You will need

- a pair of compasses;
- - the range;
- pencil;
- - thread.

Instruction

1

Draw on paper with a compass a circle of arbitrary diameter. Swipe with a ruler and pencil through the center of the segment connecting two points located on the line

**of the circle**. A ruler to measure the length of the resulting cut. For example, the diameter**of the circle**in this case is equal to 7 centimeters.2

Take the thread and place it along the length

**of the circumference**. Measure the resulting length of the thread. Let it be equal to 22 centimeters. Find**the ratio***of the length***of the circumference**to the length of its diameter - 22 cm : 7 cm = 3,1428.... Round the resulting number to two decimal places (3,14). It turned out a familiar number "PI".3

To prove this property

**of a circle**you can using a Cup or glass. Measure their diameter with a ruler. Wrap the top of the dish with a thread, measure the resulting length. Dividing the length**of the circumference**of the Cup for the length of its diameter, you will also get the number "PI", making thus this property**of the circle**opened by Archimedes.4

Using this property, you can calculate the length of any

**circumference**along the length of its diameter or radius by the formula:C = 2*p*R or C = D*p, where S - length**of the circumference**, D is the length of its diameter, R is the length of its radius.To find the area of a circle (plane bounded by the lines**of the circle**) use the formula S = π*R2, if you know the radius or the formula S = π*D2/4, if you know its diameter.Note

Did you know that fourteenth of March, for more than twenty years, the Day of "PI"? It is an informal holiday of mathematicians devoted to this interesting number, which currently involves a lot of formulas, mathematical and physical axioms. Came up with this holiday American Larry Shaw, who noticed that in the day (3.14 in the system of recording dates in the USA) was born the famous scientist Einstein.