Students can be placed in the role of mathematical archaeologists and led to discoveries. Assume that the class has discussed numeration systems including the sexagesimal Babylonian cuneiform system. They are presented with a facsimile of the face of a clay tablet from the Yale Babylonian Collection (7289):
If recognized as numerals, the symbols along the horizontal diagonal can be translated as 1, 24, 51, 10. Babylonian numerals possess a positional value. Thus, if the 1 is interpreted as one unit, the remaining numerals represent fractional components of the number represented, namely, 24/60, 51/602 and 10/603. When the numbers are combined, the mystery number is found to be 1.414 212 9.... It approximates √2 to six decimal places--impressive accuracy for 2000 B.C.E.! Two discoveries emanate from this example: the ancient Babylonians performed geometric constructions similar to those in use today, and they had a proficient technique for the extraction of square roots. Babylonian accuracy in the extraction of square roots prompts further investigation by students--just how did they do it?
Cultural and sociological information can be obtained from the solutions to historical problems. For example, the height of the mast of an Egyptian ship for the period 250 B.C.E. can be found:
Similarly, the size of a loaf of bread in fifteenth-century Venice can be deduced:
Or the hourly wages (of a twelve-hour workday) for a man in post-Civil War America can be determined: