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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]

Arc-length: [itex]r \theta[/itex]

Chord-length: [itex]2 r \sin\frac{\theta}{2}[/itex]

Curvature: [itex]\frac{1}{r}[/itex]

Area: [itex]\pi r^2[/itex]

Scientists

Recent forum threads on circle
Curvature of a circle approaches zero as radius goes to infinity
Point of tangency to a circle from a point not on the circle
Complex Circle Equation with random variable attached to Z.
Relating tensions in a vertical circle help
New way to derive sectors of a circle (easy)
 
Breakdown
Mathematics
> Geometry
>> Plane Geometry

See Also
equation of a circle
conic

Images

Extended explanation
The Circle and the Line were the two basic elements of ancient Greek geometry. The Line was drawn using a straight-edge, 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

@ 03:44 PM Apr15-10
No 'perfect circles, spheres no right triangles' exist anywhere. Fomulae with pi, sin prove this to be like 'there is no last prime number', like 'there is no smallest fraction'. Call me an idiot if you wish. Such formulae are useful in 'applications' and like teaching a child 'shapes' it makes our world 'orderly enough to function in it'.

Can you imagine if I saw the pool ball with tiny lumps ie not perfect sphere, or a 3d square as 'topology'? The brain creates order from chaos-for if it did not, can you imagine trying to drive?

abhishek2208 @ 06:48 AM Mar22-10
i think its possible.

MoonlitFractl @ 03:10 PM Mar8-10
Is it possible to have a negitive [ctex]r \theta[/ctex] ?