There were many different ways that various ancient cultures refined their calendars, all of them entailing some type of mathematical calculation. One way to measure the length of a year was by using a gnomon, or a structure that casts a shadow (for more about gnomons and sundials, see above). This was based on the apparent motion of the Sun across the sky, with the shadow not only used to tell daily time, but also to determine the summer solstice, when the shadow created by the gnomon would be at its shortest at noon. By measuring two successive summer solstices, and counting the days in between, various ancient cultures such as the Egyptians developed a more detailed calendar—and as a bonus, determined the exact times of the solstice.

Around 135 B.C.E., Greek astronomer and mathematician Hipparchus of Rhodes (c. 170-c. 125 B.C.E.) decided to compare his estimate of the vernal equinox (spring in the Northern Hemisphere occurring in March) with that made by another astronomer about 150 years earlier. By averaging the number of days, he estimated that a year was equal to 365.24667, a number only off by about 6 minutes and 16 seconds.