# Definition:Babylonian Mathematics

## Definition

**Babylonian mathematics** is the name given to the mathematics of the ancient Babylon.

Its content was arithmetical and algebraical, and considerably in advance of the mathematics of the approximately contemporaneous ancient Egypt.

## Examples

### Division of Triangular Field

A triangular field is to be divided between $6$ brothers by equidistant lines parallel to one of the sides.

Expressed in Babylonian notation:

What is the difference between the brothers' shares?

### Sextic Equation

Simpify the system of simultaneous equations:

\(\text {(1)}: \quad\) | \(\ds x y\) | \(=\) | \(\ds a\) | |||||||||||

\(\text {(2)}: \quad\) | \(\ds \dfrac {b x^2} y + \dfrac {c y^2} x + d\) | \(=\) | \(\ds 0\) |

### Sum of Squares

An area $A$, consisting of the sum of $2$ squares, is $1000$.

The side of one square is $10$ less than $\dfrac 2 3$ of the other square.

What are the sides of the squares?

### Sliding Ladder

A ladder of length $0; 30$ stands upright against a wall.

The upper end slides down a distance $0; 6$.

How far away will the lower end move out from the wall?

All lengths are expressed in Babylonian form.

### Pythagorean Triangle whose Side Ratio is $1.54$

Consider a Pythagorean triangle whose hypotenuse and one leg are in the ratio $1.54 : 1$.

What are the lengths of that hypotenuse and that leg?

## Also see

- Results about
**Babylonian mathematics**can be found here.

## Sources

- 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Squares Without Pythagoras: $11$