The crescent is not a symbol of Islam, but of the Ottoman Empire. The Ottomans are those tribes that moved to Turkey from east and middle Asia. They converted to Islam and built a huge Muslim Empire that ruled the whole Muslim world for centuries. When they took Islam as a religion they started using the lunar calendar, the calendar that was used by Muslims, Jews and early Christians. Even today, the flag of Turkey has a crescent on it. There was no crescent on any mosque built before the Ottomans era.