# Circle

A circle

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

The radius of a circle is a line from the centre of the circle to a point on the side. Mathematicians use the letter r for the length of a circle's radius. The centre of a circle is the point in the very middle.

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 of the circle. 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).

${\displaystyle d=2\ r}$

The circumference (meaning "all the way around") of a circle is the line that goes around the centre of the circle. Mathematicians use the letter C for the length of this line.

The number π (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 (π equals C divided by d). As a fraction the number π is equal to about 227 or 335/113 (which is closer) and as a number it is about 3.1415926535.

 ${\displaystyle \pi ={\frac {C}{d}}}$ ${\displaystyle \therefore }$ ${\displaystyle C=2\pi \,r}$
The area of the circle is equal to π times the area of the gray square.

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).

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

## Calculating π

π can be measured by drawing a large circle, then measuring its diameter (d) and circumference (C). This is because the circumference of a circle is always π times its diameter.

${\displaystyle \pi ={\frac {C}{d}}}$

π can also be calculated by only using mathematical methods. Most methods used for calculating the value of π have desirable mathematical properties. However, they are hard to understand without knowing trigonometry and calculus. However, some methods are quite simple, such as this form of the Gregory-Leibniz series:

${\displaystyle \pi ={\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+{\frac {4}{9}}-{\frac {4}{11}}\cdots }$

While that series is easy to write and calculate, it is not easy to see why it equals π. An easier to understand 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, calculated by the pythagorean theorem, will be inside the circle:

${\displaystyle d={\sqrt {x^{2}+y^{2}}}}$

Finding a set of points inside the circle allows the circle's area A to be estimated. For example, by using integer coordinates for a big r. Since the area A of a circle is π times the radius squared, π can be approximated by using:

${\displaystyle \pi ={\frac {A}{r^{2}}}}$
Other Languages
Afrikaans: Sirkel
Alemannisch: Kreis (Geometrie)
አማርኛ: ክብ
العربية: دائرة
aragonés: Circumferencia
armãneashti: Țercľiu
অসমীয়া: বৃত্ত
asturianu: Circunferencia
Aymar aru: Muyu
azərbaycanca: Çevrə
تۆرکجه: دایره
বাংলা: বৃত্ত
Bân-lâm-gú: Îⁿ-hêng
башҡортса: Әйләнә
беларуская: Акружнасць
беларуская (тарашкевіца)‎: Акружына
български: Окръжност
bosanski: Kružnica
brezhoneg: Kelc'h
Чӑвашла: Çавракăш
čeština: Kružnice
chiShona: Denderedzwa
Cymraeg: Cylch
dansk: Cirkel
Deutsch: Kreis
dolnoserbski: Cera krejza
eesti: Ringjoon
Ελληνικά: Κύκλος
emiliàn e rumagnòl: Serć (giumetrìa)
English: Circle
español: Circunferencia
Esperanto: Cirklo
euskara: Zirkulu
فارسی: دایره
Fiji Hindi: Circle
føroyskt: Sirkul
français: Cercle
Gaeilge: Ciorcal
Gaelg: Kiarkyl
Gàidhlig: Cearcall
galego: Círculo

ગુજરાતી: વર્તુળ
한국어: 원 (기하학)
հայերեն: Շրջանագիծ
हिन्दी: वृत्त
hornjoserbsce: Kružnica
hrvatski: Kružnica
Ido: Cirklo
Bahasa Indonesia: Lingkaran
interlingua: Circulo
isiXhosa: Isazinge
italiano: Circonferenza
עברית: מעגל
Basa Jawa: Bunderan
ქართული: წრეწირი
қазақша: Шеңбер
Kiswahili: Duara
Kreyòl ayisyen: Sèk (non)
kurdî: Gilover
لۊری شومالی: دایره
Latina: Circulus
latviešu: Riņķa līnija
Lëtzebuergesch: Krees (Geometrie)
lietuvių: Apskritimas
Limburgs: Cirkel
lumbaart: Sércc
македонски: Кружница
മലയാളം: വൃത്തം
मराठी: वर्तुळ
مصرى: دايره
Bahasa Melayu: Bulatan
монгол: Тойрог
မြန်မာဘာသာ: စက်ဝိုင်း
Nederlands: Cirkel
नेपाली: वृत
नेपाल भाषा: चाकः

Nordfriisk: Kreis (geometrii)
Norfuk / Pitkern: Sirkil
norsk: Sirkel
norsk nynorsk: Sirkel
occitan: Cercle
олык марий: Оҥго
ଓଡ଼ିଆ: ବୃତ୍ତ
oʻzbekcha/ўзбекча: Aylana
ਪੰਜਾਬੀ: ਚੱਕਰ
پنجابی: چکر
پښتو: گردکه
Patois: Soerkl
ភាសាខ្មែរ: រង្វង់
Plattdüütsch: Krink
polski: Okrąg
português: Circunferência
română: Cerc
Runa Simi: P'allta muyu
русиньскый: Круг
русский: Окружность
Scots: Raing
shqip: Rrethi
slovenčina: Kružnica
slovenščina: Krožnica
Soomaaliga: Goobo
српски / srpski: Кружница
srpskohrvatski / српскохрватски: Kružnica
suomi: Ympyrä
svenska: Cirkel
Tagalog: Bilog
தமிழ்: வட்டம்
татарча/tatarça: Әйләнә
Türkçe: Çember
українська: Коло
اردو: دائرہ
Vahcuengh: Luenz
vèneto: Sercio
Tiếng Việt: Đường tròn

Winaray: Lidong

ייִדיש: קרייז
Yorùbá: Òbìrípo

žemaitėška: Apskrėtėms