closed the line that divides the plane into two parts, the final (in itself - a circle) and infinite (outside line), provided that it has a number of specific properties is called a circle.For example, the obligation to comply with all equidistant points on the line, from one point, which is the center of the circle.For a plane defined by a circle, there are some quantitative characteristics.These include:
- range (the distance from any point on it, to the center, ṟ);
- diameter (the line that divides the circle into two equal parts, passing through two points of the circle and the center of the circle, ḏ);
- area, showing the numerical size of the circle, S;
- length of closed line describes a circle (denoted by the letter Ḻ).
Thus, Ḻ is not only a quantitative characteristic of the circle, but the closed line, so the answer to the question - how to find the circumference, is applicable to both of geometric concepts.
distance runs along the outside of the closed curve flat circular object is equal to the length of the line encircling it.This quantitative assessment of the circumference is used when measuring the physical objects, and when considering abstract geometric shapes.The term has a special meaning for geometric and trigonometric knowledge.It refers to the 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").Perimeter (for flat pieces of any shape) and a circle (for the plane figure of round shape) equals the total length of the boundary of the figure.A special case (the boundary circle) has the same dimension as the distance or path.To study the topic "How to calculate the circumference of the" need to remember the units and their translation.
According to the international SI system, any distance or path are measured in meters.This is the basic unit, but there are also derivatives.It is therefore appropriate for those who decide to theoretical and practical problems on "how to find the circumference," lead their relationship:
- 1 kilometer = 1000 meters = 10000 = 100000 decimeters = 1000000 centimeters millimeters;
- 1 mile = 1.609344 kilometers = 1609.344 meters dm = = 16,093.44 160,934.4 centimeters = 1609344 millimeters;
- 1 foot = 30.48 centimeters = 304.8 millimeters = 3.048 dm = 0.3048 meter = 0.0003048 kilometers.
There are many other units: the British (or American), old Russian, Greek, Japanese and others.In order to perform calculations with them, it is recommended to use the reference information.
For all circles characterized by one thing in common, which was established by scientists of antiquity.The ratio of length to diameter of a circle is always a constant number.For a long time, scientists using different methods (and in our time, the special software and computer technology), are trying to establish the exact value of that number.It is usually denoted by the Greek letter «π» (pronounced as pi).The approximate value at different times varied, but there was always a little more than three.The number π has no dimension.Today, scientists were able to establish after the decimal point ten trillion marks.This accuracy is essential for complex mathematical calculations.But in solving geometric problems that require to answer the question - how to find the circumference, increasingly using this number up to five or two characters: π ≈ 3,14159 ≈ 3,14.
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 length of the circle with a radius of 1 meter or 2 decimeter, or a diameter of 5 centimeters.Suffice it to multiply twice the radius or diameter of the number π.In all three cases by the formula Ḻ = π • ḏ = 3,14 • ḏ or Ḻ = 2 • π • ṟ = 2 • 3,14 • ṟ obtain the following calculation results:
- Ḻ = 3,14 • 2 • 1= 6.28 m;
- Ḻ = 3,14 • 2 • 2 = 12.56 dm;
- Ḻ = 3,14 • 5 = 15.7 cm.
task of containing the question - how to find the circumference, it is unknown if the radius or diameter, but the known area of a circle, a little complicated, but it can also be solved.Since ancient times is well known that the area of a circle is equal to the product of the number π and the square of the radius or diameter of a quarter of the square: S = π • ṟ² or S = π • ḏ ² / 4.
first calculates the radius ṟ = √ (S / π)or diameter ḏ = √ (4 • S / π), and then calculates the length of the circumference.You can consider the example of two cases where the area of a 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, whereas Ḻ = 3,14 • 4 = 12.56 m.
- ṟ = √ (78,5 / 314) = 5 cm, while Ḻ = 3,14 • 2 • 5 = 31.4 cm or ḏ = √ (4 • 78,5 / 3,14) = 10 cm, while Ḻ = 3,14 • 10 = 314 cm.