P. 11529 V

The calculation of surface areas, diagonals and volumes did not only cause problems at school today, because mathematics was an important part of teaching even in ancient times. Therefore, tasks with accompanying solutions were always welcome. For example, a student apparently wrote this text with at least five mathematical tasks, each provided with illustrative drawings and solutions. The first two tasks have survived only in fragments, but their contents can still be recognized. The remaining tasks are still complete.

This text from the second half of the 2nd century A, was written in Greek on the back of an administrative text from Theadelpheia in the Fayum in the year 138/139 AD and included various lists of workers, accounts of wheat deliveries, an overview of land areas and the like. The papyrus was reused for mathematical tasks.

The handwriting is a bit awkward and seems to come from a less experienced scribe. The drawings that have been added to each task and to which the solutions of the tasks have been added are rendered sloppily and take no account of the lengths of the lines and their relationship as described in the respective tasks. In addition, the text contains a number of errors and misunderstandings that suggest that the scribe has copied these tasks from a master copy without due care and understanding.

These are two geometrical and three stereometric tasks that are still being solved by students today in a barely modified form. In the first task the surface area and the diagonal of a rectangular parallelogram (that is a rectangle) are to be calculated. Interestingly, in solving the problem, the parallelogram is interpreted as two right-angled triangles and the diagonal is determined according to the famous Pythagorean theorem. The second task deals with a right-angled triangle and its surface area and hypotenuse. In the third task, again, the area of a triangle is to be determined. However, for this equilateral triangle it is also required to determine the middle height. The last two tasks are math word problems, in which one should calculate the volume of a stone and a tripod (which probably is to be understood as a truncated cone). These two tasks also contain the most mistakes, because the writer forgot to convert different units of measurement and thus received a wrong result.

Due to many similarities in method and in expressions with the mathematical writings of the Alexandrian Heron, the master copy that form the basis of our text may well be assigned to this mathematical school. Some tasks of our text correspond to the tasks of the writings of Heron not only in the subject, but even in measurements. The practical use of these tasks is already evident in the measurement unit used for the surface area in our text: the arura, an Egyptian measurement for fields. Therefore, one can assume that these tasks might have been used in the training of surveyors.