Lunar calendar average length of the synodic month is days. Thus it is convenient if months generally alternate between 29 and 30 days (sometimes termed respectively “"hollow"” and “"full"”). The distribution of "hollow" and "full" months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed: These fractions can be used to construct a lunar calendar, or in combination with a solar calendar
Thomas Fuller (mental calculator) skill was even used as proof that enslaved Blacks were equal to whites in intelligence, which fueled some pro-abolitionist discussion. When Fuller was about 70 years old, William Hartshorne and Samuel Coates of Pennsylvania were in Alexandria and, having heard of Fuller's powers, sent for him. They asked him two questions which satisfied their curiosity. First, when they asked him how many seconds there were in a year and a half, he answered in about two minutes, 47,304,000. Second, when they asked how many seconds a man has lived who is 70 years, 17 days and 12 hours old, he