Is Crescent the Symbol of Islam?

Is there any relation between crescent (hilal) symbol and Islam? Why is there crescent symbol over the domes of masjids and on the flags of Islamic states?

The importance of crescent in Islam is due to its being measure of beginning Ramadan and the hajj (pilgrimage) seasons

“They ask thee, (O Muhammad), of new moons, say: They are fixed seasons for mankind and for the pilgrimage.” (Al-Baqara, 189)
The fasting (sawm) of Ramadan which is a pillar of Islam begins with the appearing of crescent (hilal). In order to make sure of the exact time of fasting and eid (festival), it is accepted as fardh-al kifaya to observe the crescent moon on the setting of the 29th day of Saban and Ramadan. Hanbalis accept observing the moon as recommended (mandub).
Prophet Muhammad (pbuh):
“When you see the crescent (of the month of Ramadan), start fasting, and when you see the crescent (of the month of Shawwal), stop fasting; and if the sky is overcast (and you can’t see it) then regard the crescent (month) of Ramadan (as of 30 days).”
The ramadan crescent is required to be seen by at least two people for the Muslims to start fasting.

The Crescent is not symbol of Islam

The Crescent is neither the symbol of Islam nor regarded holy. Its importance is just based on (Ramadan) hilal.
Islam is the religion of tawhid that declares and proves oneness of Allah. Islam has not any relation with symbols, objects or formalism; it does not accept a symbol or figure as holy. This situation which reminds polytheism is completely contrary to Islam Likewise; even Prophet Muhammad (pbuh) has been the example of Islam, not the symbol of it.

The place (importance) of crescent in the Ottoman State

The Crescent which was the symbol of Byzantium city was used as a symbol in many places in the Ottoman State by Turks after the conquest of Istanbul. (1453)
Besides, since the crescent represents the power of a state, it has been embroidered on flags by Turks. Many Muslim states have also embroidered the crescent on their flags like Turks.
Since the Ottomans ruled over the most powerful Islamic State, people have known Islam by means of Ottomans and seen this glorious state as representative of Islam. Therefore, they have accepted the crescent that was used on the Ottomans’ flag as if it belongs to Islam and when they saw the Ottomans’ flag, as well as Ottomans, they remembered Islam which was their life purpose.
(Fiqh al Islam According to four Madhab, Meydan Larousse Encyclopedia)