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Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius.

The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus.

Terminology
All of the specified regions may be considered as open, that is, not containing their boundaries, or as closed, including their respective boundaries.
 * Annulus: a ring-shaped object, the region bounded by two concentric circles.
 * Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up a full circle.
 * Centre: the point equidistant from all points on the circle.
 * Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments.
 * Circumference: the length of one circuit along the circle, or the distance around the circle.
 * Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; or the length of such a line segment. This is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord for a given circle, and its length is twice the length of a radius.
 * Disc: the region of the plane bounded by a circle. In strict mathematical usage, a circle is only the boundary of the disc, while in everyday the terms "circle" and "disc" may be used interchangeably.
 * Lens: the region common to (the intersection of) two overlapping discs.
 * Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter. Usually, the radius is denoted $$r$$ and required to be a positive number. A circle with $$r=0$$ is a degenerate case consisting of a single point.
 * Sector: a region bounded by two radii of equal length with a common centre and either of the two possible arcs, determined by this centre and the endpoints of the radii.
 * Segment: a region bounded by a chord and one of the arcs connecting the chord's endpoints. The length of the chord imposes a lower boundary on the diameter of possible arcs. Sometimes the term segment is used only for regions not containing the centre of the circle to which their arc belongs to.
 * Secant: an extended chord, a coplanar straight line, intersecting a circle in two points.
 * Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as centre. In non-technical common usage it may mean the interior of the two-dimensional region bounded by a diameter and one of its arcs, that is technically called a half-disc. A half-disc is a special case of a segment, namely the largest one.
 * Tangent: a coplanar straight line that has one single point in common with a circle ("touches the circle at this point").

Etymology
The word circle derives from the Greek κίρκος/κύκλος (kirkos/kuklos), itself a metathesis of the Homeric Greek κρίκος (krikos), meaning "hoop" or "ring". The origins of the words circus and circuit are closely related.

History
Prehistoric people made stone circles and timber circles, and circular elements are common in petroglyphs and cave paintings. Disc-shaped prehistoric artifacts include the Nebra sky disc and jade discs called Bi.

The Egyptian Rhind papyrus, dated to 1700 BCE, gives a method to find the area of a circle. The result corresponds to $256⁄81$ (3.16049...) as an approximate value of $\pi$.

Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is:

In Plato's Seventh Letter there is a detailed definition and explanation of the circle. Plato explains the perfect circle, and how it is different from any drawing, words, definition or explanation. Early science, particularly geometry and astrology and astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" that could be found in circles.

In 1880 CE, Ferdinand von Lindemann proved that π is transcendental, proving that the millennia-old problem of squaring the circle cannot be performed with straightedge and compass.

With the advent of abstract art in the early 20th century, geometric objects became an artistic subject in their own right. Wassily Kandinsky in particular often used circles as an element of his compositions.

Symbolism and religious use
From the time of the earliest known civilisations – such as the Assyrians and ancient Egyptians, those in the Indus Valley and along the Yellow River in China, and the Western civilisations of ancient Greece and Rome during classical Antiquity – the circle has been used directly or indirectly in visual art to convey the artist's message and to express certain ideas. However, differences in worldview (beliefs and culture) had a great impact on artists' perceptions. While some emphasised the circle's perimeter to demonstrate their democratic manifestation, others focused on its centre to symbolise the concept of cosmic unity. In mystical doctrines, the circle mainly symbolises the infinite and cyclical nature of existence, but in religious traditions it represents heavenly bodies and divine spirits.

The circle signifies many sacred and spiritual concepts, including unity, infinity, wholeness, the universe, divinity, balance, stability and perfection, among others. Such concepts have been conveyed in cultures worldwide through the use of symbols, for example, a compass, a halo, the vesica piscis and its derivatives (fish, eye, aureole, mandorla, etc.), the ouroboros, the Dharma wheel, a rainbow, mandalas, rose windows and so forth. Magic circles are part of some traditions of Western esotericism.

Circumference
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. Thus the circumference C is related to the radius r and diameter d by: $$C = 2\pi r = \pi d.$$

Area enclosed

As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared: $$\mathrm{Area} = \pi r^2.$$

Equivalently, denoting diameter by d, $$\mathrm{Area} = \frac{\pi d^2}{4} \approx 0.7854 d^2,$$ that is, approximately 79% of the circumscribing square (whose side is of length d).

The circle is the plane curve enclosing the maximum area for a given arc length. This relates the circle to a problem in the calculus of variations, namely the isoperimetric inequality.

Equation of a circle
In an x–y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that $$(x - a)^2 + (y - b)^2 = r^2.$$

This equation, known as the equation of the circle, follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the radius is the hypotenuse of a right-angled triangle whose other sides are of length |x − a| and |y − b|. If the circle is centred at the origin (0, 0), then the equation simplifies to $$x^2 + y^2 = r^2.$$

Parametric form
The equation can be written in parametric form using the trigonometric functions sine and cosine as $$\begin{align} x &= a + r\,\cos t, \\ y &= b + r\,\sin t, \end{align}$$ where t is a parametric variable in the range 0 to 2π, interpreted geometrically as the angle that the ray from (a, b) to (x, y) makes with the positive x axis.

An alternative parametrisation of the circle is $$\begin{align} x &= a + r \frac{1 - t^2}{1 + t^2}, \\ y &= b + r \frac{2t}{1 + t^2}. \end{align}$$

In this parameterisation, the ratio of t to r can be interpreted geometrically as the stereographic projection of the line passing through the centre parallel to the x axis (see Tangent half-angle substitution). However, this parameterisation works only if t is made to range not only through all reals but also to a point at infinity; otherwise, the leftmost point of the circle would be omitted.

3-point form
The equation of the circle determined by three points $$(x_1, y_1), (x_2, y_2), (x_3, y_3)$$ not on a line is obtained by a conversion of the 3-point form of a circle equation: $$ \frac{({\color{green}x} - x_1)({\color{green}x} - x_2) + ({\color{red}y} - y_1)({\color{red}y} - y_2)} {({\color{red}y} - y_1)({\color{green}x} - x_2) - ({\color{red}y} - y_2)({\color{green}x} - x_1)} = \frac{(x_3 - x_1)(x_3 - x_2) + (y_3 - y_1)(y_3 - y_2)} {(y_3 - y_1)(x_3 - x_2) - (y_3 - y_2)(x_3 - x_1)}.$$

Homogeneous form
In homogeneous coordinates, each conic section with the equation of a circle has the form $$x^2 + y^2 - 2axz - 2byz + cz^2 = 0.$$

It can be proven that a conic section is a circle exactly when it contains (when extended to the complex projective plane) the points I(1: i: 0) and J(1: −i: 0). These points are called the circular points at infinity.

Polar coordinates
In polar coordinates, the equation of a circle is $$r^2 - 2 r r_0 \cos(\theta - \phi) + r_0^2 = a^2,$$

where a is the radius of the circle, $$(r, \theta)$$ are the polar coordinates of a generic point on the circle, and $$(r_0, \phi)$$ are the polar coordinates of the centre of the circle (i.e., r0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of the circle). For a circle centred on the origin, i.e., this reduces to. When, or when the origin lies on the circle, the equation becomes $$r = 2 a\cos(\theta - \phi).$$

In the general case, the equation can be solved for r, giving $$r = r_0 \cos(\theta - \phi) \pm \sqrt{a^2 - r_0^2 \sin^2(\theta - \phi)}.$$ Without the ± sign, the equation would in some cases describe only half a circle.

Complex plane
In the complex plane, a circle with a centre at c and radius r has the equation $$|z - c| = r.$$

In parametric form, this can be written as $$z = re^{it} + c.$$

The slightly generalised equation $$pz\overline{z} + gz + \overline{gz} = q$$

for real p, q and complex g is sometimes called a generalised circle. This becomes the above equation for a circle with $$p = 1,\ g = -\overline{c},\ q = r^2 - |c|^2$$, since $$|z - c|^2 = z\overline{z} - \overline{c}z - c\overline{z} + c\overline{c}$$. Not all generalised circles are actually circles: a generalised circle is either a (true) circle or a line.

Tangent lines
The tangent line through a point P on the circle is perpendicular to the diameter passing through P. If and the circle has centre (a, b) and radius r, then the tangent line is perpendicular to the line from (a, b) to (x1, y1), so it has the form (x1 − a)x + (y1 – b)y = c. Evaluating at (x1, y1) 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 y1 ≠ b, then the slope of this line is $$\frac{dy}{dx} = -\frac{x_1 - a}{y_1 - b}.$$

This can also be found using implicit differentiation.

When the centre 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 $$\frac{dy}{dx} = -\frac{x_1}{y_1}.$$

Properties

 * The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality).
 * The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T.
 * All circles are similar.
 * A circle circumference and radius are proportional.
 * The area enclosed and the square of its radius are proportional.
 * The constants of proportionality are 2π and π respectively.
 * The circle that is centred at the origin with radius 1 is called the unit circle.
 * Thought of as a great circle of the unit sphere, it becomes the Riemannian circle.
 * Through any three points, not all on the same line, there lies a unique circle. In Cartesian coordinates, it is possible to give explicit formulae for the coordinates of the centre of the circle and the radius in terms of the coordinates of the three given points. See circumcircle.

Chord

 * Chords are equidistant from the centre of a circle if and only if they are equal in length.
 * The perpendicular bisector of a chord passes through the centre of a circle; equivalent statements stemming from the uniqueness of the perpendicular bisector are:
 * A perpendicular line from the centre of a circle bisects the chord.
 * The line segment through the centre bisecting a chord is perpendicular to the chord.
 * If a central angle and an inscribed angle of a circle are subtended by the same chord and on the same side of the chord, then the central angle is twice the inscribed angle.
 * If two angles are inscribed on the same chord and on the same side of the chord, then they are equal.
 * If two angles are inscribed on the same chord and on opposite sides of the chord, then they are supplementary.
 * For a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.
 * An inscribed angle subtended by a diameter is a right angle (see Thales' theorem).
 * The diameter is the longest chord of the circle.
 * Among all the circles with a chord AB in common, the circle with minimal radius is the one with diameter AB.
 * If the intersection of any two chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then.
 * If the intersection of any two perpendicular chords divides one chord into lengths a and b and divides the other chord into lengths c and d, then a2 + b2 + c2 + d2 equals the square of the diameter.
 * The sum of the squared lengths of any two chords intersecting at right angles at a given point is the same as that of any other two perpendicular chords intersecting at the same point and is given by 8r2 − 4p2, where r is the circle radius, and p is the distance from the centre point to the point of intersection.
 * The distance from a point on the circle to a given chord times the diameter of the circle equals the product of the distances from the point to the ends of the chord.

Tangent

 * A line drawn perpendicular to a radius through the end point of the radius lying on the circle is a tangent to the circle.
 * A line drawn perpendicular to a tangent through the point of contact with a circle passes through the centre of the circle.
 * Two tangents can always be drawn to a circle from any point outside the circle, and these tangents are equal in length.
 * If a tangent at A and a tangent at B intersect at the exterior point P, then denoting the centre as O, the angles ∠BOA and ∠BPA are supplementary.
 * If AD is tangent to the circle at A and if AQ is a chord of the circle, then ∠DAQ = $C$arc(AQ).

Theorems

 * The chord theorem states that if two chords, CD and EB, intersect at A, then AC × AD = AB × AE.
 * If two secants, AE and AD, also cut the circle at B and C respectively, then AC × AD = AB × AE (corollary of the chord theorem).
 * A tangent can be considered a limiting case of a secant whose ends are coincident. If a tangent from an external point A meets the circle at F and a secant from the external point A meets the circle at C and D respectively, then (tangent–secant theorem).
 * The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle).
 * If the angle subtended by the chord at the centre is 90°, then, where ℓ is the length of the chord, and r is the radius of the circle.
 * If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs ($$\overset{\frown}{DE}$$ and $$\overset{\frown}{BC}$$). That is, $$2\angle{CAB} = \angle{DOE} - \angle{BOC}$$, where O is the centre of the circle (secant–secant theorem).

Inscribed angles
An inscribed angle (examples are the blue and green angles in the figure) is exactly half the corresponding central angle (red). Hence, all inscribed angles that subtend the same arc (pink) are equal. Angles inscribed on the arc (brown) are supplementary. In particular, every inscribed angle that subtends a diameter is a right angle (since the central angle is 180°).

Sagitta
The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle.

Given the length y of a chord and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle that will fit around the two lines: $$r = \frac{y^2}{8x} + \frac{x}{2}.$$

Another proof of this result, which relies only on two chord properties given above, is as follows. Given a chord of length y and with sagitta of length x, since the sagitta intersects the midpoint of the chord, we know that it is a part of a diameter of the circle. Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2)2. Solving for r, we find the required result.

Compass and straightedge constructions
There are many compass-and-straightedge constructions resulting in circles.

The simplest and most basic is the construction given the centre of the circle and a point on the circle. Place the fixed leg of the compass on the centre point, the movable leg on the point on the circle and rotate the compass.

Construction with given diameter

 * Construct the midpoint $O(2)$ of the diameter.
 * Construct the circle with centre $πR^{2}$ passing through one of the endpoints of the diameter (it will also pass through the other endpoint).

Construction through three noncollinear points

 * Name the points $C = 2πR$, $M$ and $M$,
 * Construct the perpendicular bisector of the segment $P$.
 * Construct the perpendicular bisector of the segment $Q$.
 * Label the point of intersection of these two perpendicular bisectors $R$. (They meet because the points are not collinear).
 * Construct the circle with centre $\overline{PQ}$ passing through one of the points $\overline{PR}$, $M$ or $M$ (it will also pass through the other two points).

Circle of Apollonius
Apollonius of Perga showed that a circle may also be defined as the set of points in a plane having a constant ratio (other than 1) of distances to two fixed foci, A and B. (The set of points where the distances are equal is the perpendicular bisector of segment AB, a line.) That circle is sometimes said to be drawn about two points.

The proof is in two parts. First, one must prove that, given two foci A and B and a ratio of distances, any point P satisfying the ratio of distances must fall on a particular circle. Let C be another point, also satisfying the ratio and lying on segment AB. By the angle bisector theorem the line segment PC will bisect the interior angle APB, since the segments are similar: $$\frac{AP}{BP} = \frac{AC}{BC}.$$

Analogously, a line segment PD through some point D on AB extended bisects the corresponding exterior angle BPQ where Q is on AP extended. Since the interior and exterior angles sum to 180 degrees, the angle CPD is exactly 90 degrees; that is, a right angle. The set of points P such that angle CPD is a right angle forms a circle, of which CD is a diameter.

Second, see for a proof that every point on the indicated circle satisfies the given ratio.

Cross-ratios
A closely related property of circles involves the geometry of the cross-ratio of points in the complex plane. If A, B, and C are as above, then the circle of Apollonius for these three points is the collection of points P for which the absolute value of the cross-ratio is equal to one: $$\bigl|[A, B; C, P]\bigr| = 1.$$

Stated another way, P is a point on the circle of Apollonius if and only if the cross-ratio [A, B; C, P] is on the unit circle in the complex plane.

Generalised circles
If C is the midpoint of the segment AB, then the collection of points P satisfying the Apollonius condition $$\frac{|AP|}{|BP|} = \frac{|AC|}{|BC|}$$ is not a circle, but rather a line.

Thus, if A, B, and C are given distinct points in the plane, then the locus of points P satisfying the above equation is called a "generalised circle." It may either be a true circle or a line. In this sense a line is a generalised circle of infinite radius.

Inscription in or circumscription about other figures
In every triangle a unique circle, called the incircle, can be inscribed such that it is tangent to each of the three sides of the triangle.

About every triangle a unique circle, called the circumcircle, can be circumscribed such that it goes through each of the triangle's three vertices.

A tangential polygon, such as a tangential quadrilateral, is any convex polygon within which a circle can be inscribed that is tangent to each side of the polygon. Every regular polygon and every triangle is a tangential polygon.

A cyclic polygon is any convex polygon about which a circle can be circumscribed, passing through each vertex. A well-studied example is the cyclic quadrilateral. Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called a bicentric polygon.

A hypocycloid is a curve that is inscribed in a given circle by tracing a fixed point on a smaller circle that rolls within and tangent to the given circle.

Limiting case of other figures
The circle can be viewed as a limiting case of various other figures:
 * The series of regular polygons with n sides has the circle as its limit as n approaches infinity. This fact was applied by Archimedes to approximate π.
 * A Cartesian oval is a set of points such that a weighted sum of the distances from any of its points to two fixed points (foci) is a constant. An ellipse is the case in which the weights are equal. A circle is an ellipse with an eccentricity of zero, meaning that the two foci coincide with each other as the centre of the circle. A circle is also a different special case of a Cartesian oval in which one of the weights is zero.
 * A superellipse has an equation of the form $$\left|\frac{x}{a}\right|^n\! + \left|\frac{y}{b}\right|^n\! = 1$$ for positive a, b, and n. A supercircle has b =a. A circle is the special case of a supercircle in which.
 * A Cassini oval is a set of points such that the product of the distances from any of its points to two fixed points is a constant. When the two fixed points coincide, a circle results.
 * A curve of constant width is a figure whose width, defined as the perpendicular distance between two distinct parallel lines each intersecting its boundary in a single point, is the same regardless of the direction of those two parallel lines. The circle is the simplest example of this type of figure.

Locus of constant sum
Consider a finite set of $$n$$ points in the plane. The locus of points such that the sum of the squares of the distances to the given points is constant is a circle, whose centre is at the centroid of the given points. A generalization for higher powers of distances is obtained if under $$n$$ points the vertices of the regular polygon $$P_n$$ are taken. The locus of points such that the sum of the $$2m$$-th power of distances $$d_i$$ to the vertices of a given regular polygon with circumradius $$R$$ is constant is a circle, if $$\sum_{i=1}^n d_i^{2m} > nR^{2m}, \quad \text{ where } ~ m = 1, 2, \dots, n-1;$$ whose centre is the centroid of the $$P_n$$.

In the case of the equilateral triangle, the loci of the constant sums of the second and fourth powers are circles, whereas for the square, the loci are circles for the constant sums of the second, fourth, and sixth powers. For the regular pentagon the constant sum of the eighth powers of the distances will be added and so forth.

Squaring the circle
Squaring the circle is the problem, proposed by ancient geometers, of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge.

In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (π) is a transcendental number, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. Despite the impossibility, this topic continues to be of interest for pseudomath enthusiasts.

In other p-norms
Defining a circle as the set of points with a fixed distance from a point, different shapes can be considered circles under different definitions of distance. In p-norm, distance is determined by $$ \left\| x \right\| _p = \left( \left|x_1\right|^p + \left|x_2\right|^p + \dotsb + \left|x_n\right|^p \right) ^{1/p} .$$ In Euclidean geometry, p = 2, giving the familiar $$ \left\| x \right\| _2 = \sqrt{ \left|x_1\right|^2 + \left|x_2\right|^2 + \dotsb + \left|x_n\right|^2 } .$$

In taxicab geometry, p = 1. Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. While each side would have length $$\sqrt{2} r$$ using a Euclidean metric, where r is the circle's radius, its length in taxicab geometry is 2r. Thus, a circle's circumference is 8r. Thus, the value of a geometric analog to $$\pi $$ is 4 in this geometry. The formula for the unit circle in taxicab geometry is $$|x| + |y| = 1$$ in Cartesian coordinates and $$r = \frac{1}{\left| \sin \theta\right| + \left|\cos\theta\right|}$$ in polar coordinates.

A circle of radius 1 (using this distance) is the von Neumann neighborhood of its centre.

A circle of radius r for the Chebyshev distance (L∞ metric) on a plane is also a square with side length 2r parallel to the coordinate axes, so planar Chebyshev distance can be viewed as equivalent by rotation and scaling to planar taxicab distance. However, this equivalence between L1 and L∞ metrics does not generalize to higher dimensions.

Topological definition
The circle is the one-dimensional hypersphere (the 1-sphere).

In topology, a circle is not limited to the geometric concept, but to all of its homeomorphisms. Two topological circles are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy).

Specially named circles

 * Apollonian circles
 * Archimedean circle
 * Archimedes' twin circles
 * Bankoff circle
 * Carlyle circle
 * Chromatic circle
 * Circle of antisimilitude
 * Ford circle
 * Geodesic circle
 * Johnson circles
 * Schoch circles
 * Woo circles

Of a triangle

 * Apollonius circle of the excircles
 * Brocard circle
 * Excircle
 * Incircle
 * Lemoine circle
 * Lester circle
 * Malfatti circles
 * Mandart circle
 * Nine-point circle
 * Orthocentroidal circle
 * Parry circle
 * Polar circle (geometry)
 * Spieker circle
 * Van Lamoen circle

Of certain quadrilaterals

 * Eight-point circle of an orthodiagonal quadrilateral

Of a conic section

 * Director circle
 * Directrix circle

Of a torus

 * Villarceau circles

title: Circle


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Cardinal (Catholic Church)

A cardinal (Sanctae Romanae Ecclesiae cardinalis; lit. 'cardinal of the Holy Roman Church') is a senior member of the clergy of the Catholic Church. Cardinals are created by the pope and typically hold the title for life. Collectively, they constitute the College of Cardinals. The most solemn responsibility of the cardinals is to elect a new pope in a conclave, almost always from among themselves (with a few historical exceptions), when the Holy See is vacant. During the period between a pope's death or resignation and the election of his successor, the day-to-day governance of the Holy See is in the hands of the College of Cardinals. The right to participate in a conclave is limited to cardinals who have not reached the age of 80 years by the day the vacancy occurs. In addition, cardinals collectively participate in papal consistories (which generally take place annually), in which matters of importance to the Church are considered and new cardinals may be created. Cardinals of working age are also appointed to roles overseeing dicasteries of the Roman Curia, the central administration of the Catholic Church.

Cardinals are drawn from a variety of backgrounds, being appointed as cardinals in addition to their existing roles within the Church. Most cardinals are bishops and archbishops leading dioceses and archdioceses around the world – often the most prominent diocese or archdiocese in their country. Others are titular bishops who are current or former officials within the Roman Curia (generally the heads of dicasteries and other bodies linked to the Curia). A very small number are priests recognised by the pope for their service to the Church; as canon law requires them to be generally consecrated as bishops before they are made cardinals, but some are granted a papal dispensation. There are no strict criteria for elevation to the College of Cardinals. Since 1917, a potential cardinal must already be at least a priest, but laymen have been cardinals in the past. The selection is entirely up to the pope and tradition is his only guide.

there are serving cardinals, of whom  are eligible to vote in a conclave to elect a new pope.

History

There is general disagreement about the origin of the term, but a chief consensus that "cardinalis" is etymologically from the Latin word (meaning "pivot" or "hinge") was first used in late antiquity to designate a bishop or priest who was incorporated into a church for which he had not originally been ordained. In Rome the first persons to be called cardinals were the deacons of the seven regions of the city at the beginning of the 6th century, when the word began to mean "principal", "eminent", or "superior". The name was also given to the senior priest in each of the "title" churches (the parish churches) of Rome and to the bishops of the seven sees surrounding the city. By the 8th century the Roman cardinals constituted a privileged class among the Roman clergy. They took part in the administration of the Church of Rome and in the papal liturgy. By decree of a synod of 769, only a cardinal was eligible to become Bishop of Rome. Cardinals were granted the privilege of wearing the red hat by Pope Innocent IV in 1244.

In cities other than Rome, the name cardinal began to be applied to certain churchmen as a mark of honour. The earliest example of this occurs in a letter sent by Pope Zacharias in 747 to Pippin the Younger, ruler of the Franks, in which Zacharias applied the title to the priests of Paris to distinguish them from country clergy. This meaning of the word spread rapidly, and from the 9th century various episcopal cities had a special class among the clergy known as cardinals. The use of the title was reserved for the cardinals of Rome in 1567 by Pius V.

In 1059 (five years after the East-West Schism), the right of electing the pope was reserved to the principal clergy of Rome and the bishops of the seven suburbicarian sees. In the 12th century the practice of appointing ecclesiastics from outside Rome as cardinals began, with each of them assigned a church in Rome as his titular church or linked with one of the suburbicarian dioceses, while still being incardinated in a diocese other than that of Rome.

The term cardinal at one time applied to any priest permanently assigned or incardinated to a church, or specifically to the senior priest of an important church, based on the Latin cardo (hinge), meaning "pivotal" as in "principal" or "chief". The term was applied in this sense as early as the 9th century to the priests of the tituli (parishes) of the diocese of Rome.

In the year 1563, the Ecumenical Council of Trent, headed by Pope Pius IV, wrote about the importance of selecting good cardinals: "nothing is more necessary to the Church of God than that the holy Roman pontiff apply that solicitude which by the duty of his office he owes the universal Church in a very special way by associating with himself as cardinals the most select persons only, and appoint to each church most eminently upright and competent shepherds; and this the more so, because our Lord Jesus Christ will require at his hands the blood of the sheep of Christ that perish through the evil government of shepherds who are negligent and forgetful of their office."

The earlier influence of temporal rulers, notably the kings of France, reasserted itself through the influence of cardinals of certain nationalities or politically significant movements. Traditions even developed entitling certain monarchs, including those of Austria, Spain, and France, to nominate one of their trusted clerical subjects to be created cardinal, a so-called "crown-cardinal".

In early modern times, cardinals often had important roles in secular affairs. In some cases, they took on powerful positions in government. In Henry VIII's England, his chief minister was for some time Cardinal Wolsey. Cardinal Richelieu's power was so great that he was for many years effectively the ruler of France. Richelieu's successor was also a cardinal, Jules Mazarin. Guillaume Dubois and André-Hercule de Fleury complete the list of the four great cardinals to have ruled France. In Portugal, due to a succession crisis, one cardinal, Henry of Portugal, was crowned king, the only example of a cardinal-king.

While the incumbents of some sees are regularly made cardinals, and some countries are entitled to at least one cardinal by concordat (usually earning either its primate or the metropolitan of the capital city the cardinal's hat), almost no see carries an actual right to the cardinalate, not even if its bishop is a patriarch: the notable exception is the Patriarch of Lisbon who, by Pope Clement XII's 1737 bull Inter praecipuas apostolici ministerii, is accorded the right to be elevated to the rank of cardinal in the consistory following his appointment.

Papal elections
In 1059, Pope Nicholas II gave cardinals the right to elect the Bishop of Rome in the papal bull In nomine Domini. For a time this power was assigned exclusively to the cardinal bishops, but in 1179 the Third Lateran Council restored the right to the whole body of cardinals.

Numbers
In 1586, Pope Sixtus V limited the number of cardinals to 70: six cardinal bishops, 50 cardinal priests, and 14 cardinal deacons. Pope John XXIII exceeded that limit citing the need to staff church offices. In November 1970 in Ingravescentem aetatem, Pope Paul VI established that electors would be under the age of eighty years. When it took effect on 1 January 1971, it deprived 25 cardinals of the right to participate in a conclave. In October 1975 in Romano Pontifici eligendo, he set the maximum number of electors at 120, while establishing no limit on the overall size of the college.

Popes can set aside church laws and they have regularly brought the number of cardinals under the age of 80 to more than 120, twice reaching as high as 135 with Pope John Paul II's consistories of February 2001 and October 2003. No more than 120 electors have ever participated in a conclave, but most canon lawyers believe that if their number exceeded 120 they would all participate.

Pope Paul VI also increased the number of cardinal bishops by assigning that rank, in 1965, to patriarchs of the Eastern Catholic Churches when named cardinals. In 2018, Pope Francis expanded the cardinal bishops of Roman title, because this had not been done despite recent decades' expansion in the two lower orders of cardinals, besides having all six such cardinals being over the age limit for a conclave.

Titular churches

Each cardinal is assigned a titular church upon his creation, which is always a church in the city of Rome. Through the process of opting (optazione), a cardinal can raise through the ranks from cardinal deacon to priest, and from cardinal priest to that of cardinal bishop - in which case he obtains one of the suburbicarian sees located around the city of Rome. The only exception is for patriarchs of the Eastern Catholic Churches. Nevertheless, cardinals possess no power of governance nor are they to intervene in any way in matters which pertain to the administration of goods, discipline, or the service of their titular churches. They are allowed to celebrate Mass and hear confessions and lead visits and pilgrimages to their titular churches, in coordination with the staff of the church. They often support their churches monetarily, and many cardinals do keep in contact with the pastoral staffs of their titular churches. The term cardinal is from the Latin word "cardo" meaning a hinge. Here it means a "door", an example of synecdoche, a figure of speech whereby the part refers to the whole. The "door" is the address of the titular church from which the cardinal derives his membership of the Roman clergy, who elect the pope.

The Dean of the College of Cardinals in addition to such a titular church also receives the titular bishopric of Ostia, the primary suburbicarian see. Cardinals governing a particular church retain that church.

Title and reference style
In 1630, Pope Urban VIII decreed their title to be Eminence (previously, it had been "illustrissimo" and "reverendissimo") and decreed that their secular rank would equate to prince, making them second only to the pope and crowned monarchs.

In accordance with tradition, they sign by placing the title "Cardinal" (abbreviated Card.) after their personal name and before their surname as, for instance, "John Card(inal) Doe" or, in Latin, "Ioannes Card(inalis) Doe". Some writers, such as James-Charles Noonan, hold that, in the case of cardinals, the form used for signatures should be used also when referring to them in English. However, official sources, such as the Catholic News Service, say that the correct form for referring to a cardinal in English is normally as "Cardinal [First name] [Surname]". This is the rule given also in stylebooks not associated with the church. This style is also generally followed on the websites of the Holy See and episcopal conferences. The websites of the Holy See (except for signatures), and of the Episcopal Conferences in the United States, England and Wales , Ireland  and the Australia  agree with the stylebooks. The Bishops' Conference of Scotland uses both styles side by side. On diocesan sites, the "John Cardinal Doe" style is found on, for example, those of Boston, Chicago, Dublin , New York , Toronto, Washington , Galveston-Houston , Detroit , Durban , Colombo, Bombay , and the "Cardinal John Doe" on, for example, those of Armagh ,Los Angeles , Philadelphia , St Andrews and Edinburgh , Wellington , Westminster. Oriental patriarchs who are created cardinals customarily use "Sanctae Ecclesiae Cardinalis" as their full title, probably because they do not belong to the Roman clergy.

The [First name] Cardinal [Surname] order is used in the Latin proclamation of the election of a new pope by the cardinal protodeacon, if the new pope is a cardinal, as has been the case since 1378.

The term Prince of the Church has historically been applied to cardinals of the Catholic church, and sometimes more broadly to senior members of the church hierarchy. It has been rejected by Pope Francis, who stated to a group of newly created cardinals "He (Jesus) does not call you to become 'princes' of the Church, to 'sit on his right or on his left.' He calls you to serve like Him and with Him." The term is still applied, both seriously and as a criticism of the perceived attitudes of some cardinals.

Cardinal bishops

Cardinal bishops (cardinals of the episcopal order; cardinales episcopi) are the senior order of cardinals. Though in modern times the vast majority of cardinals are also bishops or archbishops, few are "cardinal bishops". For most of the second millennium there were six cardinal bishops, each presiding over one of the seven suburbicarian sees around Rome: Ostia, Albano, Porto and Santa Rufina, Palestrina, Sabina and Mentana, Frascati, and Velletri. Velletri was united with Ostia from 1150 until 1914, when Pope Pius X separated them again, but decreed that whichever cardinal bishop became Dean of the College of Cardinals would keep the suburbicarian see he already held, adding to it that of Ostia, with the result that there continued to be only six cardinal bishops. Since 1962, the cardinal bishops have only a titular relationship with the suburbicarian sees, each of which is governed by a separate ordinary.

Until 1961, membership in the order of cardinal bishops was achieved through precedence in the College of Cardinals. When a suburbicarian see fell vacant, the most senior cardinal by precedence could exercise his option to claim the see and be promoted to the order of cardinal bishops. Pope John XXIII abolished that privilege on 10 March 1961 and made the right to promote someone to the order of cardinal bishops the sole prerogative of the pope.

In 1965, Pope Paul VI decreed in his motu proprio Ad purpuratorum Patrum Collegium that patriarchs of the Eastern Catholic Churches who were named cardinals (i.e. "cardinal patriarchs") would also be cardinal bishops, ranking after the six Roman rite cardinal bishops of the suburbicarian sees. (Latin Church patriarchs who become cardinals are cardinal priests, not cardinal bishops: for example Angelo Scola was made Patriarch of Venice in 2002 and cardinal priest of Santi XII Apostoli in 2003.) Those of cardinal patriarch rank continue to hold their patriarchal see and are not assigned any Roman title (suburbicarian see or title or deaconry).

At the June 2018 consistory, Pope Francis increased the number of Latin Church cardinal bishops to match the expansion in cardinal priests and cardinal deacons in recent decades. He elevated four cardinals to this rank granting their titular churches and deaconries suburbicarian rank pro hac vice (temporarily) and making them equivalent to suburbicarian see titles. At the time of the announcement, all six cardinal bishops of suburbicarian see titles, as well as two of the three cardinal patriarchs, were non-electors as they had reached the age of 80. Pope Francis created another cardinal bishop in the same way on 1 May 2020, bringing the number of Latin Church cardinal bishops to eleven.

The Dean of the College of Cardinals, the highest ranking cardinal, was formerly the longest serving cardinal bishop, but since 1965 is elected by the Latin Church cardinal bishops from among their number, subject to papal approval. Likewise the Vice-Dean, formerly the second longest serving, is also elected. Seniority of the remaining Latin Church cardinal bishops is still by date of appointment to the rank.

Cardinal priests
Cardinal priests (cardinales presbyteri) are the most numerous of the three orders of cardinals in the Catholic Church, ranking above the cardinal deacons and below the cardinal bishops. Those who are named cardinal priests today are generally also bishops of important dioceses throughout the world, though some hold Curial positions.

In modern times, the term "cardinal priest" is interpreted as meaning a cardinal who is of the order of priests. Originally, however, this referred to certain key priests of important churches of the Diocese of Rome, who were recognized as the cardinal priests, the important priests chosen by the pope to advise him in his duties as Bishop of Rome (the Latin cardo means "hinge"). Certain clerics in many dioceses at the time, not just that of Rome, were said to be the key personnel—the term gradually became exclusive to Rome to indicate those entrusted with electing the Bishop of Rome, the pope.

While the cardinalate has long been expanded beyond the Roman pastoral clergy and Roman Curia, every cardinal priest has a titular church in Rome, though they may be bishops or archbishops elsewhere, just as cardinal bishops were given one of the suburbicarian dioceses around Rome. Pope Paul VI abolished all administrative rights cardinals had with regard to their titular churches, though the cardinal's name and coat of arms are still posted in the church, and they are expected to celebrate Mass and preach there if convenient when they are in Rome.

While the number of cardinals was small from the times of the Roman Empire to the Renaissance, and frequently smaller than the number of recognized churches entitled to a cardinal priest, in the 16th century the college expanded markedly. In 1587, Pope Sixtus V sought to arrest this growth by fixing the maximum size of the college at 70, including 50 cardinal priests, about twice the historical number. This limit was respected until 1958, and the list of titular churches modified only on rare occasions, generally when a building fell into disrepair. When Pope John XXIII abolished the limit, he began to add new churches to the list, which Popes Paul VI and John Paul II continued to do. Today there are close to 150 titular churches, out of over 300 churches in Rome.

The cardinal who is the longest-serving member of the order of cardinal priests is titled cardinal protopriest. He had certain ceremonial duties in the conclave that have effectively ceased because he would generally have already reached age 80, at which cardinals are barred from the conclave. The current cardinal protopriest is Michael Michai Kitbunchu of Thailand.

Cardinal deacons
The cardinal deacons (cardinales diaconi) are the lowest-ranking cardinals. Cardinals elevated to the diaconal order are either officials of the Roman Curia or priests elevated after their 80th birthday. Bishops with diocesan responsibilities, however, are created cardinal priests.

Cardinal deacons derive originally from the seven deacons in the Papal Household who supervised the Church's works in the seven districts of Rome during the early Middle Ages, when church administration was effectively the government of Rome and provided all social services. They came to be called "cardinal deacons" by the late eighth century, and they were granted active rights in papal elections and made eligible for the election as pope by the decree of 769.

Cardinals elevated to the diaconal order are mainly officials of the Roman Curia holding various posts in the church administration. Their number and influence has varied through the years. While historically predominantly Italian the group has become much more internationally diverse in later years. While in 1939 about half were Italian, by 1994 the number was reduced to one third. Their influence in the election of the pope has been considered important. They are better informed and connected than the dislocated cardinals but their level of unity has been varied. Under the 1587 decree of Pope Sixtus V, which fixed the maximum size of the College of Cardinals, there were 14 cardinal deacons. Later the number increased. As late as 1939 almost half of the cardinals were members of the Curia. Pius XII reduced this percentage to 24 percent. John XXIII brought it back up to 37 percent but Paul VI brought it down to 27 percent. John Paul II maintained this ratio.

As of 2005, there were over 50 churches recognized as cardinalatial deaconries, though there were only 30 cardinals of the order of deacons. Cardinal deacons have long enjoyed the right to "opt for the order of cardinal priests" (optazione) after they have been cardinal deacons for 10 years. They may on such elevation take a vacant "title" (a church allotted to a cardinal priest as the church in Rome with which he is associated) or their diaconal church may be temporarily elevated to a cardinal priest's "title" for that occasion. When elevated to cardinal priests, they take their precedence according to the day they were first made cardinal deacons (thus ranking above cardinal priests who were elevated to the college after them, regardless of order).

When not celebrating Mass but still serving a liturgical function, such as the semiannual Urbi et Orbi papal blessing, some Papal Masses and some events at Ecumenical Councils, cardinal deacons can be recognized by the dalmatics they would don with the simple white mitre (so called mitra simplex).

Cardinal protodeacon
The cardinal protodeacon is the senior cardinal deacon in order of appointment to the College of Cardinals. If he is a cardinal elector and participates in a conclave, he announces a new pope's election and name from the central balcony of St. Peter's Basilica in Vatican City. The protodeacon also bestows the pallium on the new pope and crowns him with the papal tiara, although the crowning has not been celebrated since Pope John Paul I opted for a simpler papal inauguration ceremony in 1978. The current cardinal protodeacon is Renato Raffaele Martino.

Cardinal protodeacons since 1887

 * Giuseppe Pecci, S.J. (20 December 1887 – 8 February 1890)
 * John Henry Newman, C.O. (8 February 1890 – 11 August 1890)
 * Joseph Hergenröther (11 August 1890 – 3 October 1890)
 * Tommaso Maria Zigliara, O.P. (3 October 1890 – 1 June 1891)
 * Isidoro Verga (1 June 1891 – 22 June 1896)
 * Luigi Macchi (22 June 1896 – 29 March 1907); announced election of Pope Pius X (1903)
 * Andreas Steinhuber, S.J. (29 March 1907 – 15 October 1907)
 * Francesco Segna (15 October 1907 – 4 January 1911)
 * Francesco Salesio Della Volpe (4 January 1911 – 5 November 1916†); announced election of Pope Benedict XV (1914)
 * Gaetano Bisleti (5 November 1916 – 17 December 1928*); announced election of Pope Pius XI (1922)
 * Camillo Laurenti (17 December 1928 – 16 December 1935*)
 * Camillo Caccia-Dominioni (16 December 1935 – 12 November 1946†); announced election of Pope Pius XII (1939)
 * Nicola Canali (12 November 1946 – 3 August 1961†); announced election of Pope John XXIII (1958)
 * Alfredo Ottaviani (3 August 1961 – 26 June 1967*); announced election of Pope Paul VI (1963)
 * Arcadio Larraona Saralegui, CMF (26 June 1967 – 28 April 1969*)
 * William Theodore Heard (28 April 1969 – 18 May 1970*)
 * Antonio Bacci (18 May 1970 – 20 January 1971†)
 * Michael Browne, OP (20 January 1971 – 31 March 1971†)
 * Federico Callori di Vignale (31 March 1971 – 8 August 1971†)
 * Charles Journet (8 August 1971 – 5 March 1973*)
 * Pericle Felici (5 March 1973 – 30 June 1979*); announced elections of Pope John Paul I (1978) and Pope John Paul II (1978)
 * Sergio Pignedoli (30 June 1979 – 15 June 1980†)
 * Umberto Mozzoni (15 June 1980 – 2 February 1983*)
 * Opilio Rossi (2 February 1983 – 22 June 1987*)
 * Giuseppe Caprio (22 June 1987 – 26 November 1990*)
 * Aurelio Sabattani (26 November 1990 – 5 April 1993*)
 * Duraisamy Simon Lourdusamy (5 April 1993 – 29 January 1996*)
 * Eduardo Martínez Somalo (29 January 1996 – 9 January 1999*)
 * Pio Laghi (9 January 1999 – 26 February 2002*)
 * Luigi Poggi (26 February 2002 – 24 February 2005*)
 * Jorge Medina (24 February 2005 – 23 February 2007*); announced election of Pope Benedict XVI (2005)
 * Darío Castrillón Hoyos (23 February 2007 – 1 March 2008*)
 * Agostino Cacciavillan (1 March 2008 – 21 February 2011*)
 * Jean-Louis Tauran (21 February 2011 – 12 June 2014*); announced election of Pope Francis (2013)
 * Renato Raffaele Martino (12 June 2014 –)

* Ceased to be protodeacon upon being raised to the order of cardinal-priest † Was protodeacon at time of death

Camerlengo
The Cardinal Camerlengo of the Holy Roman Church, assisted by the Vice-Camerlengo and the other prelates of the office known as the Apostolic Camera, has functions that in essence are limited to a period of sede vacante of the papacy. He is to collate information about the financial situation of all administrations dependent on the Holy See and present the results to the College of Cardinals, as they gather for the papal conclave.

Cardinals who are not bishops

Until 1918, any cleric, even one only in minor orders, could be created a cardinal (see "lay cardinals", below), but enrolled only in the order of cardinal deacons. For example, in the 16th century, Reginald Pole was a cardinal for 18 years before he was ordained a priest. The 1917 Code of Canon Law mandated that all cardinals, even cardinal deacons, had to be priests, and, in 1962, Pope John XXIII set the norm that all cardinals be consecrated as bishops, even if they are only priests at the time of appointment. As a consequence of these two changes, canon 351 of the 1983 Code of Canon Law requires that a cardinal be at least in the order of priesthood at his appointment, and that those who are not already bishops must receive episcopal consecration. Several cardinals near to or over the age of 80 when appointed have obtained dispensation from the rule of having to be a bishop. These were all appointed cardinal-deacons, but Roberto Tucci and Albert Vanhoye lived long enough to exercise the right of option and be promoted to the rank of cardinal-priest. No cardinal who was not a bishop has participated in a papal conclave since the 1962 rule change.

A cardinal who is not a bishop is entitled to wear and use the episcopal vestments and other pontificalia (episcopal regalia: mitre, crozier, zucchetto, pectoral cross, and ring). He has both actual and honorary precedence over archbishops, and bishops who are not cardinals. However, he cannot perform the sacrament of ordination or other rites reserved solely to bishops.

"Lay cardinals"
At various times, there have been cardinals who had only received first tonsure and minor orders but not yet been ordained as deacons or priests. Though clerics, they were inaccurately called "lay cardinals". Teodolfo Mertel was among the last of the lay cardinals. When he died in 1899 he was the last surviving cardinal who was not at least ordained a priest. With the revision of the Code of Canon Law promulgated in 1917 by Pope Benedict XV, only those who are already priests or bishops may be appointed cardinals. Since the time of Pope John XXIII a priest who is appointed a cardinal must be consecrated a bishop, unless he obtains a dispensation.

Cardinals in pectore or secret cardinals
In addition to the named cardinals, the pope may name secret cardinals or cardinals in pectore (Latin for in the breast). During the Western Schism, many cardinals were created by the contending popes. Beginning with the reign of Pope Martin V, cardinals were created without publishing their names until later, a practice termed creati et reservati in pectore. A cardinal named in pectore is known only to the pope. In the modern era, popes have named cardinals in pectore to protect them or their congregations from political reprisals. If conditions change, the pope makes the appointment public. The cardinal in question then ranks in precedence with those made cardinals at the time of his in pectore appointment. If a pope dies before revealing the identity of an in pectore cardinal, the person's status as cardinal expires. The last pope known to have named a cardinal in pectore is Pope John Paul II, who named four, including one whose identity was never revealed.

Vesture and privileges
When in choir dress, a Latin Church cardinal wears scarlet garments—the blood-like red symbolizes a cardinal's willingness to die for his faith. Excluding the rochet — which is always white—the scarlet garments include the cassock, mozzetta, and biretta (over the usual scarlet zucchetto). The biretta of a cardinal is distinctive not merely for its scarlet color, but also for the fact that it does not have a pompon or tassel on the top as do the birettas of other prelates. Until the 1460s, it was customary for cardinals to wear a violet or blue cape unless granted the privilege of wearing red when acting on papal business. His normal-wear cassock is black but has scarlet piping and a scarlet fascia (sash). Occasionally, a cardinal wears a scarlet ferraiolo which is a cape worn over the shoulders, tied at the neck in a bow by narrow strips of cloth in the front, without any 'trim' or piping on it. It is because of the scarlet color of cardinals' vesture that the bird of the same name has become known as such.

Eastern Catholic cardinals continue to wear the normal dress appropriate to their liturgical tradition, though some may line their cassocks with scarlet and wear scarlet fascias, or in some cases, wear Eastern-style cassocks entirely of scarlet.

In previous times, at the consistory at which the pope named a new cardinal, he would bestow upon him a distinctive wide-brimmed hat called a galero. This custom was discontinued in 1969 and the investiture now takes place with the scarlet biretta. In ecclesiastical heraldry, however, the scarlet galero is still displayed on the cardinal's coat of arms. Cardinals had the right to display the galero in their cathedral, and when a cardinal died, it would be suspended from the ceiling above his tomb. Some cardinals will still have a galero made, even though it is not officially part of their apparel.

To symbolize their bond with the papacy, the pope gives each newly appointed cardinal a gold ring, which is traditionally kissed by Catholics when greeting a cardinal (as with a bishop's episcopal ring). Before the new uniformity imposed by John Paul II, each cardinal was given a ring, the central piece of which was a gem, usually a sapphire, with the pope's stemma engraved on the inside. There is now no gemstone, and the pope chooses the image on the outside: under Pope Benedict XVI it was a modern depiction of the crucifixion of Jesus, with Mary and John to each side. The ring includes the pope's coat of arms on the inside.

Cardinals have in canon law a "privilege of forum" (i.e., exemption from being judged by ecclesiastical tribunals of ordinary rank): only the pope is competent to judge them in matters subject to ecclesiastical jurisdiction (cases that refer to matters that are spiritual or linked with the spiritual, or with regard to infringement of ecclesiastical laws and whatever contains an element of sin, where culpability must be determined and the appropriate ecclesiastical penalty imposed). The pope either decides the case himself or delegates the decision to a tribunal, usually one of the tribunals or congregations of the Roman Curia. Without such delegation, no ecclesiastical court, even the Roman Rota, is competent to judge a canon law case against a cardinal.

Additionally, canon law gives cardinals the faculty of hearing confessions validly and licitly everywhere, whereas other priests and bishops must be granted this faculty and might be restricted in its use by the local bishop.

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title: Cardinal (Catholic Church)


text:
Cantigas de Santa Maria

The Cantigas de Santa Maria (, ; "Canticles of Holy Mary") are 420 poems with musical notation, written in the medieval Galician-Portuguese language during the reign of Alfonso X of Castile El Sabio (1221–1284). Traditionally, they are all attributed to Alfonso, though scholars have since established that the musicians and poets of his court were responsible for most of them, with Alfonso being credited with a few as well.

It is one of the largest collections of monophonic (solo) songs from the Middle Ages and is characterized by the mention of the Virgin Mary in every song, while every tenth song is a hymn.

The Cantigas have survived in four manuscript codices: two at El Escorial, one at Madrid's National Library, and one in Florence, Italy. The E codex from El Escorial is illuminated with colored miniatures showing pairs of musicians playing a wide variety of instruments. The Códice Rico (T) from El Escorial and the one in the Biblioteca Nazionale Centrale of Florence (F) are richly illuminated with narrative vignettes.

Description
The Cantigas are written in the early Medieval Galician variety of Galician-Portuguese, using Galician spelling; this was because of Galician-Portuguese being fashionable as a lyrical language in Castile at the time, as well as Alfonso X having passed part of his early years in Galicia and so probably being a fluent speaker since his childhood.

The Cantigas are a collection of 420 poems, 356 of which are in a narrative format relating to Marian miracles; the rest of them, except an introduction and two prologues, are of songs of praise or involve Marian festivities. The Cantigas depict the Virgin Mary in a very humanized way, often having her play a role in earthly episodes.

The authors are unknown, although several studies have suggested that Galician poet Airas Nunes might have been the author of a large number of the Cantiga poems. King Alfonso X — named as Affonso in the Cantigas — is also believed to be an author of some of them as he refers himself in first person. Support for this theory can be found in the prologue of the Cantigas. Also, many sources credit Alfonso owing to his influence on other works within the poetic tradition, including his introduction on religious song. Although King Alfonso X's authorship is debatable, his influence is not. While the other major works that came out of Alfonso's workshops, including histories and other prose texts, were in Castilian, the Cantigas are in Galician-Portuguese, and reflect the popularity in the Castilian court of other poetic corpuses such as the cantigas d'amigo and cantigas d'amor.

The metrics are extraordinarily diverse: 280 different formats for the 420 Cantigas. The most common are the virelai and the rondeau. The length of the lines varies between two and 24 syllables. The narrative voice in many of the songs describes an erotic relationship, in the troubadour fashion, with the Divine. The music is written in notation which is similar to that used for chant, but also contains some information about the length of the notes. Several transcriptions exist. The Cantigas are frequently recorded and performed by early music groups, and quite a few CDs featuring music from the Cantigas are available.

Codices
The Cantigas are preserved in four manuscripts:

 * To (códice de Toledo, Biblioteca Nacional de España, MS 10069, link to manuscript)

 * T (códice rico, Biblioteca de El Escorial, MS T.I.1, link to manuscript)

 * F (códice de Florencia, Florence, Biblioteca Nazionale, MS b.r. 20, link to manuscript)

 * E (códice de los músicos, Biblioteca de El Escorial MS B.I.2, link to manuscript)

E contains the largest number of songs (406 Cantigas, plus the Introduction and the Prologue); it contains 41 carefully detailed miniatures and many illuminated letters. To is the earliest collection and contains 129 songs. Although not illustrated, it is richly decorated with pen flourished initials, and great care has been taken over its construction. The T and F manuscripts are sister volumes. T contains 195 surviving cantigas (8 are missing due to loss of folios) which roughly correspond in order to the first two hundred in E, each song being illustrated with either 6 or 12 miniatures that depict scenes from the cantiga. F follows the same format but has only 111 cantigas, of which 7 have no text, only miniatures. These are basically a subset of those found in the second half of E, but are presented here in a radically different order. F was never finished, and so no music was ever added. Only the empty staves display the intention to add musical notation to the codex at a later date. It is generally thought that the codices were constructed during Alfonso's lifetime, To perhaps in the 1270s, and T/F and E in the early 1280s up until the time of his death in 1284.

The music
The musical forms within the Cantigas, and there are many, are still being studied. There have been many false leads, and there is little beyond pitch value that is very reliable. Mensuration is a particular problem in the Cantigas, and most attempts at determining meaningful rhythmic schemes have tended, with some exceptions, to be unsatisfactory. This remains a lively topic of debate and study. Progress, while on-going, has nevertheless been significant over the course of the last 20 years.

title: Cantigas de Santa Maria