Babylonian Mathematics/Examples/Division of Triangular Field/Mistake

Source Work

1992: David Wells: Curious and Interesting Puzzles:

The Puzzles:

Dividing a Field: $12$

Mistake

A triangular field is to be divided between six brothers by equidistant lines parallel to one side. The length of the marked side is $6, 30$ and the area is $11, 22, 30$. What is the difference between the brothers' shares?

Answer: The difference between each successive share is $37, 55$ or $37 \frac {11} {12}$.

Correction

The author is lax here in his interpretation of where the radix point lies.

In order for the question both to make sense and to be consistent, it is necessary to interpret the numbers as:

the area is $11, 22; 30$

and:

the difference between each successive share is $37; 55$

where $;$ denotes the radix point.

Note that this is at odds with the interpretation as given in the explanatory section leading up to this question, where $11, 22, 30$ is interpreted as $11; 22, 30$, that is, $11 + \dfrac {22} {60} + \dfrac {30} {60 \times 60}$.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Dividing a Field: $12$