Washington Apple Pi

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Degrees of separation: compasses go digital

© 2010 Lawrence I. Charters

Washington Apple Pi Journal, reprint information

See accompanying article on Theodolite.

If you remember back to those idyllic days when you were taking trigonometry, you recall that a circle is divided up into 360 degrees, and each degree is divided up into 60 minutes of arc, and each minute is divided into 60 seconds of arc. Dividing a circle into 360 degrees dates back to both Babylon (the year was divided into 360 days) and India; the Rigveda divided life, the heavens, and the year into 360 units. Once you completed trigonometry, you probably promptly forgot all of this – until you bought a GPS unit for your car, or found it included with your mobile phone. Suddenly, those 360 degrees became important again.

A compass is the classic representation of the division of a circle. North is always at zero, at the very top, and the degrees march around clockwise to East at 90, south at 180, West at 270, and North back at zero (or 360). A compass heading of 45 degrees, then, would be heading to the northeast.

Longitude (representing a location by determining how far east or west it is) and latitude (representing a location by how far north or south it is) are projections of a compass onto a globe. Moving from a flat plain to a sphere doesn’t fit terribly well, so cartographers invented the Prime Meridian and the Equator.

The French had their Prime Meridian running through Paris (through the Louvre, once a royal palace), the British had their Prime Meridian running through the Naval Observatory at Greenwich, east of London, and the U.S. had its own Prime Meridian running through the Naval Observatory in the western wilderness District of Columbia (well, it was pretty wild in 1830). As international commerce became more common, these multiple standards proved confusing, so the Prime Meridian – zero degrees longitude – is now “universally”* defined as running through Greenwich, and the 180th Meridian runs through the Pacific. Together they form a perfect circle through the North and South Poles.

Longitude is measured in degrees, minutes and seconds West or East of the Prime Meridian; the Prime Meridian at the U.S. Naval Observatory, for example, is 77º 3’ 2.3” W, or less than a quarter of the way west around the world from Greenwich. Kyoto, Japan has its Prime Meridian (used for 18th and 19th century maps) at 135º 74’ E, three quarters of the way east around the world from Greenwich.

Latitude is determined in degrees North or South from the Equator. If you are on the Equator, your latitude is zero. If you are at the North Pole, your latitude is 90º N, and the South Pole is 90º S. The 45th latitude North runs, in the U.S., from Oregon to Maine, and is halfway between the Equator and the North Pole.

Over time, the degrees, minutes and seconds format got a bit confusing, especially as humans don’t normally think of things in units of 360 or 60. With the advent of GPS, an opportunity came to simplify things, resulting in digital degrees. The Washington Apple Pi office in Rockville, for example, is at 39º 01’ 03.75” N, 77º 03’ 09.80” W in classic notation, or 39º 1.063’ N, 77º 3.163’ W in decimal minutes, or 39.017709º -77.052723º in decimal degrees.** The minus sign before longitude indicates something is West of Greenwich; a minus sign before Latitude would indicate something is South of the Equator.

Decimal degrees are gradually becoming the new standard format for location. The National Weather Service uses decimal degrees on its forecast pages, and most GPS units use decimal degrees. Google Earth allows you to configure it to display location in decimal degrees, degrees with decimal minutes, classic degrees, minutes and seconds, and two other formats. Apple’s Compass application on the iPhone is very retro: it offers just degrees, minutes and seconds.

With this background, you should have no trouble finding the Pi General Meeting at 38.829º -77.306º, which is Enterprise Hall at George Mason University, in Fairfax, VA.

* If the universe is defined as one planet.
** The accompanying article on Theodolite shows a photo of the Pi office building but gives slightly different coordinates. However, that photo was taken from across the street, and reflects the position from which it was taken, slightly to the east and south.