question #1 Sahih Muslim 1080b, Book 13, Hadith 5 : How is the beginning and end of Ramadan determined according to Islamic teachings?

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.