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The Rule of Thumb in Mathematics

Posted in: History , Math

Since the process of counting is facilitated by the use of the fingers and toes, it is not surprising that primitive man, like a child, used his fingers and toes as a tally to check off the things he counted. Traces of this ancient way of counting are imbedded in our own language, the word digit meaning not only the numbers 1, 2, 3… but a finger or a toe as well. The use of the fingers undoubtedly accounts for the adoption of our system of counting in tens, hundreds (tens of tens), thousands (tens of hundreds), and so forth


There is little question that geometry, like the number system, was fostered in primitive civilizations to satisfy man’s needs. Fundamental geometric concepts came from observation of figures formed by physical objects. It is likely that the concept of angle, for example, first came from observation of the angles formed at the elbows and knees. In many languages, including modern German, the word for the side of an angle is the word for leg. We ourselves speak of the arms of a right triangle.


Because the Babylonians introduced place value in connection with the base sixty, the Greeks and Europeans used this system in all mathematical and astronomical calculations until the sixteenth century and it still survives in the division of angles and hours into 60 minutes and 60 seconds. Base ten was developed by the Hindus and introduced into Europe during the late Middle Ages.

Taken from Mathematics in Western Culture by Morris Kline.

In case you were wondering how the sexagesimal system looked like for the Babylonians here’s a picture of it:

sexagesimal system