|
Circle
In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the centre. more...
 Home
Necklaces & Pendants
 Chains
Chokers
Lariats
Other Styles
Pendants, Lockets
 3-Stone
 Cubic Zirconia
Diamond
Other Stones
Angel
Animals
Astrology
Cameos
Circle
Cluster
Coin
Cross
Amethyst
Crystal
Cubic Zirconia
Diamond
Garnet
Gold, Plate/Fill (w/o Stone)
Gold, Solid (w/o Stone)
Jade
Other Stones, Materials
Pearl
Pearl, Imitation
Sapphire
Silver (w/o Stone)
Topaz
Dog Tag
Flowers
Diamond
Gold, Plate/Fill (w/o Stone)
Gold, Solid (w/o Stone)
Jade
Other Stones, Materials
Pearl
Pearl, Imitation
Hearts, Love
Amethyst
Crystal
Cubic Zirconia
Diamond
Garnet
Gold, Plate/Fill (w/o Stone)
Gold, Solid (w/o Stone)
Jade
Other Stones, Materials
Pearl
Pearl, Imitation
Ruby
Sapphire
Topaz
Horseshoe
Letters, Initials
Lockets
Diamond
Gold, Plate/Fill (w/o Stone)
Gold, Solid (w/o Stone)
Other Stones, Materials
Silver (w/o Stone)
Other Styles
Solitaires
Abalone
Agate
Amazonite
Amber
Amethyst
Aquamarine
Carnelian
Chalcedony
Citrine
Coral
Crystal
Cubic Zirconia
Diamond
Emerald
Garnet
Glass
Iolite
Jade
Jasper
Labradorite
Lapis
Moonstone
Mother-of-Pearl
Onyx
Opal
Other Stones, Materials
Pearl
Pearl, Imitation
Peridot
Quartz
Ruby
Sapphire
Sodalite
Tanzanite
Tigers Eye
Topaz
Tourmaline
Turquoise
Stars
Strands/Strings
Tennis, Graduated
Other Wedding Jewelry
Wedding Apparel
Wedding Rings
Wedding Sets
Wedding Supplies
Wholesale Lots
Circles are simple closed curves which divide the plane into an interior and exterior. The circumference of a circle means the length of the circle, and the interior of the circle is called a disk. An arc is any continuous portion of a circle.
A circle is a special ellipse in which the two foci coincide (i.e., are the same point). Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone.
Analytic results
Equation of a circle
In an x-y coordinate system, the circle with centre (a, b) and radius r is the set of all points (x, y) such that
 If the circle is centred at the origin (0, 0), then this formula can be simplified to
- and its tangent will be
- where x1, y1 the coordinates of the common point.
When expressed in parametric equations, (x, y) can be written using the trigonometric functions sine and cosine as
where t is a parametric variable, understood as the angle the ray to (x, y) makes with the x-axis.
In homogeneous coordinates each conic section with equation of a circle is
- ax2 + ay2 + 2b1xz + 2b2yz + cz2 = 0.
It can be proven that a conic section is a circle if and only if the point I(1,i,0) and J(1,-i,0) lie on the conic section. These points are called the circular points at infinity.
In polar coordinates the equation of a circle is
- In the complex plane, a circle with a centre at c and radius r has the equation | z − c | 2 = r2. Since
 p, q and complex g is sometimes called a generalized circle. It is important to note that not all generalized circles are actually circles.
Slope
The slope of a circle at a point (x, y) can be expressed with the following formula, assuming the centre is at the origin and (x, y) is on the circle:
Read more at Wikipedia.org
|
|
