How to find the circumference of a circle

A closed line dividing the plane into two parts is finite (inside itself is a circle) and infinite (outside the line), provided that it has several specific properties, is called a circle. For example, it is necessary to observe the equidistance of all points lying on this line from one point that is the center of the circle. For a plane bounded by a circle, there are several quantitative characteristics. These include:

• Radius (the distance from any point lying on it to the center, ṟ);
• Diameter (the line dividing the circle into two equal parts, passing through two points of the circle and the center of the circle, ḏ);
• An area numerically indicating the size of the circle, S;
• Length of a closed line describing a circle (denoted by the letter ).

Thus, Ḻ is not only a quantitative characteristic of a circle, but a closed line, so the answer to the question - how to determine the circumference of a circle, is applicable to both geometric concepts.

The distance along the outer closed curve of a flat object of circular shape is equal to the length of the line surrounding it. This quantitative evaluation of the circle is used in the measurement of physical objects, as well as in the consideration of abstract geometric shapes. The term is of particular importance for geometric and trigonometric knowledge. It refers to a physical quantity, which is a particular case of such a concept as perimeter. In Greek, the word sounds "περίμετρον" ("circumference") or "περιμετρέο" ("measure around"). The perimeter (for a flat figure of any shape) and the circle (for a flat figure of circular shape) are equal to the total length of the border of the figure. A particular case (the boundary of a circle) has the same dimension as the distance or path. To study the topic "How to calculate the circumference of a circle," you need to remember the units of measurement and their translation.

According to the international SI system, any distance or path is measured in meters. This is the basic unit, but there are also derivatives. Therefore, it is appropriate for those who solve theoretical and practical problems on the topic "how to find the circumference", to bring their ratio:

• 1 kilometer = 1000 meters = 10000 decimeters = 100,000 centimeters = 1,000,000 millimeters;
• 1 mile = 1,609,344 kilometers = 1609.344 meters = 16093.44 decimeters = 160934.4 centimeters = 1609344 millimeters;
• 1 foot = 30.48 centimeters = 304.8 millimeters = 3,048 decimeters = 0.3048 meters = 0.0003048 kilometers.

There are many other units of measurement: British (or American), Old Russian, Greek, Japanese and others. In order to perform calculations with them, it is recommended to use reference information.

For all circles, there is one common property, which was established by scientists of antiquity. The ratio of the length to the diameter of the circle always remains constant. Since ancient times, scientists, using various methods (and nowadays special software products and computer technologies), are trying to establish the exact meaning of this number. It is usually denoted by the Greek letter "π" (pronounced as pi). The approximate value changed at different times, but there were always a little more than three. The number π has no dimension. Today scientists managed to establish after the decimal point ten trillion signs. This accuracy is necessary for complex mathematical calculations. But when solving geometric problems, where it is required to answer the question - how to find the circumference, more often use this number to within five or two characters: π ≈ 3,14159 ≈ 3,14.

It is known that Ḻ / ḏ = π = 3,14 or Ḻ / 2 ṟ = π = 3,14. Therefore, one can easily answer the question - how to find the circumference of a circle with a radius equal to 1 meter or 2 decimeters, or a diameter equal to 5 centimeters. It is sufficient to multiply the doubled radius or diameter by the number π. For all three cases, the following results are obtained from the formula Ḻ = π • ḏ = 3,14 • ḏ or Ḻ = 2 • π • ṟ = 2 • 3,14 • :

1. Ḻ = 3,14 • 2 • 1 = 6,28 m;
2. Ḻ = 3,14 • 2 • 2 = 12,56 dm;
3. Ḻ = 3.14 5 5 = 15.7 cm.

The problem, which contains the question - how to find the circumference of a circle, if its radius or diameter is unknown, but the area of the circle is known, is slightly more complicated, but it can also be solved. Since ancient times it is known that the area of the circle is equal to the product of the number π by the square of the radius or by the fourth part of the square of the diameter: S = π • ṟ² or S = π • ḏ ² / 4.

First, calculate the radius ṟ = √ (S / π) or the diameter ḏ = √ (4 • S / π), and then calculate the circumference. We can consider the case of two cases where the area of the circle is 12.56 m² and 78.5 cm²:

1. Ṟ = √ (12.56 / 3.14) = 2 m, then Ḻ = 3.14 • 2 • 2 = 12.56 m or ḏ = √ (4 • 12.56 / 3.14) = 4 m, Then Ḻ = 3,14 • 4 = 12,56 m.
2. Ṟ = √ (78.5 / 3.14) = 5 cm, then Ḻ = 3.14 • 2 • 5 = 31.4 cm or ḏ = √ (4 • 78.5 / 3.14) = 10 cm, Then Ḻ = 3.14 × 10 = 31.4 cm.