From Wikipedia, the free encyclopedia
Circle illustration showing a radius, a diameter, the center and the circumference
.^ (See sun symbol below the picture of the Eye of Horus ) A dot or point in the center of a circle symbolizes the blending of male and female forces. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
The common distance of the points of a circle from its center is called its
radius.
.^ Sometimes this cross is seen with four additional "arms" dividing the circle into eight instead of four sections. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
^ Compare its two intersecting lines with Sun Sign 2 , its curved arms (following the shape of the circle) with Swastika 2, and its dark areas with the Iron Cross . Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
.^ The Caucasian Chalk Circle defines morality in terms of social 'use.' Bertolt Brecht (18981956) 20 September 2009 10:40 UTC www.csuchico.edu [Source type: FILTERED WITH BAYES]
^ We'll examine figures with circular boundaries like the vesica, and its use as art motifs. Geometry in Art & Architecture Unit 9 10 February 2010 13:27 UTC www.dartmouth.edu [Source type: FILTERED WITH BAYES]
However, in strict technical usage, "circle" refers to the perimeter while the interior of the circle is called a
disk. The
circumference of a circle is the perimeter of the circle (especially when referring to its length).
Further terminology
Chord, secant, tangent, and diameter.


.^ CIRCLE (quartered): The sacred circle filled with a cross, four equal lines pointing from the center to the spirits of the north, east, south, and west  or to the basic element: earth, water, air (or wind), and fire. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
^ Compare its two intersecting lines with Sun Sign 2 , its curved arms (following the shape of the circle) with Swastika 2, and its dark areas with the Iron Cross . Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
.^ Augustine described the nature of God as a circle whose centre was everywhere, and its circumference nowhere. EMERSON"CIRCLES" hypertext 20 September 2009 10:40 UTC www.vcu.edu [Source type: Original source]
^ A great circle perpendicular to the plane of the ecliptic, passing through its poles. circle@Everything2.com 10 February 2010 13:27 UTC www.everything2.com [Source type: FILTERED WITH BAYES]
^ Circle of the sphere , a circle upon the surface of the sphere, called a great circle when its plane passes through the center of the sphere; in all other cases, a small circle . circle@Everything2.com 10 February 2010 13:27 UTC www.everything2.com [Source type: FILTERED WITH BAYES]
.^ Putting the clear transparency on the projector, I drew a large circle, then added two overlapping triangles (one pointing up, one pointing down), forming a hexagram. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
The diameter of a circle is twice its radius.
.^ Recall that the diameter of a circle will fit around the perimeter of the circle three times, plus a bit more, actually p times, where 3.1416. Geometry in Art & Architecture Unit 9 10 February 2010 13:27 UTC www.dartmouth.edu [Source type: FILTERED WITH BAYES]
^ Literature is a point outside of our hodiernal circle, through which a new one may be described. EMERSON"CIRCLES" hypertext 20 September 2009 10:40 UTC www.vcu.edu [Source type: Original source]
^ Putting the clear transparency on the projector, I drew a large circle, then added two overlapping triangles (one pointing up, one pointing down), forming a hexagram. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
In this sense, the midpoint of a diameter is the centre and so it is composed of two radii.
.^ Compare its two intersecting lines with Sun Sign 2 , its curved arms (following the shape of the circle) with Swastika 2, and its dark areas with the Iron Cross . Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
.^ A great circle perpendicular to the plane of the ecliptic, passing through its poles. circle@Everything2.com 10 February 2010 13:27 UTC www.everything2.com [Source type: FILTERED WITH BAYES]
^ Circle of the sphere , a circle upon the surface of the sphere, called a great circle when its plane passes through the center of the sphere; in all other cases, a small circle . circle@Everything2.com 10 February 2010 13:27 UTC www.everything2.com [Source type: FILTERED WITH BAYES]
A
tangent to a circle is a straight line that touches the circle at a single point.
.^ The lines of the "A" often extend outside the circle. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
^ Putting the clear transparency on the projector, I drew a large circle, then added two overlapping triangles (one pointing up, one pointing down), forming a hexagram. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
^ Compare its two intersecting lines with Sun Sign 2 , its curved arms (following the shape of the circle) with Swastika 2, and its dark areas with the Iron Cross . Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
An
arc of a circle is any
connected part of the circle's circumference. A
sector is a region bounded by two radii and an arc lying between the radii, and a
segment is a region bounded by a chord and an arc lying between the chord's endpoints.
History
.^ This was symbolized in art by God holding a pair of compasses, a common motif in the Middle Ages. Geometry in Art & Architecture Unit 9 10 February 2010 13:27 UTC www.dartmouth.edu [Source type: FILTERED WITH BAYES]
Notice also the circular shape of the
halo
.^ To most people, this is true enough, but to those paying attention, Circle has been making some of the most original modern rock music since the beginning of the ‘90s. CIRCLE on MySpace Music  Free Streaming MP3s, Pictures & Music Downloads 10 February 2010 13:27 UTC www.myspace.com [Source type: FILTERED WITH BAYES]
.^ Character makes an overpowering present; a cheerful, determined hour, which fortifies all the company, by making them see that much is possible and excellent that was not thought of. EMERSON"CIRCLES" hypertext 20 September 2009 10:40 UTC www.vcu.edu [Source type: Original source]
In mathematics, the study of the circle has helped inspire the development of geometry and calculus.
.^ Circles can be " called "/invoked/set up in many different ways, but the common standard is to call each of the elements (with calling the watchtowers being the most used there), then bind the four energies together. circle@Everything2.com 10 February 2010 13:27 UTC www.everything2.com [Source type: FILTERED WITH BAYES]
^ I believe this plan will likely be successful as there are many callers that cannot control the phone networks of their friends and family members. Alltel My Circle 10 February 2010 13:27 UTC blog.tmcnet.com [Source type: FILTERED WITH BAYES]
^{[citation needed]}
Some highlights in the history of the circle are:
 1700 BC – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as an approximate value of π.^{[1]}
.
Analytic results
Length of circumference
For more details on this topic, see
Pi.
.^ Formulae vital to the geometric aspect of a circle : Circumfrence : c = {pi} * d Area : a = {pi} * r^2 Diameter : d = 2r Arc Length  The distance from one point on the circumference to another point on the circumference traveling along the edge of the circle. circle@Everything2.com 10 February 2010 13:27 UTC www.everything2.com [Source type: FILTERED WITH BAYES]
Thus the length of the circumference (
c) is related to the radius (
r) by
or equivalently to the diameter (d) by
Area enclosed
Area of the circle =
π × area of the shaded square
Main article:
Area of a disk
Equivalently, denoting diameter by d,
that is, approximately 79% of the
circumscribing square (whose side is of length
d).
.^ Compare its two intersecting lines with Sun Sign 2 , its curved arms (following the shape of the circle) with Swastika 2, and its dark areas with the Iron Cross . Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
This relates the circle to a problem in the
calculus of variations, namely the
isoperimetric inequality.
Equations
Cartesian coordinates
Circle of radius
r = 1, center (
a,
b) = (1.2, 0.5)
.^ Putting the clear transparency on the projector, I drew a large circle, then added two overlapping triangles (one pointing up, one pointing down), forming a hexagram. Symbols and their meaning 10 February 2010 13:27 UTC www.crossroad.to [Source type: FILTERED WITH BAYES]
If the circle is centered at the origin (0, 0), then the equation simplifies to
where
t is a
parametric variable, interpreted geometrically as the angle that the ray from the origin to (
x,
y) makes with the
xaxis. Alternatively, a rational parametrization of the circle is:
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.
Polar coordinates
where a is the radius of the circle, r_{0} is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive xaxis to the line connecting the origin to the centre of the circle. For a circle centred at the origin, i.e. r_{0} = 0, this reduces to simply r = a. When r_{0} = a, or when the origin lies on the circle, the equation becomes
 .
In the general case, the equation can be solved for r, giving
 ,
the solution with a minus sign in front of the square root giving the same curve.
Complex plane
In the
complex plane, a circle with a center at
c and radius (
r) has the equation
. In parametric form this can be written
z = re^{it} + c.
The slightly generalized equation
for real
p,
q and complex
g is sometimes called a
generalised circle. This becomes the above equation for a circle with
, since
. Not all generalised circles are actually circles: a generalized circle is either a (true) circle or a
line.
Tangent lines
.^ Literature is a point outside of our hodiernal circle, through which a new one may be described. EMERSON"CIRCLES" hypertext 20 September 2009 10:40 UTC www.vcu.edu [Source type: Original source]
If
P = (
x_{1},
y_{1}) and the circle has center (
a,
b) and radius
r, then the tangent line is perpendicular to the line from (
a,
b) to (
x_{1},
y_{1}), so it has the form (
x_{1}−
a)x+(
y_{1}−
b)y =
c. Evaluating at (
x_{1},
y_{1}) determines the value of
c and the result is that the equation of the tangent is
 (x_{1} − a)x + (y_{1} − b)y = (x_{1} − a)x_{1} + (y_{1} − b)y_{1}
or
 (x_{1} − a)(x − a) + (y_{1} − b)(y − b) = r^{2}.
If y_{1}≠b then slope of this line is
 .
When the center of the circle is at the origin then the equation of the tangent line becomes
 x_{1}x + y_{1}y = r^{2},
and its slope is
 .
Properties
.