# Coordinates to an Orthogonal Order

Excerpt from the appendix of Flexible Signposts to Coded Territories (AKV/2012)

Coordinates to an Orthogonal Order

1. Hippodamian Grid
The Hippodamian System is an urban planning concept that organizes the layout of cities into a system of streets aligned in relation to the cardinal points, which intersect orthogonally. The concept’s namesake, the Greek philosopher, mathematician, physician and urban planner Hyppodamus of Miletos (498BC-408BC) is  attributed as the “father” of urban planning. The grid cities of Thurii, Rhodes, Miletus and Piraeus are among those he supposedly has planned.
The objective of the Hippodamian Grid is to enhance harmony and rational social order, conserve land area, provide more orderly circulation throughout the city, provide a more efficient delivery of water, and removal of sewage and garbage disposal.
The grid layout had its critics, as it was understood to substantiate social segregation. According to Aristotle: Hippodamus “invented the division of cities by classes”.

2. Ptolemy Coordinate System
Claudius Ptolemaeus (90 to 170 CE), the author of Geographia, was the first to place a latitude and longitude grid system on a map, using it to chart the entire known world. Geography consisted of eight volumes, of which the first thoroughly discussed the geographic knowledge of the Greco-Roman world and the problems of representing the spherical earth on a flat sheet of paper. The other seven volumes were a gazetteer providing topographic lists of 8000 places and the data correlating them, enabling their positioning.

3. Mercator Projection
The Mercator projection is a cylindrical map projection coined by the Flemish geographer and cartographer Gerardus Mercator in 1569.
It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, as straight segments.
Being a conformal projection, angles are preserved around all locations. However scale varies from place to place, distorting the size of geographical objects and conveying a distorted idea of the overall geometry of the planet. At latitudes greater than 70° north or south, the Mercator projection is practically unusable.

4. Universal Transverse Mercator (UTM)
The Military Grid Reference System is the geocoordinate standard used by NATO militaries for locating points on the earth. The MGRS is derived from the Universal Transverse Mercator (UTM) grid system which was developed by the United States Army Corps of Engineers in the 1940s.
It is a horizontal position representation, i.e. it is used to identify locations on the earth independently of vertical position, but differs from the traditional method of latitude and longitude in several respects. Prior to the development of the UTM coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the interwar period. Calculating the distance between two points on these maps could be performed more easily in the field than was possible using the trigonometric formulas required under the graticule-based system of latitude and longitude.
The transverse Mercator projection is a variant of the Mercator projection.

Source 1-3: 3000 Jahre arithmetischer Raumordnung, Earnest Bindel, Verlag Neues Geistesleben, Tübingen, 1958
Source 4: Military Grid Reference System: The Geographer’s Craft Project, Peter H. Dana, The University of Colorado, Boulder, 1994