A closed line dividing a plane into two parts is finite (inside itself is a circle) and infinite (outside the line), provided that it has several specific properties, it is called a circle. For example, it is imperative that all points lying on this line are equidistant 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 (distance from any point lying on it to the center, ṟ);
- diameter (a line dividing the circle into two equal parts passing through two points of the circle and the center of the circle, ḏ);
- area numerically showing the size of the circle, S;
- the length of the closed line describing the circle (indicated by the letter Ḻ).
Thus, Ḻ is not only a quantitative characteristic of a circle, but also a closed line, so the answer to the question - how to find out the circumference, is applicable to both geometric concepts.
The distance running along an external closed curve of a flat object of circular shape is equal to the length of the line surrounding it. This quantification of the circumference is used when measuring physical objects, as well as when considering abstract geometric shapes. The term has special meaning for geometric and trigonometric knowledge. It refers to a physical quantity, which is a special case of such a thing as a perimeter. In Greek, the word sounds "περίμετρον" ("circle") 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 special case (the boundary of the circle) has the same dimension as the distance or path. To study the topic "How to calculate the circumference", you need to remember the units 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 = 1,000 meters = 10,000 decimeters = 100,000 centimeters = 1,000,000 millimeters;
- 1 mile = 1.609344 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: British (or American), Old Russian, ancient Greek, Japanese and others. In order to make calculations with them, it is recommended to use reference information.
All circles are characterized by one common property, which was established by scientists of antiquity. The ratio of the length to the diameter of the circle always remains a constant number. For a long time, scientists, using various methods (and nowadays special software products and computer technologies), are trying to establish the exact value of this number. It is customary to designate the Greek letter "π" (pronounced 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 set ten trillion signs after the decimal point. Such 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, they often use this number with an accuracy of five or two signs: π ≈ 3.14159 ≈ 3.14.
It is known that Ḻ / ḏ = π = 3.14 or Ḻ / 2 ṟ = π = 3.14. Therefore, you 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 enough to multiply the doubled radius or diameter by the number π. For all three cases, using the formula Ḻ = π • ḏ = 3.14 • ḏ or Ḻ = 2 • π • ṟ = 2 • 3.14 • ṟ, the following calculation results are obtained:
- Ḻ = 3.14 • 2 • 1 = 6.28 m;
- Ḻ = 3.14 • 2 • 2 = 12.56 dm;
- Ḻ = 3.14 • 5 = 15.7 cm.
The problem containing the question - how to find the circumference if its radius or diameter is unknown, but the area of the circle is known, is a little complicated, but it can also be solved. It has long been known that the area of a circle is equal to the product of the number π by the square of the radius or 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. You can consider the example of two cases when the area of the circle is 12.56 m² and 78.5 cm²:
- 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.
- 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.