Sun’s direct rays are on the latitudes marked tropic of Capricorn [winter in the North-
ern Hemisphere; summer in the Southern Hemisphere] or tropic of Cancer [winter in
the Southern Hemisphere; summer in the Northern Hemisphere]).
As the measurement of the solar (and lunar) cycle became more accurate, calendars
became increasingly sophisticated. But no calendar dominated until the last few cen-
turies, with many cultures deriving their own calendars—some even combining lunar
and solar cycles in a type of Moon-Sun or luni-solar calendar. This is why although there
is one “standard calendar” used by most countries around the world, certain cultures still
use their traditional calendars, including the Chinese, Jewish, and Muslim calendars.
How did some ancient cultures refinetheir calendars?
There were many different ways that various ancient cultures refined their calendars,
and all of them entailed 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 p. 57). 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 BCE, Greek astronomer and mathematician Hipparchus of Rhodes (c.
170–c. 125 BCE) decided to compare his estimate of the vernal (spring in the Northern
Hemisphere, occurring in March) equinox 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 days, a number only off by about six minutes and 16 seconds. 61
MATHEMATICS THROUGHOUT HISTORY
Why does the Western calendar start with the birth of Christ?
T
he story behind the Western calendar—the one that developed into the cal-
endar used most often today—started in the middle of the 6th century. Pope
John I asked Dacian monk and scholar Dionysius Exiguus (“Dennis the Small,”
c. 470–c. 540; he was born in what is now Romania) to calculate the dates on
which Easter would fall in future years. Dionysius, often called the inventor of
the Christian calendar, decided to abandon the calendar numbering system that
counted years from the beginning of Roman Emperor Diocletian’s reign.
Instead, being of Christian persuasion, he replaced it with a system that started
with the birth of Christ. He labeled that year “1,” mainly because there was no
concept of zero in Roman numerals.