# 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 sectionconic 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.
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 arcarc,
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
. 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 pipi,
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.
) times twice the radius distance r, or C=2πr. The area A bounded by a circle is given by Ar2. 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 antiquitygeometric 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.
). 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

The simplest and most fundamental of geometric shapes; a continuous curved line, every point of which is equidistant from a central point.

## 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 widdershins, is considered negative.

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:

Cyford, Janet: The Ring of Chairs: A Medium’s Story. Baltimore: Thirteen-O-Seven Press, 2000
Shepard, Leslie A: Encyclopedia of Occultism & Parapsychology. New York: Avon Books, 1978
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 R2.

## 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]
(mathematics)
The set of all points in the plane at a given distance from a fixed point.
A unit of angular measure, equal to one complete revolution, that is, to 2π radians or 360°. Also known as turn.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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 = r2 where r is the radius and (h, k) are the coordinates of the centre; area πr2; circumference: 2πr 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
6. Hockey See striking circle
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

## Circle

(dreams)
The circle symbolizes infinity, the circle of life and the eternal unknown. You, the dreamer, may have come to a greater degree of spiritual awareness, so the dream could be spiritual in nature. Carl Jung called most circular images a “mandala.” It is one of the most important dream symbols that represent the psychic center of personality. It is symbolic of wholeness, completeness, and unity of the self. However, as always, examine all of the details in the dream, as well as its tone and mood, and rule out the possibility of “going in circles” as the primary message in the dream.
Bedside Dream Dictionary by Silvana Amar Copyright © 2007 by Skyhorse Publishing, Inc.
References in periodicals archive ?
"Dai turned to me and said it was time to circle the wagons.
No doubt the Tory party will circle the wagons today in Parliament, with Conservative MPs whipped to express confidence in one of their own.
THe only player to start every one of misfiring Ireland's four Test warm-up defeats says the squad will circle the wagons in the face of the widespread negativity they are now facing.
And the entire work of a generation of peacemakers was put at risk as the authority of the largest unionist party was undermined, causing DUP strategists frantically to circle the wagons and leave Iris out to dry.
But Munster somehow managed to circle the wagons, dig in, and come out with a 10-point victory in the Arms Park.
It's now up to Sanchez to circle the wagons for a daunting trip to Manchester next month.
Even a poor quality side will make life very difficult for their opponents if they circle the wagons.
Fishermens' leader Mike Park said: "We are looking for them to circle the wagons round the industry and say 'that's enough, no more', and give us the backing we need to survive."
IRISHMAN Ken Doherty needed to circle the wagons last night to reach his second successive PowerHouse UK Championship final.
"We have to circle the wagons and get ready for the Scots," admitted O'Sullivan.
"We saw in the Gulf War that Americans tend to pull up the shutters and circle the wagons," he said.
"Dai just stayed very calm and said to me, 'Derwyn, it's time to circle the wagons'.

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