One of the fundamental shapes in geometry. The unit circle can be described by the equation x2+y2=1; in other words, every pair of real numbers (x,y) which satisfy this equation corresponds to a point (x,y) on the edge of the unit circle. When speaking of circles, it is common to mention only the radius, since every circle has symmetry to a high degree. Below, I use R to denote the radius of the circle. R=24chars.

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,z'`                       `'c,
,x'`                           `'w,
.u'`                               `'n.
dy                                     qb
/7                                       VA
4y                                         VD
,I'                                         `U,
dp                                           qb
,j'                                           `t,
AV                                  R          VA
69                      .______________________96
VA                                             AV
`t,                                           ,j'
qb                                           dp
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\D                                         4y
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`'n.                               .u'`
`'w,                           ,x'`
`'c,                       ,z'`
`'Tux.,             ,.szF'`
`'TTOK@@@@@HQTT'`
```

The above circle was formed using the pythagorean triple (5,12,13), i.e. the points (5/13,12/13), (12/13,5/13), (-5/13,12/13), (-12/13,5/13), (5/13,-12/13), (12/13,-5/13), (-5/13,-12/13) and (-12/13,-5/13).

Some properties of any circle of radius R centered on the origin:

Area=pi*R2
Circumference=2*pi*R

x2+y2=R2 is the generating equation; letting x=R*cos(t) and y=R*sin(t) for angles t will also generate the circle (all points (x,y) on the edge of said circle).