Mock Reciprocal Table

The standard Old Babylonian reciprocal table gave the reciprocals of regular sexagesimal numbers between 2 and 81. (A number is called regular if its reciprocal is a terminating sexagesimal number.) Of the 50 or so known texts, most are incomplete and many are damaged. Some of the tablets also have a couple of extra lines at the beginning. The table below gives the complete standard list and is taken from MCT p11.

The standard format for each line is "igi-n-gál-bi 1/n", where n and 1/n are the reciprocal pair of numbers.

    2    30           16    3,45          45    1,20
    3    20           18    3,20          48    1,15
    4    15           20    3             50    1,12
    5    12           24    2,30          54    1, 6,40
    6    10           25    2,24        1       1
    8     7,30        27    2,13,20     1, 4      56,15
    9     6,40        30    2           1,12      50
   10     6           32    1,52,30     1,15      48
   12     5           36    1,40        1,20      45
   15     4           40    1,30        1,21      44,26,40
This table is also reproduced in A. Aaboe, Episodes from the Early History of Mathematics, Fig 1.2.

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Last modified: 7 June 2001
Duncan J. Melville

dmelville@stlawu.edu