Circle

In Euklid geometry , a circle is the set of all points on the field within a certain distance, called the radius, from a certain point, called the center. The circle is an example of simple closed curves , dividing the field into the inside and the outside.

Elements of the circle

 The elements contained in the circle, is as follows:

• n a point inside the circle is the reference to determine the distance to the set point of the building so that the same circle. Lngkiaran element in the form of points, namely:
  1. Center point (P)
     is the distance between the center of the circle the price is constant and is called the radius.

• Elements that form a circle ruler, namely:
  1. The radius (R)
     is a straight line connecting the center with a circle.
  2. Bowstring (TB)
     is a straight line inside the circle which cuts the circle at two different points (TB).
  3. Arc (B)
     is a curved line either open or closed which coincides with the circle.
  4. Circumference of a circle (K)
     is the longest arc on the circle.
  5. Diameter (D)
     is the largest bow string whose length is twice the radius. It shares the same diameter circle area.
  6. Apotema
     is the shortest line between the bowstring and the center circle.

• Elements that form the circle area, namely:
  1. Pie (J)
     is an area of ​​a circle bounded by the arc and two radii that are on both ends.
  2. Borderline (T)
     is an area of ​​a circle bounded by an arc with a rope bow.
  3. Discs (C)
     represents all areas inside the circle. The extent of the radius squared multiplied by pi. The disc is the largest pie.  

Equation 

A circle has equation

with is the radius of the circle and are the coordinates of the center circle

Parametric Equations

Circles can also be formulated in an equation parameterik, namely

which if allowed to undergo t will be a circular trajectory in xy space.

Area of circle

Area of ​​circle having the formula

that can be derived by integrating the area of ​​a circle element

in polar coordinates, namely

In the same way can also be calculated vast semi-circle, quarter circle, and parts of the circle. Also do not miss to calculate the area of ​​a ring circle with a radius of and outer radius .

Addition section element

Area of ​​circle can be calculated with the cut it up as the elements of a pie for later rearranged into a rectangle whose width can be easily calculated. In pictures r means the same as R is the radius of the circle.

Area of pie

Broad segment of a circle can be calculated if the area of a circle made ​​a function of R and θ, namely;

with the restriction θ value is between 0 and 3π. When the value θ 2π, the calculated segment is the largest segment, or area of a circle.

Area of a circle ring

A circular ring has an area that depends on the radius in and outer radius , Ie

where for this formula back into the formula area of ​​a circle.

Area of a circle cut ring

By combining the two previous formulas, can be obtained

which is the area of ​​a ring was intact.

Around the circle

Circumference of a circle has the formula:

The length of arc

Length of arc of a circle can be calculated using the formula

derived from the formula for calculating the length of a curve

where used

as a curve in a circle. Sign suggests that there are two curves, namely the top and bottom. Both are identical (remember the definition of a circle), so that really only needs to be calculated once and the result multiplied by two.

Source : Wikipedia.org