# 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:

the length of the marked side is $6; 30$
the area of the triangle is $11, 22; 30$.

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?

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.