Historical sequences of problems from different time periods and cultures can be assembled and assigned as exercises for students to solve and compare. For example, facility in the use of the Pythagorean theorem was valued in all societies:
More mathematically mature societies puzzled over indeterminate equations:
At times, in instructional situations, the use of historical problems reinforces and clarifies the concept being taught. For example, a discussion on the technique of "completing the square" to find the roots of a quadratic equation is enhanced by reference to actual Babylonian problems from which the concept originated (McMillan, 1984). Consider a problem from 2000 B.C.E.:
If the side of the square in question is taken to be x, then the problem becomes one of solving the equation
x2 + (2/3)x = 35/60
which in Babylonian methodology would be depicted as shown here:
Thus by geometrically completing the square, the new area (see below) is seen to be 35/60 + 1/9 and the algebraic solution situation becomes one of solving
(x + 1/3)2 = 35/60 + 1/9.
Assisted by the use of a hand calculator, modern students would find that x = 1/2 or x = -7/6, and the positive root agrees with the solution found by the Babylonians.