Читать книгу The Little Book of Mathematical Principles, Theories & Things - Robert Solomon - Страница 9

A quadratic equation includes the square of the unknown. Thousands of years ago mathematicians in Babylonia knew how to solve quadratic equations.

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The measurement of land has always been important to any civilization. To find the area of a square piece of land you multiply the side by itself, which is called the square of the side. The Latin for square is quadratus, and this is where the word quadratic comes from. There is always a square term.

Algebraically, a quadratic equation is of the form:

ax² + bx + c = 0

where a, b and c are numbers.

The solution (in other words the formula for x) is very well known in school mathematics all over the world.

This, of course, uses modern algebraic notation. However, a method for solving quadratic equations has been known for thousands of years.

A Babylonian clay tablet in the British Museum in London contains the solution to the following problem:

The area of a square added to the side of the square comes to 0.75. What is the side of the square?

The working shown on the tablet is illustrated on the left of the table overleaf (see page 12). The modern algebraic equivalent is shown on the right.

Babylonian tablet	Modern notation
I have added the area and the side of my square. 0.75You write down 1, the coefficientYou break half of 1. 0.5You multiply 0.5 and 0.5. 0.25You add 0.25 and 0.75. 1This is the square of 1Subtract 0.5, which you multiplied0.5 is the side of the square	x2 + x = 0.75Coefficient of x is 1Half of 1 is 0.5(0.5)2 = 0.250.25 + 0.75 = 1√1 = 11 – 0.5 = 0.5x = 0.5

In general, the method gives the following formula to solve the equation x² + bx = c:

This is more or less the same as the modern formula given above, where a = 1.