text:
The Cook, the Thief, His Wife & Her Lover
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The Cook, The Thief, His Wife & Her Lover
Theatrical release poster
Directed by
Peter Greenaway
Produced by
Pascale Dauman
Kees Kasander
Daniel Toscan du Plantier
Denis Wigman
Written by
Peter Greenaway
Starring
Richard Bohringer
Michael Gambon
Helen Mirren
Alan Howard
Music by
Michael Nyman
Cinematography
Sacha Vierny
Edited by
John Wilson
Production
companies
Allarts
Elsevier-Vendex
Distributed by
Palace Pictures, Miramax
Release date
11 September 1989 (1989-09-11) (TIFF)
13 October 1989 (1989-10-13) (United Kingdom)
1 November 1989 (1989-11-01) (France)
Running time
124 minutes[1]
Country
United Kingdom
France
Language
English
Box office
$7.7 million (North America)[2]
The Cook, the Thief, His Wife & Her Lover is a 1989 British-French romantic black comedy crime drama film written and directed by Peter Greenaway, starring Richard Bohringer, Michael Gambon, Helen Mirren, and Alan Howard in the titular roles. The film's graphic scatology, violence, and nude scenes, as well as its lavish cinematography and formalism, were noted at the time of its release.
Contents
[hide]
1 Plot
2 Cast
3 Production
3.1 Writing
3.2 Music
3.3 Design
4 Release
4.1 Versions
4.2 Critical reception
5 Soundtrack
6 References
7 External links
Plot[edit]
English gangster Albert Spica has taken over the high-class Le Hollandais Restaurant, run by French chef Richard Boarst. Spica makes nightly appearances at the restaurant with his retinue of thugs. His oafish behavior causes frequent confrontations with the staff and his own customers, whose patronage he loses, but whose money he seems not to miss.
Forced to accompany Spica is his reluctant, well-bred wife, Georgina, who soon catches the eye of a quiet regular at the restaurant, bookshop owner Michael. Under her husband's nose, Georgina carries on an affair with Michael with the help of the restaurant staff. Ultimately Spica learns of the affair, forcing Georgina to hide out at Michael's book depository. Boarst sends food to Georgina through his young employee Pup, a boy soprano who sings while working. Spica tortures the boy before finding the bookstore's location written in a book the boy is carrying. Spica's men storm Michael's bookshop while Georgina is visiting the boy in hospital. They torture Michael to death by force-feeding him pages from his books. Georgina discovers his body when she returns.
Overcome with rage and grief, she begs Boarst to cook Michael's body, and he eventually complies. Together with all the people that Spica wronged throughout the film, Georgina confronts her husband finally at the restaurant and forces him at gunpoint to eat a mouthful of Michael's cooked body. Spica obeys, gagging. Georgina then shoots him in the head, calling him a cannibal.
Cast[edit]
Richard Bohringer as Richard Boarst, "The Cook": The head chef of "Le Hollandais". He resents Albert Spica, who has taken control of the restaurant.
Michael Gambon as Albert Spica, "The Thief": A violent gangster and owner of "Le Hollandais", with pretensions of being a gourmet, but his coarse and violent behavior wreaks destruction on everyone around him.
Helen Mirren as Georgina Spica, "The Wife": The sophisticated and battered wife of Albert Spica, from whom she has unsuccessfully tried to escape.
Alan Howard as Michael, "The Lover": An erudite bookshop owner who dines at "Le Hollandais" every night while reading a book. He carries on a doomed affair with Georgina.
Tim Roth as Mitchel, a dim-witted goon in Spica's gang.
Ciarán Hinds as Cory, a pony-tailed pimp who is ejected from Spica's gang after he protests Spica's brutal treatment of his girls.
Gary Olsen as Spangler, a brutal member of Spica's gang.
Ewan Stewart as Harris, a less brutal member of Spica's gang.
Roger Ashton-Griffiths as Turpin, the bespectacled book-keeper in Spica's gang.
Liz Smith as Grace, Spica's mother, somnolent and no more suited to the enjoyment of fine dining than her son.
Ian Dury as Terry Fitch, in a rare acting appearance, as a rival gangster.
Diane Langton as May Fitch, Terry's wife.
Paul Russell as Pup, a kitchen boy who brings food to Georgina and Michael while they are in hiding at Michael's bookshop. He is a boy soprano who sings while washing dishes.
Emer Gillespie as Patricia, one of Cory's luckless girls who tells Spica about his wife's affair.
Ron Cook as Mews, a bespectacled member of Spica's gang.
Alex Kingston as Adele, a red dressed waitress at the restaurant.
Roger Lloyd-Pack as Geoff, a fellow gangster and diner.
Bob Goody as Starkie, a member of Spica's gang.
Production[edit]
Writing[edit]
Peter Greenaway has said that the Jacobean play 'Tis Pity She's a Whore provided him with the main template for his screenplay.[3]
Music[edit]
Michael Nyman's score prominently incorporated his 1985 composition, Memorial.
Design[edit]
Jean-Paul Gaultier designed the costumes. Italian chef Giorgio Locatelli prepared the food used as props.
Release[edit]
Versions[edit]
The film's original running time was 124 minutes. Due to the content, the MPAA gave Miramax a choice of either an X rating or go unrated (adults only) for theatrical release. Unrated was chosen in light of the X rating being more associated with pornographic films. Two versions of the film were released on VHS in the 1990s. One was an R-rated cut running 95 minutes (mainly for large video store chains); the other was the original version.
Critical reception[edit]
The film received largely positive reviews from critics. On Rotten Tomatoes, it currently holds a 90% score based on 39 reviews, with an average rating of 7.4/10. The site's consensus states: "This romantic crime drama may not be to everyone's taste, but The Cook, the Thief, His Wife & Her Lover is an audacious, powerful film."[4] Roger Ebert of the Chicago Sun-Times gave the film four out of four stars,[5] noting that the film's raw emotion and violent interpersonal conflict was a departure from Greenaway's typically cerebral and intellectual films.
Soundtrack[edit]
Main article: The Cook, the Thief, His Wife & Her Lover (soundtrack)
The Cook, the Thief, His Wife & Her Lover is the twelfth album release by Michael Nyman and the ninth to feature the Michael Nyman Band. The album includes the first commercially released recording of "Memorial".
There is some music not included on the soundtrack album: the love theme for Michael and Georgina, which is "Fish Beach" from Drowning by Numbers, the song performed as a show in the restaurant, sung by actress and singer Flavia Brilli, or a doubly pulsed variation of "Memorial" that occurs about halfway through the film. Edits of "Memorial" appear throughout the film, with the entire twelve-minute movement accompanying the final scene and end credits, but one variation is uniquely created for the film.
References[edit]
Jump up ^ "THE COOK, THE THIEF, HIS WIFE & HER LOVER (18)". British Board of Film Classification. 14 September 1989. Retrieved 27 September 2013.
Jump up ^ The Cook, the Thief, His Wife & Her Lover at Box Office Mojo
Jump up ^ Vernon Gras and Marguerite Gras (eds.), Peter Greenaway: Interviews, Jackson, MS, University Press of Mississippi, 2000; p. 69
Jump up ^ "The Cook, the Thief, His Wife & Her Lover (1989)". Rotten Tomatoes. Flixster. Retrieved 30 January 2016.
Jump up ^ "The Cook, the Thief, His Wife, and Her Lover Movie Review (1999)". Roger Ebert. 1 January 1999. Retrieved 30 January 2016.
External links[edit]
Wikiquote has quotations related to: The Cook, the Thief, His Wife & Her Lover
Official website
The Cook, the Thief, His Wife & Her Lover on IMDb
The Cook, the Thief, His Wife & Her Lover at Box Office Mojo
The Cook, the Thief, His Wife & Her Lover at Rotten Tomatoes
[hide]
v
t
e
Films directed by Peter Greenaway
Vertical Features Remake (1978)
The Falls (1980)
The Draughtsman's Contract (1982)
The Coastline (1983)
A Zed & Two Noughts (1985)
The Belly of an Architect (1987)
Drowning by Numbers (1988)
The Cook, the Thief, His Wife & Her Lover (1989)
A TV Dante (1989)
Prospero's Books (1991)
The Baby of Mâcon (1993)
Stairs 1 Geneva (1994)
The Pillow Book (1996)
8½ Women (1999)
The Tulse Luper Suitcases (2003)
Nightwatching (2007)
Rembrandt's J'Accuse (2008)
Castle Amerongen (2011)
Goltzius and the Pelican Company (2012)
Eisenstein in Guanajuato (2015)
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value: Готвачът, крадецът, неговата жена и нейният любовник – Bulgarian

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value: Der Koch, der Dieb, seine Frau und ihr Liebhaber – German

value: El cocinero, el ladrón, su mujer y su amante – Spanish

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value: Le Cuisinier, le voleur, sa femme et son amant – French

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value: Il cuoco, il ladro, sua moglie e l'amante – Italian

value: The Cook, the Thief, His Wife and Her Lover – Dutch

value: コックと泥棒、その妻と愛人 – Japanese

value: Kokken, tyven, hans kone og hennes elsker – Norwegian

value: Kucharz, złodziej, jego żona i jej kochanek – Polish

value: The Cook, the Thief, His Wife & Her Lover – Portuguese

value: Повар, вор, его жена и её любовник – Russian

value: The Cook, the Thief, His Wife & Her Lover – Simple English

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text:
Angle
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Not to be confused with Angel.
This article is about angles in geometry. For other uses, see Angle (disambiguation).
Basic angle types
Types of angles
2D angles
Right
Interior
Exterior
2D angle pairs
Adjacent
Vertical
Complementary
Supplementary
Transversal
3D angles
Dihedral
An angle formed by two rays emanating from a vertex.
In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.[1] Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.
Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.
The word angle comes from the Latin word angulus, meaning "corner"; cognate words are the Greek ἀγκύλος (ankylοs), meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".[2]
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.[3]
Contents
[hide]
1 Identifying angles
2 Types of angles
2.1 Individual angles
2.2 Equivalence angle pairs
2.3 Vertical and adjacent angle pairs
2.4 Combining angle pairs
2.5 Polygon related angles
2.6 Plane related angles
3 Measuring angles
3.1 Angle addition postulate
3.2 Units
3.3 Positive and negative angles
3.4 Alternative ways of measuring the size of an angle
3.5 Astronomical approximations
4 Angles between curves
5 Bisecting and trisecting angles
6 Dot product and generalisations
6.1 Inner product
6.2 Angles between subspaces
6.3 Angles in Riemannian geometry
6.4 Hyperbolic angle
7 Angles in geography and astronomy
8 See also
9 Notes
10 References
11 External links
Identifying angles[edit]
In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) to serve as variables standing for the size of some angle. (To avoid confusion with its other meaning, the symbol π is typically not used for this purpose.) Lower case Roman letters (a, b, c, . . . ) are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples.
In geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC (i.e. the lines from point A to point B and point A to point C) is denoted ∠BAC (in Unicode U+2220 ∠ ANGLE) or B A C ^ {\displaystyle {\widehat {\rm {BAC}}}} . Sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex ("angle A").
Potentially, an angle denoted, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign (see Positive and negative angles). However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, and no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to C, and ∠CAB to the anticlockwise (positive) angle from C to B.
Types of angles[edit]
"Oblique angle" redirects here. For the cinematographic technique, see Dutch angle.
Individual angles[edit]
Right angle.
Reflex angle.
Acute (a), obtuse (b), and straight (c) angles. The acute and obtuse angles are also known as oblique angles.
Angles smaller than a right angle (less than 90°) are called acute angles ("acute" meaning "sharp").
An angle equal to 1/4 turn (90° or π/2 radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular.
Angles larger than a right angle and smaller than a straight angle (between 90° and 180°) are called obtuse angles ("obtuse" meaning "blunt").
An angle equal to 1/2 turn (180° or π radians) is called a straight angle.
Angles larger than a straight angle but less than 1 turn (between 180° and 360°) are called reflex angles.
An angle equal to 1 turn (360° or 2π radians) is called a full angle, complete angle, or a perigon.
Angles that are not right angles or a multiple of a right angle are called oblique angles.
The names, intervals, and measured units are shown in a table below:
Name acute right angle obtuse straight reflex perigon
Units
Interval
Turns (0, 1/4) 1/4 (1/4, 1/2) 1/2 (1/2, 1) 1
Radians (0, 1/2π) 1/2π (1/2π, π) π (π, 2π) 2π
Degrees (0, 90)° 90° (90, 180)° 180° (180, 360)° 360°
Gons (0, 100)g 100g (100, 200)g 200g (200, 400)g 400g
Equivalence angle pairs[edit]
Angles that have the same measure (i.e. the same magnitude) are said to be equal or congruent. An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g. all right angles are equal in measure).
Two angles which share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles.
A reference angle is the acute version of any angle determined by repeatedly subtracting or adding straight angle (1/2 turn, 180°, or π radians), to the results as necessary, until the magnitude of result is an acute angle, a value between 0 and 1/4 turn, 90°, or π/2 radians. For example, an angle of 30 degrees has a reference angle of 30 degrees, and an angle of 150 degrees also has a reference angle of 30 degrees (180 – 150). An angle of 750 degrees has a reference angle of 30 degrees (750 – 720).[4]
Vertical and adjacent angle pairs[edit]
Angles A and B are a pair of vertical angles; angles C and D are a pair of vertical angles.
When two straight lines intersect at a point, four angles are formed. Pairwise these angles are named according to their location relative to each other.
A pair of angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles or vertically opposite angles. They are abbreviated as vert. opp. ∠s.[5]
The equality of vertically opposite angles is called the vertical angle theorem. Eudemus of Rhodes attributed the proof to Thales of Miletus.[6][7] The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical Note,[7] when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure the vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: all straight angles are equal, equals added to equals are equal, and equals subtracted from equals are equal.
In the figure, assume the measure of Angle A = x. When two adjacent angles form a straight line, they are supplementary. Therefore, the measure of Angle C = 180 − x. Similarly, the measure of Angle D = 180 − x. Both Angle C and Angle D have measures equal to 180 − x and are congruent. Since Angle B is supplementary to both Angles C and D, either of these angle measures may be used to determine the measure of Angle B. Using the measure of either Angle C or Angle D we find the measure of Angle B = 180 − (180 − x) = 180 − 180 + x = x. Therefore, both Angle A and Angle B have measures equal to x and are equal in measure.
Angles A and B are adjacent.
Adjacent angles, often abbreviated as adj. ∠s, are angles that share a common vertex and edge but do not share any interior points. In other words, they are angles that are side by side, or adjacent, sharing an "arm". Adjacent angles which sum to a right angle, straight angle or full angle are special and are respectively called complementary, supplementary and explementary angles (see "Combine angle pairs" below).
A transversal is a line that intersects a pair of (often parallel) lines and is associated with alternate interior angles, corresponding angles, interior angles, and exterior angles.[8]
Combining angle pairs[edit]
There are three special angle pairs which involve the summation of angles:
Complementary angles are angle pairs whose measures sum to one right angle (1/4 turn, 90°, or π/2 radians). If the two complementary angles are adjacent their non-shared sides form a right angle. In Euclidean geometry, the two acute angles in a right triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees.
The adjective complementary is from Latin complementum, associated with the verb complere, "to fill up". An acute angle is "filled up" by its complement to form a right angle.
The difference between an angle and a right angle is termed the complement of the angle.[9]
If angles A and B are complementary, the following relationships hold:
sin 2  A + sin 2  B = 1 cos 2  A + cos 2  B = 1 tan  A = cot  B sec  A = csc  B {\displaystyle {\begin{aligned}&\sin ^{2}A+\sin ^{2}B=1&&\cos ^{2}A+\cos ^{2}B=1\\[3pt]&\tan A=\cot B&&\sec A=\csc B\end{aligned}}}
(The tangent of an angle equals the cotangent of its complement and its secant equals the cosecant of its complement.)
The prefix "co-" in the names of some trigonometric ratios refers to the word "complementary".
Two angles that sum to a straight angle (1/2 turn, 180°, or π radians) are called supplementary angles.
If the two supplementary angles are adjacent (i.e. have a common vertex and share just one side), their non-shared sides form a straight line. Such angles are called a linear pair of angles.[10] However, supplementary angles do not have to be on the same line, and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.
If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary.
The sines of supplementary angles are equal. Their cosines and tangents (unless undefined) are equal in magnitude but have opposite signs.
In Euclidean geometry, any sum of two angles in a triangle is supplementary to the third, because the sum of internal angles of a triangle is a straight angle.
Two angles that sum to a complete angle (1 turn, 360°, or 2π radians) are called explementary angles or conjugate angles.
The difference between an angle and a complete angle is termed the explement of the angle or conjugate of an angle.
The complementary angles a and b (b is the complement of a, and a is the complement of b).
A reflex angle and its conjugate are explementary angles, and their sum is a complete angle.
The angles a and b are supplementary angles.
Polygon related angles[edit]
Internal and external angles.
An angle that is part of a simple polygon is called an interior angle if it lies on the inside of that simple polygon. A simple concave polygon has at least one interior angle that is a reflex angle.
In Euclidean geometry, the measures of the interior angles of a triangle add up to π radians, 180°, or 1/2 turn; the measures of the interior angles of a simple convex quadrilateral add up to 2π radians, 360°, or 1 turn. In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2)π radians, or 180(n − 2) degrees, (2n − 4) right angles, or (n/2 − 1) turn.
The supplement of an interior angle is called an exterior angle, that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical angles and hence are equal. An exterior angle measures the amount of rotation one has to make at a vertex to trace out the polygon.[11] If the corresponding interior angle is a reflex angle, the exterior angle should be considered negative. Even in a non-simple polygon it may be possible to define the exterior angle, but one will have to pick an orientation of the plane (or surface) to decide the sign of the exterior angle measure.
In Euclidean geometry, the sum of the exterior angles of a simple convex polygon will be one full turn (360°). The exterior angle here could be called a supplementary exterior angle. Exterior angles are commonly used in Logo Turtle Geometry when drawing regular polygons.
In a triangle, the bisectors of two exterior angles and the bisector of the other interior angle are concurrent (meet at a single point).[12]:p. 149
In a triangle, three intersection points, each of an external angle bisector with the opposite extended side, are collinear.[12]:p. 149
In a triangle, three intersection points, two of them between an interior angle bisector and the opposite side, and the third between the other exterior angle bisector and the opposite side extended, are collinear.[12]:p. 149
Some authors use the name exterior angle of a simple polygon to simply mean the explement exterior angle (not supplement!) of the interior angle.[13] This conflicts with the above usage.
Plane related angles[edit]
The angle between two planes (such as two adjacent faces of a polyhedron) is called a dihedral angle.[9] It may be defined as the acute angle between two lines normal to the planes.
The angle between a plane and an intersecting straight line is equal to ninety degrees minus the angle between the intersecting line and the line that goes through the point of intersection and is normal to the plane.
Measuring angles[edit]
The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be equal or congruent or equal in measure.
In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the cumulative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.
The measure of angle θ (in radians) is the quotient of s and r.
In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The ratio of the length s of the arc by the radius r of the circle is the measure of the angle in radians.
The measure of the angle in another angular unit is then obtained by multiplying its measure in radians by the scaling factor k/2π, where k is the measure of a complete turn in the chosen unit (for example 360 for degrees or 400 for gradians):
θ = k s 2 π r . {\displaystyle \theta =k{\frac {s}{2\pi r}}.}
The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered. (Proof. The formula above can be rewritten as k = θr/s. One turn, for which θ = n units, corresponds to an arc equal in length to the circle's circumference, which is 2πr, so s = 2πr. Substituting n for θ and 2πr for s in the formula, results in k = nr/2πr = n/2π.) [Note 1]
Angle addition postulate[edit]
The angle addition postulate states that if B is in the interior of angle AOC, then
m ∠ A O C = m ∠ A O B + m ∠ B O C {\displaystyle m\angle AOC=m\angle AOB+m\angle BOC}
The measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC. In this postulate it does not matter in which unit the angle is measured as long as each angle is measured in the same unit.
Units[edit]
See also: Angular unit
Units used to represent angles are listed below in descending magnitude order. Of these units, the degree and the radian are by far the most commonly used. Angles expressed in radians are dimensionless for the purposes of dimensional analysis.
Most units of angular measurement are defined such that one turn (i.e. one full circle) is equal to n units, for some whole number n. The two exceptions are the radian and the diameter part.
Turn (n = 1)
The turn, also cycle, full circle, revolution, and rotation, is complete circular movement or measure (as to return to the same point) with circle or ellipse. A turn is abbreviated τ, cyc, rev, or rot depending on the application, but in the acronym rpm (revolutions per minute), just r is used. A turn of n units is obtained by setting k = 1/2π in the formula above. The equivalence of 1 turn is 360°, 2π rad, 400 grad, and 4 right angles. The symbol τ can also be used as a mathematical constant to represent 2π radians. Used in this way (k = τ/2π) allows for radians to be expressed as a fraction of a turn. For example, half a turn is τ/2 = π.
Quadrant (n = 4)
The quadrant is 1/4 of a turn, i.e. a right angle. It is the unit used in Euclid's Elements. 1 quad. = 90° = π/2 rad = 1/4 turn = 100 grad. In German the symbol ∟ has been used to denote a quadrant.
Sextant (n = 6)
The sextant (angle of the equilateral triangle) is 1/6 of a turn. It was the unit used by the Babylonians,[15] and is especially easy to construct with ruler and compasses. The degree, minute of arc and second of arc are sexagesimal subunits of the Babylonian unit. 1 Babylonian unit = 60° = π/3 rad ≈ 1.047197551 rad.
θ = s/r rad = 1 rad.
Radian (n = 2π = 6.283 . . . )
The radian is the angle subtended by an arc of a circle that has the same length as the circle's radius. The case of radian for the formula given earlier, a radian of n = 2π units is obtained by setting k = 2π/2π = 1. One turn is 2π radians, and one radian is 180/π degrees, or about 57.2958 degrees. The radian is abbreviated rad, though this symbol is often omitted in mathematical texts, where radians are assumed unless specified otherwise. When radians are used angles are considered as dimensionless. The radian is used in virtually all mathematical work beyond simple practical geometry, due, for example, to the pleasing and "natural" properties that the trigonometric functions display when their arguments are in radians. The radian is the (derived) unit of angular measurement in the SI system.
Clock position (n = 12)
A clock position is the relative direction of an object described using the analogy of a 12-hour clock. One imagines a clock face lying either upright or flat in front of oneself, and identifies the twelve hour markings with the directions in which they point.
Hour angle (n = 24)
The astronomical hour angle is 1/24 of a turn. As this system is amenable to measuring objects that cycle once per day (such as the relative position of stars), the sexagesimal subunits are called minute of time and second of time. These are distinct from, and 15 times larger than, minutes and seconds of arc. 1 hour = 15° = π/12 rad = 1/6 quad. = 1/24 turn = 16 2/3 grad.
(Compass) point or wind (n = 32)
The point, used in navigation, is 1/32 of a turn. 1 point = 1/8 of a right angle = 11.25° = 12.5 grad. Each point is subdivided in four quarter-points so that 1 turn equals 128 quarter-points.
Hexacontade (n = 60)
The hexacontade is a unit of 6° that Eratosthenes used, so that a whole turn was divided into 60 units.
Pechus (n = 144–180)
–The pechus was a Babylonian unit equal to about 2° or 2 1/2°.
Binary degree (n = 256)
The binary degree, also known as the binary radian (or brad), is 1/256 of a turn.[16] The binary degree is used in computing so that an angle can be efficiently represented in a single byte (albeit to limited precision). Other measures of angle used in computing may be based on dividing one whole turn into 2n equal parts for other values of n.[17]
Degree (n = 360)
The degree, denoted by a small superscript circle (°), is 1/360 of a turn, so one turn is 360°. The case of degrees for the formula given earlier, a degree of n = 360° units is obtained by setting k = 360°/2π. One advantage of this old sexagesimal subunit is that many angles common in simple geometry are measured as a whole number of degrees. Fractions of a degree may be written in normal decimal notation (e.g. 3.5° for three and a half degrees), but the "minute" and "second" sexagesimal subunits of the "degree-minute-second" system are also in use, especially for geographical coordinates and in astronomy and ballistics.
Diameter part (n = 376.99 . . . )
The diameter part (occasionally used in Islamic mathematics) is 1/60 radian. One "diameter part" is approximately 0.95493°. There are about 376.991 diameter parts per turn.
Grad (n = 400)
The grad, also called grade, gradian, or gon, is 1/400 of a turn, so a right angle is 100 grads. It is a decimal subunit of the quadrant. A kilometre was historically defined as a centi-grad of arc along a great circle of the Earth, so the kilometer is the decimal analog to the sexagesimal nautical mile. The grad is used mostly in triangulation.
Milliradian
The milliradian (mil or mrad) is defined as a thousandth of a radian, which means that a rotation of one turn consists of 2000π mil (or approximately 6283.185... mil), and almost all scope sights for firearms are calibrated to this definition. In addition there are three other derived definitions used for artillery and navigation which are approximately equal to a milliradian. Under these three other definitions one turn makes up for exactly 6000, 6300 or 6400 mils, which equals spanning the range from 0.05625 to 0.06 degrees (3.375 to 3.6 minutes). In comparison, the true milliradian is approximately 0.05729578... degrees (3.43775... minutes). One "NATO mil" is defined as 1/6400 of a circle. Just like with the true milliradian, each of the other definitions exploits the mil's handby property of subtensions, i.e. that the value of one milliradian approximately equals the angle subtended by a width of 1 meter as seen from 1 km away (2π/6400 = 0.0009817… ≈ 1/1000).
Minute of arc (n = 21,600)
The minute of arc (or MOA, arcminute, or just minute) is 1/60 of a degree = 1/21,600 turn. It is denoted by a single prime ( ′ ). For example, 3° 30′ is equal to 3 × 60 + 30 = 210 minutes or 3 + 30/60 = 3.5 degrees. A mixed format with decimal fractions is also sometimes used, e.g. 3° 5.72′ = 3 + 5.72/60 degrees. A nautical mile was historically defined as a minute of arc along a great circle of the Earth.
Second of arc (n = 1,296,000)
The second of arc (or arcsecond, or just second) is 1/60 of a minute of arc and 1/3600 of a degree. It is denoted by a double prime ( ″ ). For example, 3° 7′ 30″ is equal to 3 + 7/60 + 30/3600 degrees, or 3.125 degrees.
Positive and negative angles[edit]
Although the definition of the measurement of an angle does not support the concept of a negative angle, it is frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference.
In a two-dimensional Cartesian coordinate system, an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis, while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns. With positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise and negative rotations are clockwise.
In many contexts, an angle of −θ is effectively equivalent to an angle of "one full turn minus θ". For example, an orientation represented as −45° is effectively equivalent to an orientation represented as 360° − 45° or 315°. Although the final position is the same, a physical rotation (movement) of −45° is not the same as a rotation of 315° (for example, the rotation of a person holding a broom resting on a dusty floor would leave visually different traces of swept regions on the floor).
In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined relative to some reference, which is typically a vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.
In navigation, bearings are measured relative to north. By convention, viewed from above, bearing angles are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so a north-west orientation corresponds to a bearing of 315°.
Alternative ways of measuring the size of an angle[edit]
There are several alternatives to measuring the size of an angle by the angle of rotation. The grade of a slope, or gradient is equal to the tangent of the angle, or sometimes (rarely) the sine. A gradient is often expressed as a percentage. For very small values (less than 5%), the grade of a slope is approximately the measure of the angle in radians.
In rational geometry the spread between two lines is defined as the square of the sine of the angle between the lines. As the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.
Astronomical approximations[edit]
Astronomers measure angular separation of objects in degrees from their point of observation.
0.5° is approximately the width of the sun or moon.
1° is approximately the width of a little finger at arm's length.
10° is approximately the width of a closed fist at arm's length.
20° is approximately the width of a handspan at arm's length.
These measurements clearly depend on the individual subject, and the above should be treated as rough rule of thumb approximations only.
Angles between curves[edit]
The angle between the two curves at P is defined as the angle between the tangents A and B at P.
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. Various names (now rarely, if ever, used) have been given to particular cases:—amphicyrtic (Gr. ἀμφί, on both sides, κυρτός, convex) or cissoidal (Gr. κισσός, ivy), biconvex; xystroidal or sistroidal (Gr. ξυστρίς, a tool for scraping), concavo-convex; amphicoelic (Gr. κοίλη, a hollow) or angulus lunularis, biconcave.[18]
Bisecting and trisecting angles[edit]
Main articles: Bisection § Angle bisector, and Angle trisection
The ancient Greek mathematicians knew how to bisect an angle (divide it into two angles of equal measure) using only a compass and straightedge, but could only trisect certain angles. In 1837 Pierre Wantzel showed that for most angles this construction cannot be performed.
Dot product and generalisations[edit]
In the Euclidean space, the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula
u ⋅ v = cos  ( θ ) ‖ u ‖ ‖ v ‖ . {\displaystyle \mathbf {u} \cdot \mathbf {v} =\cos(\theta )\left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.
Inner product[edit]
To define angles in an abstract real inner product space, we replace the Euclidean dot product ( · ) by the inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } , i.e.
⟨ u , v ⟩ = cos  ( θ ) ‖ u ‖ ‖ v ‖ . {\displaystyle \langle \mathbf {u} ,\mathbf {v} \rangle =\cos(\theta )\ \left\|\mathbf {u} \right\|\ \left\|\mathbf {v} \right\|.}
In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with
Re  ( ⟨ u , v ⟩ ) = cos  ( θ ) ‖ u ‖ ‖ v ‖ . {\displaystyle \operatorname {Re} \left(\langle \mathbf {u} ,\mathbf {v} \rangle \right)=\cos(\theta )\ \left\|\mathbf {u} \right\|\left\|\mathbf {v} \right\|.}
or, more commonly, using the absolute value, with
| ⟨ u , v ⟩ | = | cos  ( θ ) | ‖ u ‖ ‖ v ‖ . {\displaystyle \left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|=|\cos(\theta )|\ \left\|\mathbf {u} \right\|\ \left\|\mathbf {v} \right\|.}
The latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces span  ( u ) {\displaystyle \operatorname {span} (\mathbf {u} )} and span  ( v ) {\displaystyle \operatorname {span} (\mathbf {v} )} spanned by the vectors u {\displaystyle \mathbf {u} } and v {\displaystyle \mathbf {v} } correspondingly.
Angles between subspaces[edit]
The definition of the angle between one-dimensional subspaces span  ( u ) {\displaystyle \operatorname {span} (\mathbf {u} )} and span  ( v ) {\displaystyle \operatorname {span} (\mathbf {v} )} given by
| ⟨ u , v ⟩ | = | cos  ( θ ) | ‖ u ‖ ‖ v ‖ {\displaystyle \left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|=|\cos(\theta )|\left\|\mathbf {u} \right\|\ \left\|\mathbf {v} \right\|}
in a Hilbert space can be extended to subspaces of any finite dimensions. Given two subspaces U {\displaystyle {\mathcal {U}}} , W {\displaystyle {\mathcal {W}}} with dim  ( U ) := k ≤ dim  ( W ) := l {\displaystyle \dim({\mathcal {U}}):=k\leq \dim({\mathcal {W}}):=l} , this leads to a definition of k {\displaystyle k} angles called canonical or principal angles between subspaces.
Angles in Riemannian geometry[edit]
In Riemannian geometry, the metric tensor is used to define the angle between two tangents. Where U and V are tangent vectors and gij are the components of the metric tensor G,
cos  θ = g i j U i V j | g i j U i U j | | g i j V i V j | . {\displaystyle \cos \theta ={\frac {g_{ij}U^{i}V^{j}}{\sqrt {\left|g_{ij}U^{i}U^{j}\right|\left|g_{ij}V^{i}V^{j}\right|}}}.}
Hyperbolic angle[edit]
A hyperbolic angle is an argument of a hyperbolic function just as the circular angle is the argument of a circular function. The comparison can be visualized as the size of the openings of a hyperbolic sector and a circular sector since the areas of these sectors correspond to the angle magnitudes in each case. Unlike the circular angle, the hyperbolic angle is unbounded. When the circular and hyperbolic functions are viewed as infinite series in their angle argument, the circular ones are just alternating series forms of the hyperbolic functions. This weaving of the two types of angle and function was explained by Leonhard Euler in Introduction to the Analysis of the Infinite.
Angles in geography and astronomy[edit]
In geography, the location of any point on the Earth can be identified using a geographic coordinate system. This system specifies the latitude and longitude of any location in terms of angles subtended at the centre of the Earth, using the equator and (usually) the Greenwich meridian as references.
In astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the centre of the Earth, each intersecting one of the stars. The angle between those lines can be measured, and is the angular separation between the two stars.
In both geography and astronomy, a sighting direction can be specified in terms of a vertical angle such as altitude /elevation with respect to the horizon as well as the azimuth with respect to north.
Astronomers also measure the apparent size of objects as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5°, when viewed from Earth. One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can be used to convert such an angular measurement into a distance/size ratio.
See also[edit]
Angle bisector
Angular velocity
Argument (complex analysis)
Astrological aspect
Central angle
Clock angle problem
Dihedral angle
Exterior angle theorem
Great circle distance
Inscribed angle
Irrational angle
Phase angle
Protractor
Solid angle for a concept of angle in three dimensions.
Spherical angle
Transcendent angle
Trisection
Zenith angle
Notes[edit]
Jump up ^ This approach requires however an additional proof that the measure of the angle does not change with changing radius r, in addition to the issue of "measurement units chosen." A smoother approach is to measure the angle by the length of the corresponding unit circle arc. Here "unit" can be chosen to be dimensionless in the sense that it is the real number 1 associated with the unit segment on the real line. See R. Dimitric for instance.[14]
Jump up ^ Sidorov 2001
Jump up ^ Slocum 2007
Jump up ^ Chisholm 1911; Heiberg 1908, pp. 177–178
Jump up ^ "Mathwords: Reference Angle". www.mathwords.com. Archived from the original on 23 October 2017. Retrieved 26 April 2018.
Jump up ^ Wong & Wong 2009, pp. 161–163
Jump up ^ Euclid (c. 300 BC). The Elements. Check date values in: |date= (help) Proposition I:13.
^ Jump up to: a b Shute, Shirk & Porter 1960, pp. 25–27.
Jump up ^ Jacobs 1974, p. 255.
^ Jump up to: a b Chisholm 1911
Jump up ^ Jacobs 1974, p. 97.
Jump up ^ Henderson & Taimina 2005, p. 104.
^ Jump up to: a b c Johnson, Roger A. Advanced Euclidean Geometry, Dover Publications, 2007.
Jump up ^ D. Zwillinger, ed. (1995), CRC Standard Mathematical Tables and Formulae, Boca Raton, FL: CRC Press, p. 270 as cited in Weisstein, Eric W. "Exterior Angle". MathWorld.
Jump up ^ R. Dimitric: On angles and angle measurements Archived 2013-09-27 at the Wayback Machine.
Jump up ^ J.H. Jeans (1947), The Growth of Physical Science, p. 7; Francis Dominic Murnaghan (1946), Analytic Geometry, p. 2
Jump up ^ ooPIC Programmer's Guide (archived) oopic.com
Jump up ^ Angles, integers, and modulo arithmetic Archived 2011-06-30 at Wikiwix Shawn Hargreaves blogs.msdn.com
Jump up ^ Chisholm 1911; Heiberg 1908, p. 178
References[edit]
Henderson, David W.; Taimina, Daina (2005), Experiencing Geometry / Euclidean and Non-Euclidean with History (3rd ed.), Pearson Prentice Hall, p. 104, ISBN 9780131437487
Heiberg, Johan Ludvig (1908), Heath, T. L., ed., Euclid, The Thirteen Books of Euclid's Elements, 1, Cambridge: Cambridge University Press .
Sidorov, L.A. (2001) [1994], "Angle", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Jacobs, Harold R. (1974), Geometry, W.H. Freeman, pp. 97, 255, ISBN 0-7167-0456-0
Slocum, Jonathan (2007), Preliminary Indo-European lexicon — Pokorny PIE data, University of Texas research department: linguistics research center, retrieved 2 Feb 2010
Shute, William G.; Shirk, William W.; Porter, George F. (1960), Plane and Solid Geometry, American Book Company, pp. 25–27
Wong, Tak-wah; Wong, Ming-sim (2009), "Angles in Intersecting and Parallel Lines", New Century Mathematics, 1B (1 ed.), Hong Kong: Oxford University Press, pp. 161–163, ISBN 978-0-19-800177-5
Attribution
This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911), "Angle", Encyclopædia Britannica, 2 (11th ed.), Cambridge University Press, p. 14
External links[edit]
Wikimedia Commons has media related to Angles (geometry).
"Angle", Encyclopædia Britannica, 2 (9th ed.), 1878, pp. 29–30
Proximity construction of an angle in decimal degrees with the third intercept theorem
Angle Bisectors in a Quadrilateral at cut-the-knot
Constructing a triangle from its angle bisectors at cut-the-knot
Various angle constructions with compass and straightedge
Complementary Angles animated demonstration. With interactive applet
Supplementary Angles animated demonstration. With interactive applet
Angle definition pages with interactive applets that are also useful in a classroom setting. Math Open Reference
Construction of an angle[permanent dead link] Site geometry
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Co (function prefix)

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Interior angle

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Exterior angle

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Orientation (mathematics)

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Plane (mathematics)

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Circular arc

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Compasses (drafting)

value: {\displaystyle \theta =k{\frac {s}{2\pi r}}.}

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Quadrant (circle)

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Binary degree

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Binary radian

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Grad (angle)

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Minute of arc

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Second of arc

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Vector (geometric)

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Tangent (trigonometric function)

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Rational geometry

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Spread (rational trigonometry)

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Compass and straightedge

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Principal angles

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Astronomical coordinate systems

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Angular separation

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Vertical angle

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Altitude angle

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Elevation angle

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Small-angle formula

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Great circle distance

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Irrational angle

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Transcendent angle

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Zenith angle

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Cambridge, England

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value: Encyclopædia Britannica Eleventh Edition

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text:
Arizona Public Service
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Arizona Public Service
Type
Public
Industry
Electricity generation & distribution
Founded
1885
Headquarters
Phoenix, Arizona, United States
Products
Electricity
Parent
Pinnacle West Capital Corporation (formerly named AZP Group)
Website
www.aps.com
Arizona Public Service Company is the largest electric utility in Arizona, United States and the principal subsidiary of publicly traded S&P 500 member Pinnacle West Capital Corporation (NYSE: PNW), which in turn had been formerly named AZP Group, when Arizona Public Service reorganized as that holding company in 1985.
With 4,000 MW of generating capacity, APS serves more than one million customers in 11 counties throughout most of the state, but mainly concentrated in northern and central Arizona.[1] APS is one of the two major suppliers of electricity to the Phoenix metropolitan area (the other being Salt River Project).[2]
APS is regulated by the Arizona Corporation Commission (ACC), the state agency that, by mandate of Article 15, Section 2 of the state's constitution, regulates energy utilities in Arizona, with the notable exception of SRP, the rural electrical districts, and the City of Mesa electric utility serving Downtown Mesa and the immediate vicinity (with the rest of the city being served by SRP).
The holding company, Pinnacle West Capital, through its APS utility sells wholesale and retail power to the wider western United States and also provides energy-related services. Through another major subsidiary, Pinnacle West also developed and managed real estate in Arizona.[1] Pinnacle West left the real estate business in 2010.[3]
The utility company also operates three nuclear reactors. Its Palo Verde Nuclear Generating Station in Arizona, the largest nuclear plant in the U.S., came under scrutiny by the Nuclear Regulatory Commission in 2005 when operational problems began to cause prolonged outages.[1]
Contents
[hide]
1 History
1.1 Pinnacle West Capital
2 Service territory
3 Major power outage
3.1 Blackout settlement
4 Solar Generation
5 See also
6 References
7 External links
History[edit]
In 1884, the Phoenix Light and Fuel Company was formed to provide electricity and heat to the people of the three-year-old town of Phoenix. It changed its name to Pacific Gas and Electric in 1906 and to Central Arizona Light and Power in 1920. Also in 1920, it paid a dividend, and continued the annual dividend without interruption for the next 69 years.
The company became a subsidiary of the giant conglomerate American Power and Light in 1925, but became an independent company once again in 1945. In 1949, it merged with Northern Arizona Power and Light. In 1952, it merged with Arizona Edison and changed its name to Arizona Public Service.[4]
The stock doubled in price through the long bear market of the 1970s, while paying a 10% dividend yield. By then it had become an electric and natural gas utility fueled 94.4% by coal plants, 5.2% by natural gas, and 0.4% by oil. The company traded its common stock on the New York Stock Exchange, and in 1976, the company issued a preferred stock (formerly NYSE: PR ARP PR) with a 10.5% dividend, callable in 1990.[5]
APS also performed well through the early 1980s recession, reaching peak earnings of over US$255 million in 1983. However, by then the company had accumulated over US$2.1 billion in long-term debt.[5]
In 1982, APS issued another preferred stock (formerly NYSE: PR O ARP PR O) with an 11.9% dividend, callable in 1987. And in 1983, it issued a third preferred stock (formerly NYSE: PR Q ARP PR Q) paying an adjustable rate between 6 and 12%, through 1986.[5]
1984 was a down year for both earnings and the stock price, which at its low that year had lost almost half its value from the 1983 peak.[5]
Pinnacle West Capital[edit]
Pinnacle West Capital Corporation
Type
Public company
Traded as
NYSE: PNW
S&P 500 Component
Industry
Electric utilities
Founded
1985
Headquarters
Phoenix, Arizona, USA
Key people
Donald E. Brandt, Chairman & CEO
Revenue
$3.524 billion US$ (2007)
Operating income
$619 million US$ (2007)
Net income
$307 million US$ (2007)
Number of employees
6,339 (2016)
Website
www.pinnaclewest.com
In February 1985, Arizona Public Service Company reorganized as a holding company, AZP Group Inc., with APS as the leading subsidiary.[6] It traded under the ticker symbol AZP. 1985 earnings reached a new record high at almost US$290 million, and by the end of the year the stock price had doubled from its 1984 low.[5]
In 1987, AZP Group changed its name to Pinnacle West Capital Corporation, and began trading under the new ticker symbol PNW. The utility continued to operate as its principal subsidiary.[6] By then Pinnacle's long-term debt had grown to almost US$2.4 billion. Earnings had declined to US$260 million in 1986, but were recovering by the end 1987. However, the stock price reached an all-time peak that year, which was not surpassed for the next decade, as the company ran into troubles through the early 1990s.[5] In 1986, Pinnacle acquired MeraBank, a savings and loan. It grew to become Arizona's largest thrift, with $6.5 billion in assets. However, the thrift was seized by federal regulators in January 1990, due in part to the deterioration in prices in the Arizona real estate market.[7][8]
By 1990, the company's earnings had fallen to under US$100 million, as it struggled through the 1990-1991 recession, as well as a series of failed attempts to diversify. By 1991, the company was facing a loss of almost US$190 million, and for the first time in over 70 years, it discontinued paying its dividend. The stock price plunged 85% from its 1987 peak, to its lowest level in over twenty years. Its long-term debt by then reached over US$2.5 billion.[5]
However, by 1992, the company returned to profitability, as earnings recovered to over US$150 million. The stock price tripled from its 1991 low by the end of 1993. The company reinstated its dividend that year.[5]
By 1995, Pinnacle West Capital had been added to the S&P MidCap 400 index. That year, earnings surpassed US$200 million again, and by early the next year the stock price began approaching its old 1987 high. Also in 1995, the utility subsidiary Arizona Public Services issued 30-year Monthly Income Debt Securities paying 10%.[5]
Service territory[edit]
APS serves about two-thirds of the Phoenix metropolitan area. It primarily serves downtown and northern Phoenix, as well as a large swath to the north and east of the city. Outside of the Valley, it serves Flagstaff, Prescott, Yuma and Douglas.
Major power outage[edit]
On September 8, 2011 there was a widespread power outage affecting a region spreading west from Yuma, Arizona, to San Diego, California, and affecting parts of Northern Mexico. The outage was the result of 23 events that occurred on five power grids in a span of 11 minutes including the APS North Gila Substation.[9] Federal, regional and local officials are investigating what happened and why the outage cascaded the way it did.[10] Most of the areas affected were served by San Diego Gas & Electric, which saw its entire service area lose power.[10]
The outage appears to have been caused by the actions of an APS employee in the North Gila substation, and it is unknown why safeguards did not keep the outage limited to the Yuma area.[11]
The outage occurred days before the tenth anniversary of the September 11 attacks, and hours before the United States Department of Homeland Security warned of a potential terrorist attack leading up to the anniversary, but the Federal Bureau of Investigation and SDG&E early in their investigations ruled out terrorism. [12]
Blackout settlement[edit]
On July 7, 2014, APS agreed to a $3.25 million settlement with NERC and FERC related to the September 2011 blackout.[13]
Solar Generation[edit]
As of 2016, APS has available one gigawatt of solar generating capacity. Approximately half is generated at large solar power stations and half at small rooftop solar systems.[14]
See also[edit]
Arizona portal
Companies portal
Path 46, also called West of Colorado River, Arizona-California West-of-the-River Path (WOR)
Palo Verde Nuclear Generating Station
Four Corners Generating Station
References[edit]
^ Jump up to: a b c Pinnacle West: The Peak of the Energy Pyramid, SeekingAlpha.com, By Ted Allrich, posted on: November 20, 2006
Jump up ^ "Utilities in greater Phoenix". Greater Phoenix Economic Council. Archived from the original on November 25, 2009. Retrieved October 22, 2009.
Jump up ^ "SunCor Development files for bankruptcy". Retrieved 2015-02-03.
Jump up ^ "Stockholders Okay Calapco, Edison Merger". The Arizona Republic. 1951-12-15. p. 13.
^ Jump up to: a b c d e f g h i Standard & Poor's Stock Guide, various issues
^ Jump up to: a b Compilation of Investor-Owned Utility Transactions – Holding Companies Established Archived September 27, 2007, at the Wayback Machine., American Public Power Association, (updated 09-03)
Jump up ^ U.S. Seizes Arizona's Biggest Savings Institution New York Times February 1, 1990 [1]
Jump up ^ A Reckoning for the Utility High Rollers New York Times July 29, 1990 [2]
Jump up ^ McDonald, Jeff; Morgan, Lee (September 16, 2011). "Outage had roots in Mexico, too". Associated Pressaccessdate=September 26, 2011.
^ Jump up to: a b McDonald, Jeff; Morgan, Lee (September 9, 2011). "Blackout sparks multiple investigations". Associated Press. Retrieved September 26, 2011.
Jump up ^ Damon Gross, Cause of Widespread Outage Under Investigation; APS Works to Restore Service to Customers in Yuma Area, APS News Release, September 8, 2011. Accessed September 9, 2011
Jump up ^ "Massive Power Outage in San Diego". International Business Times. September 8, 2011. Retrieved September 10, 2011. Over 1.4 million people are suddenly without power in San Diego and surrounding areas in the Southwestern U.S. Thursday, just hours after Homeland Security warned of a possible terror strike in the days leading up to the tenth anniversary of 9/11.
Jump up ^ "Announcement - NERC" (PDF). North American Electric Reliability Corporation.
Jump up ^ "APS reaches major solar milestone". The Daily Courier. Oct 16, 2016. Retrieved Oct 16, 2016.
External links[edit]
APS official site
Pinnacle West Capital
Business data for Pinnacle West Capital: Google Finance
Yahoo! Finance
Reuters
SEC filings
APS carbon cost analysis
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