

circle
Definition/Summary

Circle: the locus of all points on a Plane that are the same distance from a given point.
Centre: that given point.
Radius: any line (strictly, line segment) between the Centre and the Circle (also, the length of that line).
Chord: any line segment between two points on the Circle.
Diameter: any Chord though the Centre (also, the length of that Chord, which is twice the Radius).
Focus and Eccentricity: a Circle is an Ellipse whose two Foci are both at the Centre, and whose Eccentricity is 0.
Disc: a Circle together with its interior.
Radian: the unit of angle, defined so that the angle round a whole Circle (360 degrees) is [itex]2\pi[/itex]. 
Equations

Diameter: [itex]2 r[/itex]
Circumference: [itex]2 \pi r[/itex]
Radian (a measure of angle): [itex]\frac{360\deg}{2 \pi}[/itex]
Arclength: [itex]r \theta[/itex]
Chordlength: [itex]2 r \sin\frac{\theta}{2}[/itex]
Curvature: [itex]\frac{1}{r}[/itex]
Area: [itex]\pi r^2[/itex] 


Breakdown

Mathematics
> Geometry
>> Plane Geometry


Extended explanation

The Circle and the Line were the two basic elements of ancient Greek geometry. The Line was drawn using a straightedge, and the Circle was drawn using a compass (a hinged instrument with a needle at one end and a marker at the other).
Would someone like to create a separate Library entry entitled "Circles and Triangles", dealing with inscribed circles etc? 
Commentary
