There was no Greek empire.
The Greek world comprised hundreds of independent city-states, some of which from time to time formed defensive leagues. Alexander took over the Persian Empire, which effectively became a Macedonian Empire for a short time until his death. After that his Macedonian successors carved out of this empire their own Hellenistic kingdoms in opposition to each other.
Meanwhile Rome progressively dominated Italy, defeated Carthage to become dominant in the western Mediterranean, then turned east and progressively defeated and absorbed the Hellenistic kingdoms into the Roman Empire.
The Macedonian empire lasted a couple of decades. The Roman empire lasted over a thousand years.
The ongoing influence of the two cultures has been significant. Latin became a component of first the languages of Spain, Portugal, France and Itally, which we call Romance languages to acknowledges, and through French and Latin, into the world-wide English language. Greek language has had a far lesser impact but is now growing in importance in coining new technical words. Western law is based on Roman law. Other cultural influences have come from Rome, much of which however has been influenced by Greek, but not Macedonia.
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In size at their peak they were not dissimilar in geographic area.
However the Macedonian one came apart within a decade after Alexander died, as his generals seized portions for themselves and fought each other; and parts of it, especially in the east, progressively reverted to native rule and custom. The Roman Empire lasted for over a thousand years, demonstrating the Roman capacity for governance, and sowing their culture.
See the maps:
http://www.roman-empire.net/maps/empire/extent/rome-modern-day-nations.html
http://ancienthistory.about.com/od/events/ig/4th-Century-Greece-and-Rome/Map-of-the-Macedonian-Empire.htm
The city of Rome was smaller in ancient times, while the ancient kingdom of Macedonia was larger. In terms of area conquered, the Roman Empire at its height was larger, but it took centuries to achieve. The Macedonian Empire is more impressive considering that it was done in the space of two lifetimes. Philip II of Macedon added Thrace to his kingdom simply by marriage, and then he united Greece. Alexander conquered the entire Persian Empire, including lands never acquired later by the Romans. Upon Alexander's untimely death, the Macedonian Empire divided, and centuries later were absorbed into the Roman sphere somewhat easily.
At this point neither, it matters at what time you are referring to. In the prime of its days, the Roman Empire was definitely larger, but it was eventually conquered by the Turks who I believe were Muslims.
The Roman Empire is bigger than Italy today
Mesopotamia came under the control progressively of the Assyrian Empire, the Babylonian Empire, the Persian Empire, the Macedonian Empire, the Roman Empire, etc etc up to today's Iraq. All the rest of the world did not occupy Macedonia.
no romes was bigger
No. He was probably of roman origin, as his parents spoke roman, neither macedonian nor dardanian, nor illyrian.
which empire:, Persian, Macedonian, Roman, Byzantine, Arab, Ottoman, French or British? Any way the answer must be the Egyptians