You will need

- Pen, paper, tables for calculating the circumference of a circle to the diameter.

Instruction

1

Write down the circumference, the diameter which you intend to define. Many centuries ago people took for making a round basket of desired size, or diameter, rods three times as long. Later, scientists proved that when dividing the length of each circumference to its diameter turns out the same is not a natural number. Its value is still being clarified, although the calculation accuracy was always high. For example, in Ancient Egypt it was expressed by the incorrect 256/8 fraction having a deviation of not more than one percent.

2

Remember that the first mathematically calculated, the ratio Archimedes. He built a correct 96-topolniki inside the circle and around it. Perimeter of inscribed polygon took the minimum possible length of a circle of perimeter described the figures for the maximum size. Archimedes the ratio of a circle's circumference and diameter equal to 3,1419. Much later the number of "extended" to eight characters, the Chinese mathematician zu of Chunji. Its calculation is 900 years old remained the most accurate. Only in the XVIII century there were counted one hundred decimal places. And 1706 of the endless decimal fraction by English mathematician William Jones acquired the name. He marked her first letter of the Greek word perimeter and circumference (periphery). Today, the computer is easy to calculate millions of digits of PI: 3,141592653589793238462643...

3

For calculations of the number PI reduce to 3.14. Turns out that for any circle with its length divided by the diameter is equal to that number: L:d=3,14.

4

Express from this statement the formula for finding the diameter. Work, to find the diameter of the circle should be the circumference divided by PI. It looks like this: d = L:3,14. It is a universal way to find the diameter when the circumference is known for its length.

5

So, a known circumference, for example, 15.7 cm, divide this figure by 3.14. The diameter is equal to 5, refer to Record this: d = 15,7 : 3,14 = 5 cm.

6

Find diameter circumference using a special table to calculate the circumference of a circle to the diameter. These tables include in different directories. For example, they are in the book "four-digit mathematical tables" by V. M. Bradis.

Useful advice

Remember the first eight digits of PI using the poem:

You just try,

And remember everything as it is:

Three, fourteen, fifteen,

Ninety-two and six.

You just try,

And remember everything as it is:

Three, fourteen, fifteen,

Ninety-two and six.

# Advice 2: How to find the circumcenter

Sometimes around a convex polygon you can draw a circle so that the tops of all the angles lying on it. Such a circle relative to the polygon should be called described. Her

**center**does not have to be inside the perimeter of the inscribed figure, but using the described properties**of the circle**, to find this point is usually not very difficult.You will need

- Ruler, pencil, protractor or straight edge, a compass.

Instruction

1

If the polygon about which it is necessary to describe a circle drawn on paper, for finding

**the centre**of the circle and quite a ruler, pencil and protractor or angle. Measure the length of any of sides of a shape, determine its middle and put in this part of the drawing auxiliary point. With the help of the set square or the protractor guide on the inside of the polygon perpendicular to the side segment to the intersection with the opposite side.2

Do the same thing with any side of the polygon. The intersection of the two constructed segments is the required point. This follows from basic properties are described

**of a circle**- its**center**in a convex polygon with any number of sides, always lies at the intersection of middle perpendiculars drawn to these parties.3

For the regular polygons defining

**the center of**a inscribed**circle**can be much easier. For example, if it is a square, then draw two diagonals and their intersection will be**the center**om of the inscribed**circle**. The regular polygon with any even number of sides, it is sufficient to connect the auxiliary segments two pairs lying opposite each other at the corners -**center**of the described**circle**must coincide with the point of their intersection. In a right triangle to solve the problem just define the middle of the longest side of the figure is the hypotenuse.4

If conditions are unknown, whether it is possible in principle to draw a circumscribed circle for that polygon, after determining the proposed point

**center**and any of the described ways you can find out. Mark on the compass the distance between the found point and any vertices, set the compass at the intended**center****of the circle**and draw a circle, every vertex must lie on this**circle**. If not, then not running one of the basic properties and describe a circle about a given polygon is impossible.# Advice 3: As at the circumference to determine the diameter

The circumference and diameter are related geometrical quantities. This means that the first of them can be translated into the second without any additional data. The mathematical constant, through which they are linked, is the number π.

Instruction

1

If a circle is presented in the form of an image on paper, and its diameter is required to determine approximately measure it directly. If its center is shown in the drawing, swipe through his line. If the center is not shown, locate it with the help of a compass. To do this, use a square with angles of 90 and 45 degrees. Attach it to a 90-degree angle to the circle so that it touched both sides, and circle. Then attach the resulting straight corner 45-degree angle of a square, draw a bisector. It passes through the center of the circle. Similarly, draw in the other place the second circle on the right angle and its bisector. They intersect in the center. This will allow you to measure the diameter.

2

To measure the diameter, it is preferable to use a ruler made from a thin sheet of material, or tailoring meter. If you only have the large ruler measure the diameter of a circle with a compass, then without changing the solution, transfer it to graph paper.

3

In the absence in terms of the problem numeric data and the presence only of the drawing, you can measure the circumference using the odometer and the diameter then calculate. To use the odometer, first rotate the wheel select the arrow exactly on the zero division. Then mark on the circle point and press the odometer to the sheet so that a bar over a wheel indicated at this point. Slide the wheel along the line of the circle until the bar again will be over by this point. Read the testimony. They are in centimetres - if necessary, convert them to millimeters.

4

The circumference (indicated in the problem or measured by the odometer), divide it by twice the number π. Get the diameter expressed in the same units of measurement as the original data. If required by the conditions, put the calculation result into more convenient units.