"The Middle Ages was a period in Western history spanning the time from the 5th to the 16th century"[0]
and
"Middle Ages, the European historical period from the 5th to the 15th century (476-1453). By analogy, the term is also used to refer to periods in nations outside of Europe having similarities in social and military development"[0]
Iran, even during that period of Islamic rule , is far from similar to Europe on both the social and military level.
"Medieval or Mediaeval (the adjectival form of "Middle Ages") may refer to: Middle Ages, the European historical period from the 5th to the 15th century (476-1453).
By analogy, the term is also used to refer to periods in nations outside of Europe having similarities in social and military development."
So using it for other regions is common. One of these regions is actually Iran. I already gave link that the term is actually used in history of Persia (today known as Iran, the page in Wikipedia is named "Iran," http://en.wikipedia.org/wiki/Iran#Middle_Ages_.28652.E2.80.9... ) for the period 652–1501.
So using it for other regions is common Given that these regions are "having similarities in social and military development".
I was suggesting that the use of the term may not have been accurate given the fact Iran was different from Europe.
Nonetheless, Al-Kāshī(1380-1429) lived under Timurid dynasty (1370–1507)[0] succeeding Iran's "Middle Ages" making him thus, not an "Iranian medieval" astronomer.
"Genghis Khan invaded Transoxiana in 1219 during his conquest of Khwarezm. Before his death in 1227, he assigned the lands of Western Central Asia to his second son Chagatai, and this region became known as the Chagatai Khanate. In 1369, Timur, of the Barlas tribe, became the effective ruler while continuing the ceremonial authority of Chagatai Khan's dynasty, and made Samarkand the capital of his future empire."
There's really no reason to make the division currently present on that page:
It's obviously an error that somebody managed to plant on that Wikipedia page. Another page is better, where medieval period at least naturally includes the last Mongolian dynasty and the early modern era starts with Safavids (1501), as "Encyclopaedia Iranica" also claims:
"The period of the Safavids, the dynasty that took control of Persia in the early 16th century, is often considered the beginning of modern Persian history"
However note also that other authors see Islamic Middle Ages lasting "down until the seventeenth century" and "it may be argued that certain
continuities existed in Islamic civilization down until the advent of modern secular and national ideologies in the
nineteenth century CE." (Medieval Islamic Civilization: An Encyclopedia: http://www.amazon.com/Medieval-Islamic-Civilization-Encyclop...)
Well, you have certainly proven that one must take anything on Wikipedia with a grain of salt. Kudos.
However the point that medieval gives the false impression that Al-Kāshī was a European astronomer still stands but unlike what you suggested before; changing the title, I hope this changed the impression.
See all my previous answers: it is absolutely normal to use "medieval" for historical periods outside of Europe, even for Japan. I also qouted printed encyclopedia "Medieval Islamic Civilization: An Encyclopedia" and "Encyclopaedia Iranica."
"The Middle Ages was a period in Western history spanning the time from the 5th to the 16th century"[0]
and
"Middle Ages, the European historical period from the 5th to the 15th century (476-1453). By analogy, the term is also used to refer to periods in nations outside of Europe having similarities in social and military development"[0]
Iran, even during that period of Islamic rule , is far from similar to Europe on both the social and military level.
0.http://en.wikipedia.org/wiki/Middle_Ages_(disambiguation)