Angles Are Measured in Degrees

¶ … Angles Are Measured in Degrees Minutes and Seconds

An Analysis of Why Angles are Measured in Degrees, Minutes and Seconds

According to Richard Kittler and Stan Darula (2004), "In the era of computers and sophisticated technology many basic principles and concepts inherited from antiquity are sometimes forgotten" (141). Given its ancient origins, the reason angles are measured in degrees, minutes and seconds today has likewise been forgotten by many modern observers. In fact, the basis for this method was developed almost five thousand years ago in Sumeria based on their use of sundials to track time. In her book, Time's Pendulum: The Quest to Capture Time -- from Sundials to Atomic Clocks, Jo Ellen Barnett reports that the convention of the 24-hour period used in the day/night cycle began in ancient Egypt, while the sixty divisions of degrees, minutes and seconds is derived from the number system based on sixty (sexagesimal) of the Mesopotamians; because the Mesopotamians had not yet invented fractional numbers, they preferred whole numbers which could be divided in several different ways, and the number 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30 (Barnett 66). This approach to dividing the day and night into like segments, combined with ancient peoples' observations about the motion of the sun, would ultimately result in the system used to measure angles today.

Darula and Kittler report that, "In the early history of mankind it was realized that a sundial or solar clock can be made from the shade thrown on a horizontal surface by a vertical stick, called a gnomon" (142). Based on their observations of the sun, these ancient peoples came to realize that annual changes of weather were inextricably related to these progressions in time, and they were used to help plan appropriate times for planting crops and performing ceremonies during auspicious periods. In this regard, these authors note that, "The agriculturally most important period was a year, and the time in it to plough, plant and harvest. It was also noticed that moon changes occurring at approximately 30-day periods, roughly coincided with weather seasons. Around 2800 BC a Sumerian king introduced a year divided into 12 months with 30 days, i.e. 360 days in a year, matching the sexagesimal Sumerian calculation base" (Darula & Kittler 142).

Eight centuries later, the gnomon was in use throughout Mesopotamia to determine day-time hours, and 60 minutes and even 60 seconds as standard time scales could be measured by water or sand clocks. During this period, approximately 2030 BC, Egyptians used obelisks as community sundials for the same purpose. The calendar was also refined by incorporating an adjustment for a year with 365 days, a figure that is closer to the exact solar year of 365.24219 days or approximately 365.25 days (365 day per a year compensated every four years by the additional day, now accomplished on by the inclusion of February 29). According to Darula and Kittler:

In the 3rd century BC Alexandria became the centre of civilisation, and it was able to collect the knowledge of Sumer, Babylon, Egypt and Greece, mingled with Persian inventions. This first 'global' Mediterranean culture produced the standard calendar adopted by Julius Caesar in 46 BC, following the system used in Egypt since 238 BC, introduced by Ptolemy III Euergetes on the suggestion of his son's teacher Erasthenes. This so-called Julian calendar is still in use, although the Christian dating has been in existence only since 532 AD. (142).

The basis for angles likewise being measured in degree, minutes and seconds was a new Sumerian-invented lightweight wheel that was supported by three sticks and roped together at its axis to divide a circle into 60 degree; this innovation resulted in sexagesimal measurements of angles within a full 360 degree circle (Darula & Kittler 142).