Thanks for asking this important question, as it's one
that not many cooks think about. Yes, the size and shape
of a pot does indeed influence what's cooking inside!
Here are a few examples that illustrate how the size and
shape of various pots suits different types of cooking.
If you're making a reduction sauce that involves boiling
away part of the liquid, you need a wide shallow pan,
as this exposes as much surface area as possible (in both
the pan and the liquid) so evaporation takes place quickly.
A pan for sauces may be somewhat deeper, but it's also
wide so it's easy to stir. Always keeping the liquid in
motion distributes the heat evenly throughout, so as the
sauce is stirred it thickens without lumping.
In contrast, a fat stubby bean pot that goes in the oven
is equally well suited to its task. Its tight fitting
lid holds moisture inside. During a long and leisurely
baking as steam rises, it condenses on the upper portion
of the curved sides, so the beans are always bathed in
moisture. As many traditional bean pots are made of clay,
the heat is transferred slowly and evenlyjust what
beans require as they soften and develop flavor.
In addition to differences in size and shape, cooking
pots and pans are also strongly influenced by the type
and quality of the materials from which they are made.