Short History on Map Projections

Abstract

Map projections appeared more than two millennia ago, when ancient Greek scientists started applying mathematical principles to studying and representing the celestial sphere. Hundreds of map projections have been invented since. There is no limit to the number of possible map projections and their usefulness motivates scientists to develop new ones. Map projections have recently been developed to represent planets or asteroids which are too irregular to be modelled with a sphere or a rotational ellipsoid. In general, map projections are a field of mathematics, just like differential or projective geometry. Few map projections are based on perspective, while all other are some sort of mapping a continuous curved surface into a plane. Famous mathematician Leonhard Euler provided the first proof that a sphere's surface can not be mapped onto a plane without distortion in 1777. Considering each map projection includes certain distortion, map projection theory primarily deals with researching map projection distortions. Most map projections can not be interpreted in a simple geometrical or physical manner and they are defined by mathematical formulae. Each map projection provides an image distorted in a different way. Studying map projections yields those distortions' characteristics. Therefore, a cartographer should apply a map projection according to desired and arbitrary properties or conditions. Map projections have developed concurrently with development of map production and cartography in general. This chapter provides a brief overview of map projection development from their beginnings to the present days, mentioning famous names such as Gerhard Mercator, Johann Heinrich Lambert, Carl Friedrich Gauß, Nicolas Auguste Tissot, John Parr Snyder and many others.