Babylonian Mathematics

Topics: Mesopotamia, Babylonia, Sexagesimal Pages: 18 (4872 words) Published: September 12, 2013
Babylonian Mathematics1
1 Introduction

Our first knowledge of mankind’s use of mathematics comes from the Egyptians and Babylonians. Both civilizations developed mathematics that was similar in scope but different in particulars. There can be no denying the fact that the totality of their mathematics was profoundly elementary2 , but their astronomy of later times did achieve a level comparable to the Greeks.

2 Basic Facts

The Babylonian civilization has its roots dating to 4000BCE with the Sumerians in Mesopotamia. Yet little is known about the Sumerians. Sumer was first settled between 4500 and 4000 BC by a non-Semitic 1 °2002, c 2 Neugebauer,

G. Donald Allen 1951

Babylonian Mathematics


people who did not speak the Sumerian language. These people now are called Ubaidians, for the village Al-Ubaid, where their remains were first uncovered. Even less is known about their mathematics. Of the little that is known, the Sumerians of the Mesopotamian valley built homes and temples and decorated them with artistic pottery and mosaics in geometric patterns. The Ubaidians were the first civilizing force in the region. They drained marshes for agriculture, developed trade and established industries including weaving, leatherwork, metalwork, masonry, and pottery. The people called Sumerians, whose language prevailed in the territory, probably came from around Anatolia, probably arriving in Sumer about 3300 BC. For a brief chronological outline of Mesopotamia see See also˜dee/MESO/TIMELINE.HTM for more detailed information. The early Sumerians did have writing for numbers as shown below. Owing to the scarcity of resources, the Sumerians adapted the ubiquitous clay in the region developing a writing that required the use of a stylus to carve into a soft clay tablet. It predated the







cuneiform (wedge) pattern of writing that the Sumerians had developed during the fourth millennium. It probably antedates the Egyptian hieroglyphic may have been the earliest form of written communication. The Babylonians, and other cultures including the Assyrians, and Hittites, inherited Sumerian law and literature and importantly their style of writing. Here we focus on the later period of the Mesopotamian civilization which engulfed the Sumerian civilization. The Mesopotamian civilizations are often called Babylonian, though this is not correct. Actually, Babylon3 was not the first great city, though the whole civilization is called Babylonian. Babylon, even during its existence, was not always 3 The first reference to the Babylon site of a temple occurs in about 2200 BCE. The name means “gate of God.” It became an independent city-state in 1894 BCE and Babylonia was the surrounding area. Its location is about 56 miles south of modern Baghdad.

Babylonian Mathematics


the center of Mesopotamian culture. The region, at least that between the two rivers, the Tigris and the Euphrates, is also called Chaldea. The dates of the Mesopotamian civilizations date from 2000-600 BCE. Somewhat earlier we see the unification of local principates by powerful leaders — not unlike that in China. One of the most powerful was Sargon the Great (ca. 2276-2221 BC). Under his rule the region was forged into an empire called the dynasty of Akkad and the Akkadian language began to replace Sumerian. Vast public works, such as irrigation canals and embankment fortifications, were completed about this time. These were needed because of the nature of the geography combined with the need to feed a large population. Because the Trigris and Euphrates would flood in heavy rains and the clay soil was not very absorptive, such constructions were necessary if a large civilization was to flourish. Later in about 2218 BCE tribesmen from the eastern hills, the Gutians, overthrew Akkadian rule giving rise to the 3rd...
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