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Nu '''cìrculu''' o '''cerchiu''' è lu locu dî [[puntu|punti]] equidistanti di nu puntu fissu chiamatu ''centru''. Ntâ nu sistema di rifirmentu cartisianu, siddu lu centru havi coordinati <math>(a,b)</math> e lu raiu è <math>R</math>, l'[[equazzioni]] [[Algibra|algèbbrica]] chi rapprisenta nu cìrculu è:<br>
{{WIP|Maurice Carbonaro}}
:<math> d = \sqrt{(x -a)^2 + (y -b)^2=R^2 }</math> ▼A '''circle''' is a [[round]] [[2D|two-dimensional]] shape, such as the letter ''o''.
The [[centre]] of a circle is the point in the very middle.
The [[radius]] of a circle is a line from the centre of the circle to a point on the side.
All [[point]]s on the circle are at the same [[distance]] from the centre. In other words, the radius is the same length all the way around the circle. Mathematicians use the letter ''r'' for the length of a circle's radius.
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 centre. Mathematicians use the letter ''d'' for the length of this line.
The diameter of a circle is equal to twice its radius (''d'' equals 2 times ''r'').
:<math>
d = 2\ r
</math>
The [[circumference]] (meaning "all the way around") of a circle is line that goes around the circle. Mathematicians use the letter ''c'' for the length of this line.
The number ''[[pi|π]]'' (written as the [[Greek language|Greek]] [[letter]] ''pi'') is a very useful number. It is the length of the circumference divided by the length of the diameter (''π'' equals ''c'' divided by ''d''). The number π is equal to about {{frac|22|7}} or 3.14159.
{|
|-
|||<math>\pi = \frac{c}{d}</math>
|-
|<math>\therefore</math>||<math>c = 2\pi \, r</math>
|}
[[Image:CircleArea.gif|thumb|right]]
The [[area]], ''a'', inside a circle is equal to the radius multiplied by itself, then multiplied by π (''a'' equals π times (''r'' times ''r'')).
:<math>a = \pi \, r^2 </math>
==Calculating π==
'''π''' can be empirically measured by drawing a large circle, then measuring its diameter and circumference, since the circumference of a circle is always π times its diameter.
'''π''' can also be calculated using purely mathematical methods. Most formulae used for calculating the value of π have desirable mathematical properties, but are difficult to understand without a background in [[trigonometry]] and [[calculus]]. However, some are quite simple, such as this form of the [[Leibniz formula for pi|Gregory-Leibniz series]]:
:<math> \pi = \frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\frac{4}{11}\cdots </math>
While that series is easy to write and calculate, it is not immediately obvious why it yields π. A more intuitive approach is to draw an imaginary circle of radius '''r''' centered at the origin. Then any point (x,y) whose distance '''d''' from the origin is less than '''r''', as given by the [[pythagorean theorem]], will be inside the circle:
▲:<math> d = \sqrt{x^2 + y^2}</math>
Finding a collection of points inside the circle allows the circle's area '''A''' to be approximated. For example, by using integer coordinate points for a big '''r'''. Since the area '''A''' of a circle is π times the radius squared, π can be approximated by using:
:<math> \pi = \frac{A}{r^2} </math>
== Other websites ==
{{commons|Circle}}
* [http://www.mathepower.com/english/kreis.php Calculate the measures of a circle online]
[[Category:Shapes]]
{{Link FA|mk}}
[[ar:دائرة]]
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