The Agricultural Revolution of the 18th century paved the way for the Industrial Revolution in Britain. New farming techniques and improved livestock breeding led to amplified food production. This allowed a spike in population and increased health. The new farming techniques also led to an enclosure movement-wikipedia
The idea is that some areas who have a higher population would always outweigh areas that have lower populations like California vs Montana. So to fix this they put in place the electoral college which allows areas with lower populations to have more say in voting processes. This is inherently undemocratic yet explains why a popular vote does not always matter.
To allow people to follow the athenians model
heavy rains at least seasonally across the region
It provides easy access to important sea trade routes
My own answer is because they just didn't care for the small land of Greece. Greece was poor and small. Invading Greece and maintaining it would probably have cost quite a lot more than what small profit it actually had. I think Xerxes was foolishly trying to set an example of how people who offended his empire would have been treated and failed, obviously. The Persians probably even thought of the Greeks as primitive, although today we know they weren't, for religious and lifestyle points of view (It is probably quite obvious how sacrificing an animal before every single battle and river crossing and marriage and many more sounded hilarious to the Persians as Zarostrian monotheists) and so miscalculated their strength at first and then totally abandoned them by the time Aristides was finished with the Delian league and had took back most of Ionia and Byzantium was returned to the Greeks.
No Persian ever thought the mistrusting Greeks would ever be united and strong enough of a military unit to be able to pose a threat to their nation. apparently though, according to Diodorus Sicculus, the Persians were interested in the lands of Sicily, because Xerxes had thought it appropriate to send a massive invasion toward the people of Syracuse at the same time that he was campaigning in Greece, the invasion being arranged and managed by the Carthaginians who were by now an ally of the Persian empire.
Note also that after the king's peace was brought about, the Persians never broke their pact, although they interfered greatly in the Peloponessian war and dictated outcomes for specific battles, or supplied Sparta with enough gold so the Spartans could greatly upgrade the size of their fleet and to be able to match or at least contest the strength of the Athenian fleet with the help of their league members.
<span>Conclusively, I suggest the Persians failed to take Greece because they did not wish to conquer it. The land was poor and rough, unsuitable for farming. It was far from the capitals and hard to control, should something happen in Greece it would take at least two to four days for a Chapar to reach the king in Susa or Persepolis. Furthermore, the people of the land were easy to revolt and demanding democracy and this was not to the liking of the monarchic Persian empire, although they allowed the Ionians to have their own popular governments, the Ionians were easier to control than the Hellenes in Greece. Thus the Greeks were best left to themselves.</span>
