
Review of Short Phrases and Links 
This Review contains major "Circle" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the center.
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 A circle is a special form of an ellipse that has the two foci at the same point (the center of the ellipse).
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 A circle is a special kind of ellipse in which the two foci happen to coincide, so the eccentricity is zero.
 A circle is a special case of an ellipse with zero eccentricity.(From U. Tenn, Ast.
 A circle is a conic section cut by a plane perpendicular to the axis of the cone.
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 The boundary of a disk is a circle, so these boundary components are circles.
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 Commercial flag books show the badges in circles, but none that I have seen, have ever explained that the white circle is not necessarily part of the badge.
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 Answer: A circle is a special case of ellipse, so both orbits are elliptical.
 For the special case of a circle, the semimajor axis is just the radius.
 In the special case that the orbiting body is always the same distance from the center, it is also the shape of a circle.
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 Aardwolf made his way to a Lowtown base of Tyger Tiger, only to have her betray him by sicking the Circle on him again.
 Aardwolf convinced Thrasher into believing that the Folding Circle had captured Silhouette, and by defeating them, he would be rescuing her.
 This diagram with seven points and seven lines (the circle through i, j, and k is considered a line) is called the Fano plane.
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 For Ω 1 (the sphere, see diagram) the ratio falls below π: indeed, a great circle on a sphere has circumference only twice its diameter.
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 The Enneagram is an occult oriented chart or diagram with many points and lines inside and touching a circle.
 A circle with a dot at its centre (Unicode U+2299 ⊙) indicates a vector pointing out of the front of the diagram, toward the viewer.
 Draw a circle of radius OA and center V. It intersects the original circle at two of the vertices of the pentagon.
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 Extend a line from each vertex of the pentagon through the center of the circle to the opposite side of that same circle.
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 Choose a point A on the circle that will serve as one vertex of the pentagon.
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 Satanists use a pentagram with two points up, often inscribed in a double circle, with the head of a goat inside the pentagram.
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 Satanists use the Pythagorean pentagram (one point down) inscribed in a double circle, with the head of Baphomet inside the pentagram.
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 Like Mufasa said, "We all have our place in the circle of life." When it comes to compost, it 's just a very small circle.
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 Mufasa takes Simba around the Pride Lands, teaching him about the "Circle of Life", the delicate balance affecting all living things.
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 A bit more formally: we represent a point on the unit circle by its angle, in radians, going from π to π for simplicity.
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 The intermediate result c is the great circle distance in radians.
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 With the notable exception of the radian, most units of angular measurement are defined such that one full circle (i.e.
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 The radian (symbol: rad, or a superscript c (half circle)) is the SI unit of plane angle.
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 Since this vertical circle is a great circle through the celestial poles, and includes the zenith of the observer, it is also a celestial meridian.
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 The celestial meridian is the great circle on the celestial sphere that passes through the celestial poles and the zenith of the observer.
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 Hour circle: a great circle on the celestial sphere that passes through the celestial poles and is therefore perpendicular to the celestial equator.
 The circumpolar stars appear to lie within a circle that is centered at the celestial pole and tangential to the horizon.
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 Polar distance (p) is angular distance from a celestial pole, or the arc of an hour circle between the celestial pole and a point on the celestial sphere.
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 As the Earth rotates, the stars appear to circle the celestial pole.
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 The Mbius strip is a nontrivial bundle over the circle.
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 A circle rotated about a chord of the circle is called a torus in some contexts, but this is not a common usage in mathematics.
 Each torus is the stereographic projection of the inverse image of a circle of latitude of the 2sphere.
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 A torus is generated when a circle is revolved about a line that does not intersect the circle.
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 Kepler's first law states: A) The orbit of a planet about the Sun is a circle with the Sun at the center.
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 The equator is an imaginary circle around the earth (or other planet or moon), halfway between the north and south poles.
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 Orbits are either circular, with the planet at the center of the circle, or elliptical, with the planet at one focus of the ellipse.
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 Kepler's first law states that a planet moves around the Sun A) in a circle, with the Sun at the center.
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 As the planet moves it's image grows larger and merges with the primary image from the star (circle with hole).
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 C) the small circle about which the planet moves as the center of the circle orbits the Earth.
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 The circle and the ellipse arise when the intersection of cone and plane is a closed curve.
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 A closed curve is thus a continuous mapping of the circle S 1; a simple closed curve is also called a Jordan curve.
 Drawing in this domain a little circle we get a closed curve which relative interior points are also boundary points of its complementary sets.
 However, this is not now since the tilt of earth is itself changing its direction, tracing a circle on the celestial sphere.
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 If the direction of the electric field E is not fixed, but rotates in a circle as the light propagates, the light is said to be circularly polarized.
 In general, if one travels along a great circle, ones bearing (the angle between the direction and true north) will continuously change.
 In the plane perpendicular to this line lies a circle whose 6 vertices have x4=0.
 An imaginary line forming a great circle around the Earth's surface, equidistant from the poles and in a plane perpendicular to the Earth's axis of rotation.
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 Vertical Circle: a plane perpendicular to the local horizon and passing through the center of the Earth.
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 One way to determine if your declination circle is aligned properly is to move the telescope until it reads 90 degrees north.
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 Since the declination of all navigational bodies is continually changing, the bodies are describing flat, spherical spirals as they circle the Earth.
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 The declination of a celestial body is its angular distance north or south of the celestial equator measured along its hour circle.
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 Trading Card Game booster set, Power of the Duelist, there is a card called "Crop Circle" with the circle in the Egyptian Eye logo for YuGiOh!.
 The heart of the crop circle is a large circle surrounded by four medium circles which are connected to four smaller circles.
 One video shows a military helicopter hovering over a mysterious ball of light that is right over a newly formed crop circle.
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 Meridian: a great circle passing through the celestial poles and through the zenith of any location on Earth.
 This results in the equator being about 0.16% longer than a meridian (as a great circle passing through the two poles).
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 Altitude: the angular distance of a celestial body above or below the horizon, measured along the great circle passing through the body and the zenith.
 Each half of this circle is a meridian, which is a line running from pole to pole and crossing the equator at a right angle.
 The circle that passes through the south point, north point and the point directly over head (zenith) is called the meridian.
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 Meridian: Great circle that passes through both the north and south poles, also called line of longitude.
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 A drum circle is a group of people gathered into a circle for the purpose of making music with percussion instruments.
 Other instruments and dance are also incorporated into the drum circle.
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 Cancellation, Squared Circle: circular date stamp with an arrangement of lines or bars outside the circle which makes the entire cancel square.
 In 1972, British wrestler Kendo Nagasaki invented a new angle for a wrestling match when he introduced a ladder to the squared circle.
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 The Olympic medals are circular in shape, while the Paralympic medals are a superellipse or squared circle.
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 The circle around a pentagram (transforming it in to a pentacle,) is a symbol of "unity, wholeness, infinity, the goddess, and protection.
 The Pentagram is a symbol of a star encased in a circle.
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 Unsurprisingly, the symbol of the OIC is a flag with a green background and an upward facing red crescent within a white circle.
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 Mandala (मण्डल) is a Sanskrit word that means "circle".
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 Mandala is Sanskrit for circle, polygon, community, connection.
 Cham, or sacred dance is always performed within the confines of a mandala (circle) and is part of tantric ritual.
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 In physics, circular motion is movement with constant speed around in a circle: a circular path or a circular orbit.
 D) a circular path along which a planet moves while the center of this circular path itself moves in a circle around the Earth.
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 Thus when we see an object moving is a circular path, we can look to the center of the circle to find the source(s) of the force causing this motion.
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 Together, these parts cover the whole circle and the four charts form an atlas for the circle.
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 Each chart omits a single point, either (−1,0) for s or (+1,0) for t, so neither chart alone is sufficient to cover the whole circle.
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 Instead of having a little particle whizzing around the nucleus in a circular path, we'd have a wave sort of strung out around the whole circle.
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 Data were obtained from incisor (white circle) and molar (black circle) periodontal ligaments.
 Note there is a black circle around the badge in the centre on this occasion.
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 A blue region indicates an open set, a red square a closed set, and a black circle a point.
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 Tangent properties The line drawn perpendicular to the end point of a radius is a tangent to the circle.
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 For example, circle in the plane can be defined as the curve c where the vector c(t)v is always perpendicular to the tangent vector c'(t).
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 An oblique equator is a great circle the plane of which is perpendicular to the axis of an oblique projection.
 For instance, if a circle and a straight line were two expressions of the same shape, perhaps a line could be thought of as a circle of infinite radius.
 All other notions as a straight line, angle, circle can be defined in terms of points as pairs of real numbers and the distances between them.
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 Inside these limits, the curve of the arc of a circle of equal altitude is hardly perceptible, and the arc is plotted and regarded as a straight line.
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 In the same way, equations can be derived for the circle, ellipse, and other conic sections and regular curves.
 The circle is a conic section obtained by the intersection of a cone with a plane perpendicular to the cone 's symmetry axis.
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 According to a broader definition, the generator of a torus need not be a circle but could also be an ellipse or any other conic section.
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 Eccentricity may be interpreted as a measure of how much the conic section deviates from a circle.
 A circle may be viewed as a special case of an ellipse with zero eccentricity, while as the ellipse becomes more flattened the eccentricity approaches one.
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 A circle has zero eccentricity, and most of the planet s have orbit s which are nearly circle s.
 A circle has zero eccentricity, and most of the planets have orbits which are nearly circles.
 When the two foci of an ellipse are at the same point, then the ellipse has zero eccentricity, and is known as a "circle".
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 The earth's orbit is not a circle, but an ellipse, and since it is an ellipse, the sun sits at one of the two foci that the ellipse has.
 In the special case where the two foci are at the same place, the drawn curve is a circle.
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 The NCP and SCP form the poles of a great circle on celestial sphere, analogous to the equator on Earth.
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 Two great circle lines l and m on a sphere are parallel at the midway line (equator) between their two points of intersection (poles).
 The starting point for measuring northsouth locations on Earth is the equator, a great circle which is everywhere equidistant from the poles.
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 The plane of this circle is called the ecliptic and is tilted by 23.44° relative to the equatorial plane.
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 Because there are ~365.25 days in a year and 360 degrees in a circle, the Sun appears to move along the ecliptic at a rate of about 1° per day.
 The Ecliptic is the Great Circle that describes the apparent path of the Sun around the Earth (but which is really the orbit of the Earth around the Sun.
 Möbius strip The Möbius strip is a nontrivial bundle over the circle.
 For example, the Möbius strip can be seen as a line bundle over the circle S 1 (at least if one extends the bounded interval to infinity).
 Circle (a part of it actually) is also the locus of points from which a given line segment is seen under a given angle.
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 The Mbius strip has a circle for a base and a line segment for the fiber.
 The Möbius strip has a circle for a base B and a line segment for the fiber F, so the Möbius strip is a bundle of the line segment over the circle.
 More results A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
 If the angle subtended by the chord at the center is 90 degrees then l = √2 × r, where l is the length of the chord and r is the radius of the circle.
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 If the angle subtended by the chord at the centre is 90 degrees then l = √2 × r, where l is the length of the chord and r is the radius of the circle.
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 We then measure the length of the arc (a segment of a circle) in degrees to either side of that point and label accordingly.
 Example 1: Find the length (s) of the arc intercepted by a central angle of size 3 radians if the radius of the circle is 5 centimeters (see Figure 1).
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 Let R be the radius of the circle, c the chord length, s the arc length, h the height of the segment, and d the height of the triangular portion.
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 After all, they're part of the Circle of Life.
 North of the Arctic Circle, the sun never sets for part of each summer, and in the winter, night is similarly unending.
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 Moving to New York in 1943, Harrison became a music critic, part of Virgil Thomson 's circle, and a friend of Charles Ives, whose music he championed.
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 The inner circle extends from the surface upward to 4,000 feet above the airport surface in a circle with a 5 nautical mile radius (about 6 statue miles).
 The Berlin Vril Society was in fact a sort of inner circle of the Thule Society.
 An even higher position, that of Reichsleiter, was intended for the most senior of Nazis who were part of the inner circle.
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 The curvature is the ratio of the area enclosed on the surface and that on the sphere as the circle is taken infinitesimally small.
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 Because a straight line can be thought of as an arc of a circle of infinite radius, its curvature is zero.
 The curvature of the circle is equal to that of the road at that point.
Categories
 Topological Spaces > Manifolds > Surfaces > Sphere
 Center
 Orbit
 Line
 Plane
Related Keywords
* Angle
* Angles
* Anterior Communicating Artery
* Axis
* Celestial Equator
* Celestial Sphere
* Center
* Centre
* Circle Group
* Circumference
* Curve
* Dance
* Deferent
* Diameter
* Earth
* Eccentricity
* Ellipse
* Form
* Friends
* Full Circle
* Great Circle
* Great Circles
* Group
* Hyperbola
* Large Circle
* Line
* Moon
* North
* Orbit
* Origin
* Osculating Circle
* Parabola
* Parallel
* Perfect Circle
* Plane
* Point
* Points
* Radius
* Rotation
* Small Circle
* Sphere
* Square
* Squaring
* Sun
* Unit Circle
* Willis

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