Circle

A circle is a round, two-dimensional shape. All points on the edge of the circle are at the same distance from the center.

The radius of a circle is a line from the center of the circle to a point on the side. Mathematicians use the letter ${\displaystyle r}$ for the length of a circle's radius. The center of a circle is the point in the very middle. It is often written as ${\displaystyle O}$.

The diameter (meaning "all the way across") of a circle is a straight line that goes from one side to the opposite and right through the center of the circle. Mathematicians use the letter ${\displaystyle d}$ for the length of this line. The diameter of a circle is equal to twice its radius (${\displaystyle d}$ equals ${\displaystyle 2}$ times ${\displaystyle r}$):^[1]

${\displaystyle d=2r}$

The circumference (meaning "all the way around") of a circle is the line that goes around the center of the circle. Mathematicians use the letter ${\displaystyle c}$ for the length of this line.^[2]

The number ${\displaystyle \pi }$ (written as the Greek letter pi) is a very useful number. It is the length of the circumference divided by the length of the diameter (${\displaystyle \pi }$ equals ${\displaystyle c}$ divided by ${\displaystyle d}$). As a fraction the number ${\displaystyle \pi }$ is equal to about ${\displaystyle {\frac {22}{7}}}$ or ${\displaystyle {\frac {355}{113}}}$ (which is closer) and as a number it is about ${\displaystyle 3.1415926536}$.

	${\displaystyle \pi ={\frac {c}{d}}}$
${\displaystyle \therefore {\textrm {(therefore)}}}$	${\displaystyle c=2\pi r}$
	${\displaystyle c=\pi d}$

The area, ${\displaystyle A}$, inside a circle is equal to the radius multiplied by itself, then multiplied by ${\displaystyle \pi }$ (${\displaystyle A}$ equals ${\displaystyle \pi }$ times ${\displaystyle r}$ times ${\displaystyle r}$).

${\displaystyle A=\pi r^{2}}$

1. ↑ Weisstein, Eric W. "Circle". mathworld.wolfram.com. Retrieved 2020-09-24.
2. ↑ "Basic information about circles (Geometry, Circles)". Mathplanet. Retrieved 2020-09-24.