Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (m²), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.

For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.

Area plays a important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.

Formal definition

An approach to defining what is meant by area is through axioms. For example, we may define area as a function ''a'' from a collection ''M'' of special kind of plane figures (termed measurable sets) to the set of real numbers which satisfies the following properties:

For all ''S'' in ''M'', $a(S)\; \backslash ge\; 0$.

If ''S'' and ''T'' are in ''M'' then so are $S\backslash cup\; T$ and $S\backslash cap\; T$ and also, $a(S\backslash cup\; T)=a(S)+a(T)-a(S\backslash cap\; T)$.

If ''S'' and ''T'' are in ''M'' with $S\backslash subset\; T$ then ''T'' − ''S'' is in ''M'' and ''a''(''T'' − ''S'') = ''a''(''T'') − ''a''(''S'').

If a set ''S'' is in ''M'' and ''S'' is congruent to ''T'' then ''T'' is also in ''M'' and ''a''(''S'') = ''a''(''T'').

Every rectangle ''R'' is in ''M''. If the rectangle has length ''h'' and breadth ''k'' then ''a''(''R'') = ''hk''.

Let ''Q'' be a set enclosed between two step regions ''S'' and ''T''. A step region is formed from a finite union of adjacent rectangles resting on a common base, i.e. $S\backslash subset\; Q\backslash subset\; T$. If there is a unique number ''c'' such that $a(S)\backslash le\; c\backslash le\; a(T)$ for all such step regions ''S'' and ''T'', then ''a''(''Q'') = ''c''.

It can be proved that such a area function actually exists. (See, for example, ''Elementary Geometry from an Advanced Standpoint'' by Edwin Moise.)

Units

Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. Thus areas can be measure in square metres (m²), square centimetres (cm²), square millimetres (mm²), square kilometres (km²), square feet (ft²), square yards (yd²), square miles (mi²), and so forth. Algebraically, these units can be thought of as the squares of the corresponding length units.

The SI unit of area is the square metre, which is considered an SI derived unit.

Conversions

The conversion between two square units is the square of the conversion between the corresponding length units. For example, since :1 foot = 12 inches, the relationship between square feet and square inches is :1 square foot = 144 square inches, where 144 = 12² = 12 × 12. Similarly:

1 square kilometer = 1,000,000 square meters

1 square meter = 10,000 square centimetres = 1,000,000 square millimetres

1 square centimetre = 100 square millimetres

1 square yard = 9 square feet

1 square mile = 3,097,600 square yards = 27,878,400 square feet

In addition,

1 square inch = 6.4516 square centimetres

1 square foot = square metres 1 square yard = square metres 1 square mile = square kilometres

Other units

There are several other common units for area. The are was the original unit of area in the metric system, with

1 are = 100 square metres

Though the are has fallen out of use, the hectare is still commonly used to measure land:

1 hectare = 100 ares = 10,000 square metres = 0.01 square kilometres

Other uncommon metric units of area include the tetrad, the hectad, and the myriad.

The acre is also commonly used to measure land areas, where

1 acre = 4,840 square yards = 43,560 square feet.

An acre is approximately 40% of a hectare.

Basic area formulae

Rectangles

The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length and , the formula for the area is :  (rectangle). That is, the area of the rectangle is the length multiplied by the width. As a special case, the area of a square with side length is given by the formula :  (square).

The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a definition or axiom. On the other hand, if geometry is developed before arithmetic, this formula can be used to define multiplication of real numbers.

Dissection formulae

Most other simple formulae for area follow from the method of dissection. This involves cutting a shape into pieces, whose areas must sum to the area of the original shape.

For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: :  (parallelogram). thumb|right|180px|Two equal triangles.However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right. It follows that the area of each triangle is half the area of the parallelogram: :$A\; =\; \backslash frac\{1\}\{2\}bh$  (triangle). Similar arguments can be used to find area formulae for the trapezoid and the rhombus, as well as more complicated polygons.

Circles

The formula for the area of a circle is based on a similar method. Given a circle of radius , it is possible to partition the circle into sectors, as shown in the figure to the right. Each sector is approximately triangular in shape, and the sectors can be rearranged to form and approximate parallelogram. The height of this parallelogram is , and the width is half the circumference of the circle, or . Thus, the total area of the circle is , or : :  (circle). Though the dissection used in this formula is only approximate, the error becomes smaller and smaller as the circle is partitioned into more and more sectors. The limit of the areas of the approximate parallelograms is exactly , which is the area of the circle.

This argument is actually a simple application of the ideas of calculus. In ancient times, the method of exhaustion was used in a similar way to find the area of the circle, and this method is now recognized as a precursor to integral calculus. Using modern methods, the area of a circle can be computed using a definite integral: :$A\; \backslash ;=\backslash ;\; \backslash int\_\{-r\}^r\; 2\backslash sqrt\{r^2\; -\; x^2\}\backslash ,dx\; \backslash ;=\backslash ;\; \backslash pi\; r^2.$

Surface area

Most basic formulae for surface area can be obtained by cutting surfaces and flattening them out. For example, if the side surface of a cylinder (or any prism) is cut lengthwise, the surface can be flattened out into a rectangle. Similarly, if a cut is made along the side of a cone, the side surface can be flattened out into a sector of a circle, and the resulting area computed.

The formula for the surface area of a sphere is more difficult: because the surface of a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work ''On the Sphere and Cylinder''. The formula is :  (sphere). where is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.

List of formulae

The above calculations show how to find the area of many common shapes.

The area of irregular polygons can be calculated using the "Surveyor's formula".

Additional formulae

Areas of 2-dimensional figures

a triangle: $\backslash tfrac12Bh$ (where ''B'' is any side, and ''h'' is the distance from the line on which ''B'' lies to the other vertex of the triangle). This formula can be used if the height ''h'' is known. If the lengths of the three sides are known then ''Heron's formula'' can be used: $\backslash sqrt\{s(s-a)(s-b)(s-c)\}$ where ''a'', ''b'', ''c'' are the sides of the triangle, and $s\; =\; \backslash tfrac12(a\; +\; b\; +\; c)$ is half of its perimeter. If an angle and its two included sides are given, the area is $\backslash tfrac12\; a\; b\; \backslash sin(C)$ where C is the given angle and a and b are its included sides. If the triangle is graphed on a coordinate plane, a matrix can be used and is simplified to the absolute value of $\backslash tfrac12(x\_1\; y\_2\; +\; x\_2\; y\_3\; +\; x\_3\; y\_1\; -\; x\_2\; y\_1\; -\; x\_3\; y\_2\; -\; x\_1\; y\_3)$. This formula is also known as the shoelace formula and is an easy way to solve for the area of a coordinate triangle by substituting the 3 points ''(x₁,y₁)'', ''(x₂,y₂)'', and ''(x₃,y₃)''. The shoelace formula can also be used to find the areas of other polygons when their vertices are known. Another approach for a coordinate triangle is to use Infinitesimal calculus to find the area.

a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points: $i\; +\; \backslash frac\{b\}\{2\}\; -\; 1$, where ''i'' is the number of grid points inside the polygon and ''b'' is the number of boundary points. This result is known as Pick's theorem.

Area in calculus

the area between the graphs of two functions is equal to the integral of one function, ''f''(''x''), minus the integral of the other function, ''g''(''x'').

an area bounded by a function ''r'' = ''r''(θ) expressed in polar coordinates is $\{1\; \backslash over\; 2\}\; \backslash int\_0^\{2\backslash pi\}\; r^2\; \backslash ,\; d\backslash theta$.

the area enclosed by a parametric curve $\backslash vec\; u(t)\; =\; (x(t),\; y(t))$ with endpoints $\backslash vec\; u(t\_0)\; =\; \backslash vec\; u(t\_1)$ is given by the line integrals

::$\backslash oint\_\{t\_0\}^\{t\_1\}\; x\; \backslash dot\; y\; \backslash ,\; dt\; =\; -\; \backslash oint\_\{t\_0\}^\{t\_1\}\; y\; \backslash dot\; x\; \backslash ,\; dt\; =\; \{1\; \backslash over\; 2\}\; \backslash oint\_\{t\_0\}^\{t\_1\}\; (x\; \backslash dot\; y\; -\; y\; \backslash dot\; x)\; \backslash ,\; dt$ (see Green's theorem) :or the ''z''-component of

::$\{1\; \backslash over\; 2\}\; \backslash oint\_\{t\_0\}^\{t\_1\}\; \backslash vec\; u\; \backslash times\; \backslash dot\{\backslash vec\; u\}\; \backslash ,\; dt.$

Surface area of 3-dimensional figures

cube: $6s^2$, where ''s'' is the length of the top side

rectangular box: $2\; (\backslash ell\; w\; +\; \backslash ell\; h\; +\; w\; h)$ the length divided by height

cone: $\backslash pi\; r\backslash left(r\; +\; \backslash sqrt\{r^2\; +\; h^2\}\backslash right)$, where ''r'' is the radius of the circular base, and ''h'' is the height. That can also be rewritten as $\backslash pi\; r^2\; +\; \backslash pi\; r\; l$ where ''r'' is the radius and ''l'' is the slant height of the cone. $\backslash pi\; r^2$ is the base area while $\backslash pi\; r\; l$ is the lateral surface area of the cone.

prism: 2 × Area of Base + Perimeter of Base × Height

General formula

The general formula for the surface area of the graph of a continuously differentiable function $z=f(x,y),$ where $(x,y)\backslash in\; D\backslash subset\backslash mathbb\{R\}^2$ and $D$ is a region in the xy-plane with the smooth boundary: : $A=\backslash iint\_D\backslash sqrt\{\backslash left(\backslash frac\{\backslash partial\; f\}\{\backslash partial\; x\}\backslash right)^2+\backslash left(\backslash frac\{\backslash partial\; f\}\{\backslash partial\; y\}\backslash right)^2+1\}\backslash ,dx\backslash ,dy.$ Even more general formula for the area of the graph of a parametric surface in the vector form $\backslash mathbf\{r\}=\backslash mathbf\{r\}(u,v),$ where $\backslash mathbf\{r\}$ is a continuously differentiable vector function of $(u,v)\backslash in\; D\backslash subset\backslash mathbb\{R\}^2$: : $A=\backslash iint\_D\; \backslash left|\backslash frac\{\backslash partial\backslash mathbf\{r\}\}\{\backslash partial\; u\}\backslash times\backslash frac\{\backslash partial\backslash mathbf\{r\}\}\{\backslash partial\; v\}\backslash right|\backslash ,du\backslash ,dv.$

Minimization

Given a wire contour, the surface of least area spanning ("filling") it is a minimal surface. Familiar examples include soap bubbles.

The question of the filling area of the Riemannian circle remains open.

See also

Equi-areal mapping

Integral

Orders of magnitude (area)—A list of areas by size.

Perimeter

Volume

References

Notes

External links

Area formulas

Conversion cable diameter to circle cross-sectional area and vice versa

*

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Name	Nate Dogg
Background	solo_singer
Birth name	Nathaniel Dwayne Hale
Birth date	August 19, 1969Clarksdale, Mississippi, U.S.
Death date	March 15, 2011Long Beach, California, U.S.
Genre	Hip hop, West Coast hip hop, R&B;, G-funk
Occupation	Singer, actor, rapper
Years active	1990–2011
Label	Death RowElektraDoggystyleAtlantic
Associated acts	213, Snoop Dogg, Warren G, 2Pac, Dr. Dre, Game, Eminem, 50 Cent, Tha Dogg Pound, Fabolous }}

Nathaniel Dwayne Hale (August 19, 1969 – March 15, 2011), better known by his stage name Nate Dogg, was an American musician. He is noted for his membership of rap trio 213 and his solo career in which he collaborated with Dr. Dre, Warren G, Tupac and Snoop Dogg on many hit releases. Nate Dogg released three solo albums, ''G-Funk Classics, Vol. 1 & 2'' in 1998, ''Music and Me'' in 2001 and ''Nate Dogg'' in 2008.

Nate Dogg died in 2011 in Long Beach, California from complications of multiple strokes.

Early life

Nate Dogg was born in Clarksdale, Mississippi. He moved to Long Beach, California when he was 14 following his parents' divorce. He was the friend and partner in the rap game with rappers Snoop Dogg, Warren G, RBX, Daz Dillinger and was the cousin of Butch Cassidy and Lil' ½ Dead. He began singing as a child in the New Hope Baptist Church in Long Beach and Life Line Baptist Church in Clarksdale, Mississippi where his father Daniel Lee Hale was pastor. At the age of 16 he dropped out of high school in Long Beach and left home to join the United States Marine Corps, serving for three years.

Career

Early career with 213

In 1990, Nate Dogg and Snoop Dogg, and their friend Warren G, formed a rap trio called 213. 213 recorded their first demo in the back of the famed V.I.P. record store in Long Beach, the demo was later heard by Dr. Dre at a house party and he was instantly hooked on the soulful voice of Nate.

Solo career

Nate Dogg made his debut on ''The Chronic''. Singing in what later become his trademark style, he was well-received by fans and critics alike, and would go on to sign with Death Row Records in 1993. Nate Dogg was also featured on Mista Grimm's "Indosmoke" with Warren G. Then in 1994 he produced his first hit single "Regulate" with Warren G. Nate Dogg was also featured in many Tupac releases, including his collaboration record ''Thug Life: Volume I''. Then in 1998 after a tumultuous time at Death Row Records he released another album. The double album was titled ''G-Funk Classics Vol. 1 & 2'' and was followed up in late 2001 with ''Music & Me'' on Elektra Records. ''Music & Me'' peaked at number three on the ''Billboard'' hip-hop charts in 2001. After a number of delays and an original release date of April 2004, his ''self-titled album'' was released under the ''Affiliated Entertainment Group'' on June 3, 2008.

Television appearances

In 2002, Nate Dogg and Isaiah Mendez appeared on a celebrity episode of the Weakest Link, making it to the last three players before being eliminated by Xzibit and Young MC.

Collaborations with other artists

Nate found success, not only in solo projects, but in collaborations with other hip-hop artists. In the 2000s, Nate's high-ranking collaborative singles, according to Rolling Stone, includes Dr. Dre's "The Next Episode," Mos Def's "Oh No," Fabolous' "Can't Deny It," Ludacris' "Area Codes," 50 Cent's "21 Questions," Mark Ronson's "Ooh Wee," Houston's "I Like That," Eminem's "'Till I Collapse" and "Shake That", and Mobb Deep's "Have a Party."

Legal issues

In the early 1990s, Hale was charged with two separate robberies, Check Changers robbery in 1991 and robbery of a San Pedro Taco Bell in 1994. He faced a maximum of nearly eleven years in prison, but he was subsequently acquitted of both charges.

In 1996, Hale was convicted of a drug-related offense in Los Angeles County.

On June 17, 2000, Hale was alleged to have kidnapped and assaulted his former girlfriend and set her mother's car on fire in Lakewood. He was arrested by a SWAT team in his home Pomona. He was accused of kidnapping, domestic violence, making terrorist threats and arson. He spent a night in the Twin Towers Correctional Facility in Los Angeles before he was released on a $1 million bail. These charges were later dismissed, but Hale faced jail time for a new charge, illegal possession of a firearm by felon. An unmarked firearm was found in his home during the June 17 arrest. Hale pleaded no contest to the misdemeanor charge, and was sentenced to probation of three years and ordered to pay a $1,000 fine.

On April 12, 2002, Hale was stopped by Arizona Department of Public Safety officers outside of Kingman, Arizona while traveling on a tour bus. He was arrested and charged with firearms-related and drug-related offenses after two pistols and four ounces of cannabis were found. Hale was booked on Mohave County Jail and subsequently released on a $3,500 bond. Weapon charges against him were dropped as an exchange to guilty plea to drug possession charge. Hale was subsequently sentenced to probation and community service. He was also ordered to attend drug counseling sessions in May 2002.

In 2006, Hale was charged with misdemeanor aggravated trespassing, telephone harassment, battery assault, dissuading a witness from reporting a crime and violation of a restraining order. In March 2008, Hale pleaded guilty to trespassing and battery and was ordered to complete a domestic violence treatment program, probation of three years, and was stripped of gun ownership rights for the next ten years.

In July 2008, Hale was charged with two felony criminal threats after allegedly sending threatening emails to his estranged wife, and one count of stalking after allegedly chasing her by car on Interstate 405 in previous month. Hale initially pleaded not guilty to these charges, which were eventually dropped in April 2009, because the alleged victim did not contact prosecutors in the case.

Additionally, Hale has a conviction of driving under the influence.

Strokes and death

On December 19, 2007, Nate Dogg suffered a stroke, according to a coordinator for his recently formed gospel choir, Innate Praise. Reports had circulated that Nate Dogg had been admitted to Pomona Valley Hospital Medical Center in Pomona, California after suffering a heart attack. Erica Beckwith, however, confirmed to MTV News that Nate Dogg was released on December 26 after being treated for a stroke and was admitted to a medical rehabilitation facility to assist him in his recovery. On January 18, 2008, it was officially reported that the stroke had rendered the left side of his body paralyzed. Doctors believed there would be a full recovery, and his voice was not affected. In September 2008, he suffered a second stroke. Nate Dogg died March 15, 2011 in Long Beach, California. On March 17, his attorney Mark Geragos confirmed that the cause of the death was from complications of multiple strokes.

Discography

''G-Funk Classics, Vol. 1 & 2'' (1998)

''Music and Me'' (2001)

''Nate Dogg'' (2008)

Filmography

''The Transporter'' song "I Got Love" (2002)

''Doggy Fizzle Televizzle'' as singer of the theme song for the sketch "The Braided Bunch" (2002–2003)

''Head of State'' as himself (also singer/composer of theme song) (2003)

''Need For Speed: Underground'' song "Keep it Comin"

''The Boondocks (2008)

Awards and nominations

During his career, Nate Dogg has been nominated for four Grammy Awards.

Category	Genre	Song	Year	Result
Best Rap/Sung Collaboration(with Eminem)	Rap	"Shake That"	2007	Nominated
Best Rap/Sung Collaboration(with Ludacris)	Rap	"Area Codes"	2002	Nominated
Best Rap Performance by a Duo or Group(uncredited with Dr. Dre and Snoop Dogg)	Rap	"The Next Episode"	2001	Nominated
Best Rap Performance by a Duo or Group(with Warren G)	Rap	"Regulate"	1995	Nominated

References

External links

Category:1969 births Category:2011 deaths Category:African American rappers Category:American people convicted of assault Category:Atlantic Records artists Category:Cardiovascular disease deaths in California Category:Crips Category:Death Row Records artists Category:Hip hop singers Category:People convicted of drug offenses Category:People from Clarksdale, Mississippi Category:People from Long Beach, California Category:Pseudonymous rappers Category:Rappers from Los Angeles, California Category:Rappers from Mississippi Category:West Coast hip hop musicians Category:United States Marines

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name	Imogen Heap
background	solo_singer
birth name	Imogen Jennifer Jane Heap
birth date	December 09, 1977
gender	Female
origin	Havering, London, England
instrument	Vocals, keyboards, array mbira, cello, clarinet, guitar, drums, keytar, nail violin, vocal percussion, synthesizer, sampler, organ, hang, vocoder
genre	Electronica, alternative, indie, synthpop, Folktronica, ambient, trip hop, rock, classical
occupation	Musician, singer, songwriter, visual artist
years active	1997–present
label	Almo Sounds (1998–2001)Megaphonic (2005–present)RCA Victor (2006–present)
associated acts	Frou FrouUrban SpeciesIAMXMIKA
website	imogenheap.com
notable instruments	}}

Imogen Jennifer Jane Heap () (born 9 December 1977 in the London Borough of Havering) is a Grammy Award-winning English singer, composer and songwriter from Romford, Havering. She is known for her work as part of the musical duo Frou Frou and her solo albums, which she writes, produces, and mixes. She has produced three solo albums, the latest of which is 2009's ''Ellipse'', which was a North American chart success and earned Heap two Grammy nominations, winning Best Engineered Album, Non-Classical.

Musical and songwriting style

For her solo work (as well as her work with Frou Frou and Acacia), Heap plays heavily produced and arranged singer-songwriter pop incorporating elements of rock, dance and electronica. As a guest player and collaborator she has played rock (Jeff Beck), hip-hop (Urban Species) and theatre/film music. A skilled multi-instrumentalist, Heap extensively uses manipulated electronic sounds as an integral part of her music. She also mixes ambient sound into her music (such as the sound of a frying pan in use cooking food, in the background of her song "My Secret Friend") and has commented that "certain sounds give the music a width and a space, and that's important."

Heap states that her song lyrics come from personal experience, but are not straightforwardly confessional. She has stated "Most of the time, the lyrics are kind of like my secret messages to my friends or my boyfriend or my mum or my dad. I would never tell them that these songs are about them or which specific lyric is about somebody. Often, when I sit down to write a lyric, it is in the heat of the moment, and something has just happened."

Biography

Early life

Heap played music from an early age, becoming classically trained in several instruments including piano, cello and clarinet. She attended Friends School, a private, Quaker-run boarding school in Saffron Walden. Heap's mother (an art therapist) and her father (a construction rock retailer) separated when she was twelve. By age thirteen, she had begun writing songs.

Heap did not get along well with the music teacher at her boarding school, so she principally taught herself sequencing, music engineering, sampling and production (on Atari computers). She also taught herself to play the guitar and drums, and subsequently two percussion/idiophone instruments, the array mbira and the Hang. After school, she went on to study at the BRIT School for Performing Arts & Technology in Croydon, South London.

Early work as musician (including work with Acacia)

After being introduced to Nik Kershaw by his manager Mickey Modern, Heap and Kershaw recorded four demos that Mickey Modern took to Rondor Music. Consequently, a few months later she signed her first record contract at 18 to independent record label Almo Sounds. Modern and Wood formed Modernwood Management, and managed Heap until 2006, when Modernwood was dissolved. Wood continues to manage the artist via his new company, Radius Music.

During 1996, Heap began working with an experimental pop band called Acacia, which featured her future collaborator Guy Sigsworth and was fronted by the singer Alexander Nilere. While never a full member of the band, Heap was a guest vocalist (as a counterpart to Nilere) and contributed to various Acacia single and album tracks. One Acacia song, "Maddening Shroud", would later be covered by Frou Frou.

Mickey Modern asked Dennis Arnold to place Imogen in the line up in the 1996 Prince's Trust Concert in Hyde Park, London organized by Harvey Goldsmith. Heap performed four songs between sets by The Who and Eric Clapton.

1998–2000: ''iMegaphone''

Heap's debut album, ''iMegaphone'' (an anagram of "Imogen Heap") was a mixture of self-penned and self-produced tracks, alongside tracks co-written and produced with established producers such as David Kahne, former Eurythmic Dave Stewart and Guy Sigsworth. The album was released in 1998 internationally via Almo Sounds, to favorable reviews comparing Heap's angst-filled songs to work by PJ Harvey, Kate Bush and Annie Lennox. Promotion for the record included a tour of America and performances around Europe. Three singles were commercially released in the UK: "Getting Scared", "Shine" and "Come Here Boy". "Oh Me, Oh My" was sent to US radio stations in place of "Shine".

Heap's early success was soon replaced by problems. Almo Sounds cut funding for UK promotion and gave Heap a deadline to deliver songs for her second album. Upon delivery of the songs, she was told that they lacked "hit potential". It was announced that the record label would be sold to Universal and its artists moved to other labels or released. Heap was one of the artists who was dropped from the label, leaving her without a record contract. ''iMegaphone'' had, however, been licensed from Almo Sounds to Aozora Records in Japan, who eventually re-released and re-promoted the album in January 2002, featuring "Blanket" and "Aeroplane" (a Frou Frou remix/remake of one of her B-sides, "Airplane" of the ''Shine'' single released in 1998). The album featured new packaging, all-new artwork, and a previously unavailable hidden track, entitled "Kidding", recorded live during her 1999 tour.

Copies of the original Almo Sounds release remain rare. A Brazilian label, Trama Records, currently claims to hold the license to the record and has started re-printing copies of the album in limited quantities. The album was released digitally on the U.S. iTunes Music Store in early 2006. After achieving commercial success with her work with Guy Sigsworth as the duo Frou Frou and her second solo album, ''Speak for Yourself''.

2001: Interim work

In the gap between the end of promotion for ''iMegaphone'' internationally and the re-promotion, Heap had also begun to think about her second solo album, and had started writing songs, both solo, as well as working with Guy Sigsworth; however, as she was without a record deal, the songs were shelved. During the time when she was unsigned, Heap appeared on two UK singles, "Meantime" (a track written by her former Acacia colleagues Guy Sigsworth and Alexander Nilere for the soundtrack to the independent British film, ''G:MT – Greenwich Mean Time'') and "Blanket" (a collaboration with Urban Species). In 2000, Heap sang on the album ''You Had It Coming'' by Jeff Beck.

2002–2003: Frou Frou

Heap had kept in contact with Guy Sigsworth (who had co-written and produced "Getting Scared" from ''iMegaphone'') and this led to the pair of them establishing the collaborative project Frou Frou.

The initial concept for Frou Frou was Sigsworth's, and the project was to have been an album written and produced by her with each track featuring a different singer, songwriter, poet or rapper. Heap explains that Sigsworth invited her over to his studio to write lyrics to a four-bar motif he had, with one condition – that she include the word "love" somewhere. The first line she came up with was "lung of love, leaves me breathless", and the ''Details'' album track, "Flicks" was born. A week later, Sigsworth phoned Heap up again, and together they wrote and recorded the future single "Breathe In".

Throughout the process, Frou Frou work was an equal partnership, with Heap and Sigsworth making equal contributions to writing, arrangement, production and instrumental performance and Heap handling all of the vocals.

In August 2002, they released the ''Details'' album and singles "Breathe In", "It's Good To Be In Love", and "Must Be Dreaming" (although the latter two were not commercially available). The album was critically acclaimed, but did not enjoy the commercial success that they had been hoping for.

In late 2003, after an extensive promotional tour of the UK, Europe and the U.S., the duo were told that their record label, Island Records would not be picking up the option for a second album.

Heap and Sigsworth remain firm friends, and have worked together since the project, including their temporary re-formation in late 2003, when they covered the Bonnie Tyler classic, "Holding Out for a Hero", which was featured during the credits of the movie ''Shrek 2'' after Jennifer Saunders version in the film. Frou Frou saw a resurgence in popularity in 2004, when their album track "Let Go" was featured in the film ''Garden State''.

In a 2005 interview Heap said of frou frou "(it) was really like a kind of little holiday from my own work. Guy and I, we have always worked together, and then over the years, it became clear that we wanted to do a whole album together. It was very organic and spontaneous - just one of those wonderful things that happens. But there was never a mention of a second record from either of us, and not uncomfortably. We're just both kind of free spirits. I love to work with a lot of different people, but I was also just gagging to see what I could do on my own. But I'm sure in the future, Guy and I will get back together to do another record, or to record a few songs together."

2004–2005: ''The O.C.'' and ''Speak for Yourself''

In December 2003, Heap announced on her Web site that she was going to write and produce her second solo album, using her site as a blog to publicise progress.

Heap set herself a deadline of one year to make the album, booking a session to master the album one year ahead in December 2004. She re-mortgaged her flat to fund production costs, including renting a studio at Atomic Studios, London (previously inhabited by UK grime artist, Dizzee Rascal), and purchasing instruments.

At the end of 2004, with the album completed, Heap premiered two album tracks online, selling them prior to the album's release – "Just for Now" and "Goodnight and Go".

In April 2005, ''The O.C.'' featured the vocoded-vocal track, "Hide and Seek" in the closing scenes of their season two finale. The track was released immediately to digital download services, such as iTunes, in the U.S., where it charted. The track was released to iTunes UK on 5 July 2005 (the same day as the UK airing of the season finale) and entered the official UK download chart.

Heap made a decision to put out the album on her own in the UK, starting her own record company, titled Megaphonic Records. The album was titled ''Speak for Yourself''.

''Speak for Yourself'' was released in the UK on 18 July 2005 on CD and iTunes UK, where it entered the top 10 chart. The initial 10,000 physical copies pressed sold out, distributed through large and independent record stores and Heap's own online shop.

In August 2005, Heap announced that she had licensed ''Speak for Yourself'' to Sony BMG imprint RCA Victor for the album release in the United States, Canada, and Mexico. The album was released in November 2005 and debuted at #144 in the Billboard Top 200 album chart. In concert, Heap performed solo, controlling the sound through her Apple PowerBook laptop, as well as singing and playing the piano and array mbira.

She returned from the U.S., already having sold over 120,000 copies.

2006–2007: The year of the 'White Rabbit'

Heap also announced, on her return to the UK, that she had signed a deal for the album to be released internationally, as well as re-promoted in the UK, with a new imprint of Sony BMG, White Rabbit, run by former Sony BMG UK A&R; vice president Nick Raphael. The deal meant that the album could have the promotional backing provided by a respected major label, whilst Heap retained sole control and the team she established for Megaphonic Records.

''Speak for Yourself'' was re-released on the label on 24 April 2006, ahead of a full promotional push on 15 May, a week after the second single, "Goodnight and Go", was commercially released in the UK.

In August 2006, Heap performed a set at the V Festival, where it was announced that "Headlock" was to be the third single to be lifted from the album, and released on 16 October 2006 in the UK.

In late September and early October, Heap embarked on a tour of the UK, holding a competition on MySpace for different support acts for each venue, before touring throughout Canada and the USA in November and December. This was her first tour of North America that included a band, incorporating upright bass, percussion, and support acts Kid Beyond and Levi Weaver on beatbox and guitar, respectively. In December 2006, Heap was featured on the front page of ''The Green Room'' magazine.

On 7 December 2006, Heap received two Grammy nominations for the 49th Annual Grammy Awards, one for Best New Artist and the other for Best Song Written For Motion Picture, Television Or Other Visual Media for "Can't Take It In".

2007–2009: ''Ellipse''

Throughout the creation of her album Ellipse, Heap posted vlogs, or VBlogs as she called them, through YouTube. She used these to comment on the album as well as update on its release. The album's release was pushed back multiple times. These included Heap being asked to perform at the annual event PopTech in October 2008. During the event, she premiered one of her album's songs, "Wait it Out".

Heap announced on her Twitter page that ''Ellipse'''s first single would be "First Train Home". On 17 August 2009 Heap made the entire album ''Ellipse'' available for live streaming via her webpage.

''Ellipse'' was released in the United Kingdom on 24 August, and in the United States on 25 August.

2011: New "concept" album

On 14 March 2011 Heap officially started work on a new record as fans sent in nearly 900 "sound seeds", or samples of everyday sounds such as a "dishwasher door", a "bicycle" or a "burning match". Heap has stated that the concept for this record will be to record one track over a two week period every 3 months. Each song and video will be released immediately.

The first song, initially titled #heapsong1 and later retitled "Lifeline", premiered worldwide on 28 March 2011 via Ustream along with a live remix by Tim Exile. "Lifeline" was released on 30 March 2011 as a digital download from Imogen's website and via iTunes, Amazon and other digital retailers. Released alongside this was a 12 page 3DiCD package (a 3D virtual CD) including crowd sourced (and paid for) images, the instrumental version of the song, the "seeds and solos only" version and "heap speaks seeds and solos" - an-18 minute commentary by Heap on how the sounds and solos were used in "Lifeline". The whole project can be viewed on the #heapsong1 / Lifeline mini site.

#heapsong2 is entitled "Propeller Seeds" and was released on 5 July 2011.

Recordings for television and film

Heap has recorded several songs for films, including a cover of the Classics IV hit "Spooky" for the soundtrack to the Reese Witherspoon film ''Just Like Heaven''. Her song "Hide and Seek" was featured in ''The Last Kiss'', starring Zach Braff (who used her former band Frou Frou's "Let Go" in his 2004 film ''Garden State''), and was also used in a 2007 episode of ''Saturday Night Live'', hosted by Shia LaBeouf. "The Moment I Said It" was also used in the episode "Seven Seconds" of the CBS crime drama ''Criminal Minds''.

In 2004, while recording her second solo album, she was commissioned to record a cover of a short nursery rhyme for the HBO television series, ''Six Feet Under'', entitled "I'm A Lonely Little Petunia (In An Onion Patch)".

In late 2005, Heap was asked to write a track for the soundtrack of ''The Chronicles of Narnia: The Lion, the Witch and the Wardrobe'' entitled "Can't Take It In", when a track that fellow Brit singer Dido submitted was deemed unfitting. Heap's track is played at the end of the film in an orchestral version produced by Heap and Harry Gregson Williams, who scored the movie. In addition, she composed a track for the film ''The Chronicles of Narnia: Prince Caspian'', but it was deemed to be too dark in tone for the film. Instead, it was included in her album ''Ellipse'' as "2-1". 2-1 has also featured in ''CSI Miami'' (Season 8 Episode 9), as well as promotional trailers for the film The Lovely Bones.

In March 2006, Heap completed a track about locusts, entitled "Glittering Cloud", for a CD of music about the plagues of Egypt entitled ''Plague Songs'', accompanying The Margate Exodus project, for musical director Brian Eno.

Heap recorded an a cappella version of the Leonard Cohen track "Hallelujah", for the season three finale of ''The O.C.'', and her "Not Now But Soon" was included on the original soundtrack for the NBC show, ''Heroes''.

Song usage

Imogen Heap and Frou Frou songs have been featured in various TV shows, movies, advertisements, and marching band productions, notably including ''CSI, The OC, SNL, Garden State'', and ''So You Think You Can Dance''.

Also notable is the sampling of Heap's song "Hide & Seek" in Jason DeRulo's single "Whatcha Say", which peaked at #1 on the ''Billboard'' Hot 100.

Collaborations

Heap has collaborated as a guest vocalist, co-writer, remixer or producer with many various artists throughout her career. Among them co-writing and producing ''By The Time'' for Mika and ''Now or Never'' for Josh Groban. The diverse range of other musicians Heap has worked with include IAMX, Jeff Beck, Temposhark, LHB, J. Peter Schwalm, Way Out West, Jon Bon Jovi, Mich Gerber, Sean Lennon, Urban Species, Matt Willis, Jon Hopkins, MIKA, Acacia, Britney Spears, Nik Kershaw, Blue October, Joshua Radin and Nitin Sawhney.

Use of technology

Heap is an outspoken advocate of using new technology to interact and collaborate with her fans. In August, 2009 she used Vokle, an online auditorium, to take questions from listeners over video chat.

Imogen also teamed up with Vokle to hold open cello auditions for her North American tour. She provided sheet music for “Aha” on her website and encouraged local fans to learn the part and audition live via Vokle. Imogen would then pick the cellist to accompany her for that particular city - sometimes with the help of viewers and her puppet Lion, Harold.

In 2010 Imogen opened her online auditions to singers and choirs and invited them to audition via submitted YouTube videos to accompany her on stage as she performed the song "Earth" from ''Ellipse''. The winner of each local show was also invited to do a 15 minute gig of their own. In the studio, the official album recording of "Earth" was made up entirely of numerous tracks of vocals.

July 2011 saw Imogen unveil a pair of high-tech musical gloves at the TED conference in Edinburgh, Scotland. The gloves which were created by Tom Mitchell, a lecturer in music systems at the University of the West of England, Bristol allow Imogen to manipulate sounds using nothing but hand gestures live on stage.

Charity

In 2008 she participated in a music album called ''Songs for Tibet: The Art of Peace'', which is an initiative to support Tibet, Dalai Lama Tenzin Gyatso and to underline the human rights situation in Tibet. The album was issued on 5 August via iTunes and on 19 August in music stores around the world. On 12 October 2008, Heap also Participated in "Run 10k: Cancer Research UK," placing fifth of the women in the actual run and raising over £1000 for the cause with the help of her fans.

In 2008 Imogen was asked to perform at POP!Tech in Camden, Maine (USA). There she performed selections from her then forthcoming album ''Ellipse''. After her set and an encouraging plea for another performance later in the conference by the audience and organizers, Imogen agreed. Having nothing else prepared though, she decided to improvise a song on the spot with parameters (tempo, key) suggested by the audience. After the show, Imogen was asked by a Poptech attendee if she would give the newly created piece of music to his charity. A ‘lightbulb’ moment occurred in Heap’s head and she saw the potential in doing these improvised pieces for local charities at each show during the tour she would soon begin.

The first of these songs materialized at Imogen’s show at Shepherd’s Bush Empire, in London on the 19th of February 2010. Using the same parameters and audience participation from POP!Tech, Imogen improvised a song titled, "The Shepherdess". After the show, Imogen made the song available worldwide as a digital download on her website asking for donations per download. All proceeds went to the Great Ormond Street Hospital where Imogen was diagnosed with osteomyelitis and underwent life-saving surgery as a little girl. Loving the concept, Imogen rolled this out for her North American Tour, donating all the proceeds for each song to a local charity from that city.

In 2011 Imogen was set to play a benefit concert in New Zealand's Christchurch city to help rebuild the Unlimited Paenga Tawhiti High School, following a severe 6.3 aftershock in February originating from the 7.1 earthquake that struck the Canterbury region in September 2010. The concert was held at the Burnside High Aurora Centre, also featuring performances from Roseanna Gamlen-Greene, and The Harbour Union including The Eastern, Lindon Puffin, Delaney Davidson and The Unfaithful Ways.

Live 4 X

In 2010, Imogen Heap partnered with Thomas Ermacora of Bubbletank to organize a series of online charitable events called ''Live 4 X''.

The initial event was inspired by the 2010 Pakistan floods. Triggered by monsoon rains, the floods left approximately one-fifth of the country of Pakistan underwater, affecting over 14 million people and damaging or destroying over 900,000 homes. Teaming up with Richard Branson’s Virgin Unite and Vokle.com, Heap and Ermacorda create an online webcast/fundraiser to raise awareness and money for the flood stricken. Hosted by comedian, creative, and internet personality Ze Frank, the webcast included a series of conversations with Cameron Sinclair of Architecture for Humanity, Mark Pearson, Gary Slutkin, and Anders Wilhelmson, (and later Richard Branson and Mary Robinson) with live performances by musicians Ben Folds, Amanda Palmer, Kate Havnevik, KT Tunstall, Josh Groban, Kaki King, Zoe Keating and Mark Isham.

The premise of ''Live 4 X'' thus established, Heap has since continued to refine the model, organize, host, and perform a number of charitable, streaming-live, concert events. By integrating live entertainment with educated discussion and technology, ''Live 4 X'' became an effective charitable outreach tool.

Following the devastating Great East Japan Earthquake and tsunami of 2011, Heap told Washington Times Communities journalist and recording artist Jennifer Grassman, that she intended to continue organizing ''Live 4 X'' events to benefit various charitable causes.

Catalog of ''Live 4 X'' events to date:

August 31, 2010 – ''Live 4 Pakistan'' raised funds for flood relief and recovery in that region. Musicians included Ben Folds, Amanda Palmer, Kate Havnevik, KT Tunstall, Josh Groban, and Zoe Keating. In an ironic turn of events, Heap, was kept from appearing on ''Live 4 Pakistan'' due to Hurricane Earl which at the time was progressing along the US eastern seaboard. Heap, stranded and unable to get an internet connection, later posted a video message as well as a performance of her song “Wait It Out” from ''Ellipse''. February 3, 2011 – ''Live 4 Capetown'' April 11, 2011 – ''Live 4 Sendai'' raised funds for Japanese tsunami recovery following the disastrous Great East Japan Earthquake of 2011. The event was also used to solicit rebuilding design ideas on behalf of Architecture for Humanity. Performers included Amanda Palmer, Ben Folds, KT Tunstall and Jamie Cullum and hosted by Ze Frank.

Film

After touring for nearly two years straight for her album Speak For Yourself Imogen continued her travels, this time with only a laptop and video camera on hand as she began her writing trip for her next album. Nine weeks later she returned to the UK with the beginnings of the award-winning ''Ellipse'' and footage (as requested by a fan to film the making of the album) from its quiet beginning. Back in Essex, Imogen sought the talents of long-time friend and film maker Justine Pearsall to continue documenting the creation of the album. The film documents every moment of joy, excitement, frustration, and even the renovation of the Imogen’s childhood home including turning her old playroom into her new home studio. ''Everything In-Between: The Story of Ellipse'' is scheduled to be released in November 2010.

On November 5, 2010 at the Royal Albert Hall, Heap conducted an orchestra (including friends and family) as they performed an original composition by Imogen herself orchestrated by Andrew Skeet. It was the score to the concept film Love The Earth - in creative partnership and co-production with Thomas Ermacora again for another Bubbletank production - in which fans were invited to submit video footage highlighting all of the breathtaking qualities of nature to be selected and edited into a film. This performance was broadcasted live worldwide.

In March for the Birds' Eye Festival at the BFi Imogen composed in collaboration with Andrew Skeet an a cappella choral score to the first ever surrealist film ‘The Seashell and the Clergyman’ (Germaine Dulac, 1927) with the Holst Singers.

Heap also performed in the Film and Music Arena at Latitude Festival in 2011.

Discography

1998: ''iMegaphone''

2005: ''Speak For Yourself''

2009: ''Ellipse''

Frou Frou

''Details'' (2002 • Island Records/MCA/Universal) (UK: #128)

"Breathe In" (single) (2002 • Island Records/Universal) (UK: #44)

"Its Good To Be In Love" (single) (2002 • Island Records/Universal)

"Must Be Dreaming" (single) (2002 • Island Records/Universal)

"Let Go" (Promotional single)

Guest appearances

''Hate'' EP by Acacia (1996 • Radar Records)

''Sway'' EP by Acacia (1996 • Radar Records)

''Maddening Shroud'' EP by Acacia (1997 • WEA)

''Cradle'' by Acacia – all tracks except "Wire" (1997 • WEA)

''Blanket'' by Urban Species – "Blanket" and "Predictably Unpredictable" (1998)

''Amor Fati'' by Mich Gerber – "Embers of Love", "Sirens Call (Qishm)" and "Mare" (2000)

''¡Viva Nueva!'' by Rustic Overtones – "Valentine's Day Massacre" (2001 • Tommy Boy Records)

''You Had It Coming'' by Jeff Beck – "Dirty Mind" and "Rollin' and Tumblin'" (2001 • Sony Music)

''Tell 'Em Who We Are'' by LHB – "Coming Up For Air" (2003 • Telstar TV)

''Contact Note'' by Jon Hopkins – "Second Sense" (2004 • Just Music)

''It's Better To Have Loved EP'' by Temposhark – "Not That Big (Metronomy Remix)" (2005 • Paper & Glue)

''Foiled'' by Blue October – "Congratulations" (2006 • Universal Records)

''Musikain'' by J. Peter Schwalm – "P.I.N." (2006 • Musikain Records)

''The Invisible Line'' by Temposhark – "Not That Big" (2007 • Paper & Glue)

''London Undersound'' by Nitin Sawhney – "Bring It Home" (2008 • Cooking Vinyl)

''Kingdom of Welcome Addiction'' by IAMX – "My Secret Friend" (2009 • Metropolis Records)

''The Boy Who Knew Too Much'' by Mika – "By The Time" (2009 • Casablanca Records)

''Live at Ronnie Scott's - Jeff Beck - (2008 • Eagle Records) - (2009 • DVD)

Compilation appearances

''New Dawn (Class of '94)'' – "Missing You" – (1994)

''I Still Know What You Did Last Summer'' soundtrack – "Getting Scared" – (1998 • Warner Music Group)

''Virtual Sexuality'' soundtrack – "Come Here Boy" – (1998 • EMI)

''G:MT – Greenwich Mean Time'' soundtrack – "Mean Time" (with GMT) – (1999 • Island Records/Universal)

''Serve Chilled'' – "Blanket" (with Urban Species) – (1999 • Hed Kandi)

''Women Talking Dirty'' soundtrack – "Getting Scared" – (2001 • Polygram International)

''American Psycho 2: All American Girl'' soundtrack – "Angry Angel" – (2002 • Rondor Music (London) Ltd)

''Garden State'' – "Let Go" – (2004 • Epic Records/Sony BMG)

''Nearing Grace'' Soundtrack – "The Walk" – (2005 • Sony BMG)

''Music from the OC: Mix 4'' – "Goodnight and Go" – (2005 • Warner Music Group)

''Six Feet Under, Vol. 2: Everything Ends'' – "I'm A Lonely Little Petunia (In An Onion Patch)" – (2005 • Astralwerks/EMI)

''Just Like Heaven'' Soundtrack – "Spooky" – (2005 • Sony BMG)

''Music from the OC: Mix 5'' – "Hide and Seek" – (2005 • Warner Music Group)

''The Chronicles of Narnia: The Lion, the Witch and the Wardrobe'' – "Can't Take It In" – (2005 • Disney Records/EMI)

''The Last Kiss'' soundtrack – "Hide and Seek" – (2005 • Lakeshore Pictures)

''Plague Songs'' – "Glittering Clouds (Locusts)" – (2006 • 4AD)

''So You Think You Can Dance (US)'' – "Hide and Seek" – (2006)

''So You Think You Can Dance (US)'' – "Let Go" – (2006)

''The Black Donnellys'' – "The Moment I Said It" – (2007)

''In Search of Sunrise 6'' – "Hide and Seek" (Tiëstos' In Search Of Sunrise Remix) – (2007)

''The Holiday'' – "Just For Now" and "Let Go" (Under 'Frou Frou') – (2006)

''So You Think You Can Dance'' – "The Moment I Said It" – (2007)

''Heroes'' Original Soundtrack – "Not Now, But Soon" – (2008 • NBC Records)

''Criminal Minds'' – "The Moment I Said It" – (2008)

''Songs For Tibet – The Art of Peace''' – "Hide & Seek 2" – (2008)

''Greys Anatomy'' – "Bad Body Double" – (2009)

''So You Think You Can Dance (US)'' - "Aha!" - (2009)

''The Vampire Diaries'' - "Wait it Out" - (2009)

''Melrose Place - "Aha!" - (2009)

''Powder Blue'' - "Blanket" - (2009)

''Chuck'' – "Wait it Out" – (2010)

''CSI: NY'' - "Wait it Out" - (2010)

References

External links

Official website

Imogen Heap, french website.

Imogen Heap's New Music Business Model

Bob Lefsetz on Imogen Heap

Auralgasms Interview From January 2006

Imogen Heap video interview on TiFFcast, November 2006

Portrait of Imogen Heap on 365portraits.com

Imogen Heap plays the Array mbira on numerous recordings and in concert

Review of First Train Home at Daily Music Guide

Interview with Jessica Lewis at "Exclaim!"

Interview with Imogen Heap for www.4ortherecord.com

Photo Report @ Milano (2010)

Category:1977 births Category:Living people Category:English female singers Category:Female rock singers Category:People from Havering (district) Category:English singer-songwriters Category:People educated at the BRIT School Category:Ableton Live users Category:Grammy Award winners Category:English electronic musicians Category:People educated at Friends School Saffron Walden

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