# circle

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## circle,

closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section**conic section**

or

**conic**

, curve formed by the intersection of a plane and a right circular cone (conical surface). The ordinary conic sections are the circle, the ellipse, the parabola, and the hyperbola.

**.....**Click the link for more information. cut by a plane perpendicular to the axis of the cone. The term

*circle*is also used to refer to the region enclosed by the curve, more properly called a circular region. The radius of a circle is any line segment connecting the center and a point on the curve; the term is also used for the length

*r*of this segment, i.e., the common distance of all points on the curve from the center. Similarly, the circumference of a circle is either the curve itself or its length of arc

**arc,**

in geometry, a curved line or any part of it; in particular, a portion of the circumference of a circle. The length

*s*of an arc of a circle of radius

*r*and subtending a central angle of θ radians is

*s*=

*r*

**.....**Click the link for more information. . A line segment whose two ends lie on the circumference is a chord; a chord through the center is the diameter. A secant is a line of indefinite length intersecting the circle at two points, the segment of it within the circle being a chord. A tangent to a circle is a straight line touching the circle at only one point, the point of contact, or tangency, and is always perpendicular to the radius drawn to this point. A circle is inscribed in a polygon if each side of the polygon is tangent to the circle; a circle is circumscribed about a polygon if all the vertices of the polygon lie on the circumference. The length of the circumference

*C*of a circle is equal to π (see pi

**pi,**

in mathematics, the ratio of the circumference of a circle to its diameter. The symbol for pi is π. The ratio is the same for all circles and is approximately 3.1416.

**.....**Click the link for more information. ) times twice the radius distance

*r,*or

*C*=2π

*r.*The area

*A*bounded by a circle is given by

*A*=π

*r*

^{2}. Greek geometry left many unsolved problems about circles, including the problem of squaring the circle, i.e., constructing a square with an area equal to that of a given circle, using only a straight edge and compass; it was finally proved impossible in the late 19th cent. (see geometric problems of antiquity

**geometric problems of antiquity,**

three famous problems involving elementary geometric constructions with straight edge and compass, conjectured by the ancient Greeks to be impossible but not proved to be so until modern times.

**.....**Click the link for more information. ). In modern mathematics the circle is the basis for such theories as inversive geometry and certain non-Euclidean geometries. The circle figures significantly in many cultures. In religion and art it frequently symbolizes heaven, eternity, or the universe.

## Circle

## Circle

(religion, spiritualism, and occult)Unlike many other religions that have permanent, **consecrated **places of worship, a **Witch **may consecrate any area deemed suitable at any time, for the length of that ritual only, giving her far greater flexibility and convenience. That area is enclosed in a circle. Witches used to meet in a field, or a clearing in a woods, or any other open place convenient to all members.

Witches refer to their **ritual **Circle as the place "between the worlds," neither in this world nor in the next. This is the place where all the rituals take place and where **magic **is performed, if needed. Circles have long been considered sacred, whether consecrated or not. A Roman ambassador in a foreign land would draw a circle around himself with his staff, indicating that he should be safe from attack. A circle of flour was drawn on the floor around the bed of a sick person, by the Babylonians, to keep demons away. German Jews would draw a circle around the bed of a woman in labor, in the Middle Ages, to protect her from evil spirits. Britain, and other parts of Europe, contains dozens of ancient stone circles, erected in times past for a variety of religious and magical reasons.

The dimensions of a circle depend on who is drawing it and for what purpose. A **Wiccan **circle is usually nine feet in diameter, although it can be smaller or larger depending upon the number of people it must enclose. In **Ceremonial Magic**, on the other hand, the drawing has to be exact and actually forms three concentric circles of nine feet, ten feet, and eleven feet diameter, with various **Words of Power **written between the lines. A ceremonial circle is to keep forces *out*; to keep negative entities from encroaching on the magician. The Wiccan circle is to keep *in *the power raised in the rituals, which is of a positive nature.

The Wiccan circle is first marked on the ground, to indicate exactly where the sacred space lies. If the meeting is to take place out of doors, then the circle can be indicated by simply scratching a line on the ground. If the meeting is indoors, then it can be marked with a piece of chalk or charcoal, or by laying down a length of cord or actually painting a circle on the floor. Some modern Witches have a circle permanently marked on a piece of carpet, which can be rolled up and put away between meetings.

With the area marked, the construction of the magic circle starts with a tracing of the line by the presiding **priest **with a **sword **or **athamé**. Some traditions first ritually sweep the area with a **broom**, removing all negativity. The line is then sprinkled with **salted water **and passed over with a **censer**. This **circumambulation **is carried out clockwise, or ** deosil**. To move counter-clockwise, or

**, is considered negative.**

*widdershins*In order to orient the circle to the four cardinal points, candles are placed at the east, south, west and north. In the center (or to one side, depending on the tradition) stands the **altar **on which the **coven tools **or those of the individual Witch are placed. All within the circle are also consecrated, so that nothing unpurified is within it.

Although ritually cast and consecrated, it is possible to pass out of and back into the circle. This is done ritually, carefully "opening" the circle and then resealing it (see **pentagram**) after the passage of the individual. Such opening and closing should be kept to an absolute minimum; ideally, the circle should not be disturbed during the ritual.

The Wiccan deities are invited into the circle to share the ritual with the Witches. Unlike in Ceremonial Magic, there is no commanding or conjuring of the gods or of any spirits or entities. All should be within the circle of their own free will. At the end of the ritual, the gods are thanked and the circle is opened.

Since Wiccan rituals are held inside a circle, the term "circle" is also a synonym for a meeting. Witches therefore speak of "having a weekly circle" or of "planning a healing circle."

## Circle

(religion, spiritualism, and occult)Sitters at a **séance** invariably are seated in a circle, either around a table or with an open area in the center. Hence, séances are often referred to as “circles.” A **Spiritualist** circle usually calls for a **medium** to be among the number. There can be any number of people at the sitting, but twelve is usually preferred. This circle is made up, as far as possible, of equal numbers of positive and negative energies. Although most females are sensitive and negative and most males positive and magnetic, there are exceptions, and energies do not necessarily indicate gender. Some circles are arranged with the negative energy on one side of the medium and the positive energy on the other. Circles are also sometimes arranged with the negative and positive energies alternating around the circle.

Janet Cyford *(The Ring of Chairs)* said, “The movement of energy in the **development circle** is clockwise. A ring of closed energy forms when we join with others and sit in a ring of chairs.” The circle of people may hold hands or, if there is a table in the center, may rest their hands on the table with each touching his or her neighbor’s hands. Usually the medium is included in the circle though sometimes the medium sits apart from the circle, either inside or in front of a **cabinet**.

**Sources:**

*The Ring of Chairs: A Medium’s Story.*Baltimore: Thirteen-O-Seven Press, 2000

*Encyclopedia of Occultism & Parapsychology*. New York: Avon Books, 1978

## Circle

a closed, plane curve, all points of which are equidistant from a given fixed point in the plane, called the center of the circle. A segment *R* that connects the center of a circle with any point on the circle, and also the length of this segment, is called the radius of the circle. The ratio of the circumference of a circle to the diameter of the circle is identical for all circles. This ratio is a transcendental number, which is designated by the Greek letter *π* = 3.14159 …. The circumference of a circle is found from the formula *l* = 2 *π R.* A portion of a plane that is bounded by a circle and contains the center of the circle is called a disk; the area of a disk is equal to *π R ^{2}.*

## Circle

a village in the USA, in eastern Alaska; situated on the Yukon River. Population, less than 100 (1970). Circle is the center of a gold-mining region. It was founded circa 1890.

## What does it mean when you dream about a circle?

A circle encompasses many meanings in numerous areas: the wholeness of numbers in mathematics, the spiritual oneness depicted by the circle and the mandala, protection from evil by the ritual drawing of a circle, bringing attention to something by circling it. It may also express frustrations, as when one doodles in circles or goes around in circles. Socially, it may represent being “in” the right circle of friends. The love relationship is sometimes symbolized by the wearing of a ring, around the finger, the neck, or in the nose. In Jungian psychology the circle is a symbol of the self archetype. (See also Zero.)

## circle

[′sər·kəl]## circle

**1.**

*Maths*a closed plane curve every point of which is equidistant from a given fixed point, the centre. Equation: (

*x --h*)

^{2}+ (

*y --k*)

^{2}

*= r*

^{2}where

*r*is the radius and (

*h, k*) are the coordinates of the centre; area πr

^{2}; circumference: 2π

*r*CHECK FORMULA

**2.**the figure enclosed by such a curve

**3.**

*Theatre*the section of seats above the main level of the auditorium, usually comprising the dress circle and the upper circle

**4.**a parallel of latitude

**5.**

*History*one of a number of Neolithic or Bronze Age rings of standing stones, such as Stonehenge, found in Europe and thought to be associated with some form of ritual or astronomical measurement