Comparison of shadow length between1October 1 15 and winter solstice.

The ancients generally observed the changes of the sun shadow around the winter solstice, and determined the longest day of the sun shadow as the winter solstice. By observing the shadow length of 23 and 24 days before and after the winter solstice, Zu Chongzhi obtained the specific date and time of the winter solstice by using the symmetrical relationship of the shadow length before and after the winter solstice. According to ancient records, the shadow at noon on1October 10 is 10 feet 7 inches and a half before winter, and a little over 10 feet 8 inches after winter/25 and 26 at noon. Based on these data, Zu Chongzhi calculated the winter date from that year to December.