question #3 Sahih Muslim 1080b, Book 13, Hadith 5 : What is the significance of the lunar calendar in determining Islamic months and fasting periods?

The month is thus and thus. (He then withdrew his thumb at the third time). He then said: Fast when you see it, and break your fast when you see it, and if the weather is cloudy calculate it (the months of Sha’ban and Shawwal) as thirty days.