. These wouldn't be "proof by pictures," since they may
not constitute a proof at all.  One example is the relationship
between a quantity that varies inversely to the square of the
distance to a source, and surface area of a sphere centered at
the source. Such an illustration gives insight into gravity, for
example; that it behaves as light intensity does. This is more
significant than merely that "$g=mM/r^k$ for some $k$, and that
$k$ happens to be $2$".  Another example is the integral over
$\mathbb R$ of $1/(1+x^2)$ which is $\pi$. My first experience
with this calc problem was as a child, watching the landscape
from the window of a moving car on the highway. A tree, say 1
unit from the road, spins (relative to me, of course) at a rate
of $1/(1+x^2)$