Every student knows that if you take a compass, set its point at one point, and then turn it around its axis, you can get a curve called a circle. How to calculate the radius through the circumference, we will describe in the article.
Circle concept
According to the mathematical definition, a circle is understood to mean such a curve, the whole set of points of which are at the same distance from one point - from the center. The curve is closed and limits the inside of a flat figure, which is usually called a circle.
Circle Elements:
- Radius (R) - a segment connecting the center with any point on the circle.
- Diameter (D) - a segment that connects two points of a circle and passing through its center. Its length is equal to two radii, that is, D = 2 * R.
- A chord is any secant line intersecting a circle at two points. The biggest chord is the diameter.
- An arc is any part of a circle. It is measured either in degrees or in units of length.
- Perimeter - circumference.
The important properties of a circle are as follows:
- Any line that passes through the center of the circle and intersects it is the axis of symmetry for this figure.
- The circle goes into itself due to rotation at any angle around an axis passing through the center of the figure and perpendicular to its plane.
Circle perimeter
Interest in calculating the circumference arose in ancient Babylon and was associated with the need to determine the perimeter of the wheel, knowing the length of its radius.
Through the radius, the circumference of the circle according to the formula can be calculated: L = 2 * pi * R, where pi = 3.14159 is the number pi.
Using it is quite simple. For example, we determine how long a circle will have if its diameter is 10 cm.
Since the diameter is 2 times larger than the radius, we obtain that R = D / 2 = 10/2 = 5 cm. Substituting in the formula for the perimeter, we obtain: L = 2 * pi * R = 2 * 3.14159 * 5 = 31 , 4159 cm.
Since the number pi is a constant, it follows from the above expression that the circumference of a circle will always be more than 6 times its radius (6.28).