Concept:
The Greek Geometric period was an important phase in ancient Greek art history. It is especially known for its pottery decorated with geometric patterns such as circles, triangles, zigzags, and meanders.
Step 1:
The Geometric style refers to a form of Greek pottery decoration where artists used mathematical and geometric designs to decorate the pottery surface.
Step 2:
This style developed after the collapse of the Mycenaean civilization and during the Greek Dark Ages.
Step 3:
Greek Geometric pottery commonly featured horizontal bands filled with repeated patterns, human figures, animals, and ceremonial scenes arranged in a highly stylized manner.
Step 4:
Historians generally date the Greek Geometric period from approximately 1000 B.C. to 700 B.C.
Step 5:
Among the given choices, the period 1000--700 B.C. correctly matches the era of Greek geometric painted pottery.
\[
\boxed{\text{(4) 1000--700 B.C.}}
\]