The piece which is connecting two points of a circle and passing through its center has a constant ratio with the closed line which does not have self-crossing which all points are at identical distance from the center. Same it is possible to formulate more simply: diameter of any circle is about 3 times less than its length.
It is required to you
- The handle, paper, tables for calculation of length of a circle on diameter.
Instruction
1. Write down length of a circle which diameter you intend to determine. A lot more centuries people withdrew for production of a round basket of the necessary size, or diameter, rods three times longer. Later scientists proved that at division of length of each circle into its diameter the same not natural number turns out. Its size was specified all the time though the accuracy of calculations was always high. For example, in Ancient Egypt it was expressed the improper fraction 256/8 having a deviation no more than one percent.
2. Remember that for the first time Archimedes mathematically calculated this ratio. He constructed the correct 96-tiugolnik in a circle and around it. The perimeter of the entered polygon took for minimum possible length of a circle, perimeter of the described figure – for the maximum size. According to Archimedes the ratio of length of a circle and diameter is equal to 3.1419. Much later this number was "extended" to eight signs by the Chinese mathematician to Tsz Chunchzhi. Its calculations remained 900 years the most exact. Only in the 18th century hundred signs after a comma were counted. And since 1706 this recurring decimal decimal thanks to the English mathematician William Jones got a name. He designated it by the first letter of the Greek words perimeter and a circle (periphery). Today the computer easily calculates millions of signs of number of Pi: 3.141592653589793238462643 …
3. For calculations reduce Pi's number to 3.14. It will turn out that for any circle its length divided into diameter is equal to this number: L:d=3.14.
4. Express from this statement a formula for finding of diameter. It will turn out to find diameter of a circle it is necessary to divide length of a circle into Pi's number. It looks so: d = L: 3.14. It is a universal way to find diameter when at a circle its length is known.
5. So, circle length, let us assume, of 15.7 cm is known, divide this figure into 3.14. Diameter will be equal to 5 cm. Write down it so: d = 15.7: 3.14 = 5 cm.
6. Find diameter on circle length, using special tables for calculation of length of a circle on diameter. These tables include in different reference books. For example, they are in the book "Four-digit Mathematical Tables" by V.M. Bradis.