Babylon was situated in the area known as Mesopotamia (Greek for "between the rivers"). Mesopotamia was in the Near East in roughly the same geographical position as modern Iraq. Two great rivers flow through this land: the Tigris and the Euphrates. Along these two rivers lay many great trading cities such as Ur and Babylon on the Euphrates. Most of central Mesopotamia would have been desert except in the vicinity of the two rivers: the Tigris and the Euphrates which carry water to the area. These rivers formed the huge alluvial plain on which the agricultural prosperity of the region was built.

It was this area where Babylon was built. To the west of Mesopotamia stretches the Arabian desert. It is inhabited by nomads: the forerunners of the modern Bedouin. These nomads played a significant part in the history of Mesopotamia and of Babylon. Northern Mesopotamia encompasses the foothills of mountains of eastern Anatolia.

This is the area of Assyria. It has a wetter environment. This means crops could be grown partially without irrigation. Most of central Mesopotamia would have been desert except in the vicinity of the two rivers: the Tigris and the Euphrates which carry water to the area. These rivers formed the huge alluvial plain on which the agricultural prosperity of the region was built. It was this area where Babylon was built.

To the west of Mesopotamia stretches the Arabian desert. It is inhabited by nomads: the forerunners of the modern Bedouin. These nomads played a significant part in the history of Mesopotamia and of Babylon. To the east of Mesopotamia lay the land of Elam. Elam lay in present west Iran on the Zagros mountains. Central and southern Mesopotamia: the area south of modern Baghdad forms the area called Babylonia though it incorporates many other cities as well as Babylon. It was here where the conditions were correct because it had one commodity in huge amounts: clay.

Width is square root - half-difference: 20.

Hundreds of these 'rectangular' problems are known. In many cases, just the problem is stated, but in others the procedure is given so that we can see how they solved the particular types of problems. Interestingly, we have no examples of the two basic types given above. They must have been considered too easy to bother writing them down. However, in the case of more complicated types of problems (such as being given the difference of the length and width and the area minus the square of the difference) the first step is to reduce the problem to one of the two standard types above and then solve it with the standard procedure.

The first major analysis of Babylonian rectangular problems was by Solomon Gandz in 1937, in a massive paper in Osiris. He divided Mesopotamian quadratic problems into nine types, o which the simple ones given above are Types I and II. In that paper, Gandz also speculated as to how the Babylonians derived their procedures and noted similarities between their approaches and the procedures of Diophantus, contrasting these with both the Arabic and modern approaches.