The moon cycle from new moon through full moon and back to new moon again was used by many nations to regulate their activities and forms the basis of the Islamic lunar calendar. A calendar based on the first visibility of the lunar crescent is difficult to predict in advance since this observation depends on the clarity of the atmosphere and other local conditions. The interesting observational problem of when it is possible to spot the new moon has been analyzed in the scientific literature as an aid to historians who are seeking to interpret the writings of ancient civilizations.