In whatever field of the economy, a person has worked, freely or involuntarily he enjoys mathematical knowledge accumulated over many centuries. With devices and mechanisms containing circumference, we are confronted daily. The round shape has a wheel, pizza, many vegetables and fruits in the context form a circle, as well as plates, cups, and much more. However, not everyone can correctly calculate the length of the circle.
To calculate the circumference length, you must first remember what a circle is. This is a set of all points of the plane equidistant from this. And the circle is the geometric location of the plane points inside the circle. From the above, it follows that the perimeter of the circle and the length of the circle is the same thing.
Ways to find the length of the circle
In addition to the mathematical method of finding the perimeter of the circle, there are practical.
- Take a rope or cord and wrap one time around.
- Then the rope is measured, the resulting number and will be the length of the circle.
- Rolling a round item once and calculate the length of the path. If the subject is very small, you can wind up several times with its twine, then sprinkle the thread, measure and divide to the number of turns.
- Find the desired value by the formula:
L \u003d 2πr \u003d πd ,
where L is the desired length;
π is a constant, approximately equal to 3.14 R - the radius of the circle, the distance from its center to any point;
D - diameter, it is equal to two radius.
Application of formula to find the length of the circle
- Example 1. The treadmill passes around the circumference with a radius of 47.8 meters. Find the length of this treadmill, adopting π \u003d 3.14.
L \u003d 2πR \u003d 2 * 3,14 * 47.8 ≈ 300 (m)
Answer: 300 meters
- Example 2. The wheel of the bicycle, turning 10 times, drove 18.85 meters. Find a radius of the wheel.
18.85: 10 \u003d 1.885 (M) is the perimeter of the wheel.
1,885: π \u003d 1,885: 3,1416 ≈ 0.6 (m) - the desired diameter
Answer: Wheel diameter 0.6 meters
Amazing number π.
Despite the seeming simplicity of the formula, for some reason, many difficult to remember it. Apparently, this is due to the fact that in the formula there is an irrational number π, which is not present in the formulas of the area of \u200b\u200bother figures, for example, a square, triangle or rhombus. It is just necessary to remember that this is a constant, that is, a constant, meaning the ratio of the circumference of the circle to the diameter. About 4 thousand years ago, people noticed that the ratio of the perimeter of the circle to its radius (or diameter) is equally for any circles.
The ancient Greeks brought the number π fraction 22/7. For a long time π was calculated as the average between the lengths of the inscribed and described polygons into the circle. In the third century, our era, the Chinese mathematician conducted a calculation for a 3072-square and received an approximate value π \u003d 3,1416. It must be remembered that π is always constantly for any circumference. His designation of the Greek letter π appeared in the 18th century. This is the first letter of Greek words περιφέρεια - a circle and περίμετρος - perimeter. In the eighteenth century, it was proved that this value is irrational, that is, it cannot be submitted as M / N, where M is an integer, and N is a natural number.
In school mathematics, it usually does not need a high accuracy of calculations, and π is taken equal to 3.14.
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