What is "flatness"

flatness \flat"ness\, n.

1. The quality or state of being flat.

2. Eveness of surface; want of relief or prominence; the state of being plane or level.

3. Want of vivacity or spirit; prostration; dejection; depression.

4. Want of variety or flavor; dullness; insipidity.

5. Depression of tone; the state of being below the true pitch; -- opposed to sharpness or acuteness.

mid-15c., "state or quality of being flat," from flat (adj.) + -ness.

n. 1 The state of being flat 2 The state of being two-dimensional; planar : planarity 3 The state of being bland : dullness 4 mattness, the quality of a painted surface which scatters or absorbs the light falling on it, so as to be substantially free from gloss or sheen 5 (context oenology English) Lack of bouquet and freshness of a wine, through too much aeration or infection with film yeasts 6 (context statistics English) slim-tailedness or platykurticity

1. n. the property of having two dimensions [syn: two-dimensionality, planeness]

2. the property of having little or no contrast; lacking highlights or gloss [syn: lusterlessness, lustrelessness, mat, matt, matte]

Flatness may refer to:

• Flatness (art)
• Flatness (cosmology)
• Flatness (electrical engineering)
• Flatness (liquids)
• Flatness (manufacturing), a geometrical tolerance required in certain manufacturing situations
• Flatness (mathematics)
• Flat module in abstract algebra
• Flatness (systems theory), a property of nonlinear dynamic systems
• Flat intonation

Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that has the flatness property is called a flat system. Flat systems have a (fictitious) flat output, which can be used to explicitly express all states and inputs in terms of the flat output and a finite number of its derivatives. Flatness in systems theory is based on the mathematical notion of flatness in commutative algebra and is applied in control theory.

In mathematics, the flatness (symbol: ⏥) of a surface is the degree to which it approximates a mathematical plane. The term is often generalized for higher-dimensional manifolds to describe the degree to which they approximate the Euclidean space of the same dimensionality. (See curvature.)

Flatness in homological algebra and algebraic geometry means, of an object A in an abelian category, that  −  ⊗ A is an exact functor. See flat module or, for more generality, flat morphism.

Category:Geometry

The concept of "curvature of space" is fundamental to cosmology. A space without curvature is called a "flat space" or Euclidean space . Whether the universe is “flat″ could determine its ultimate fate; whether it will expand forever, or ultimately collapse back into itself. The geometry of spacetime has been measured by the Wilkinson Microwave Anisotropy Probe (WMAP) to be nearly flat. According to the WMAP 5-year results and analysis, “WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density (within a 1% margin of error). This is equivalent to a mass density of 9.9 × 10 g/cm, which is equivalent to only 5.9 protons per cubic meter.” The WMAP data are consistent with a flat geometry, with Ω = 1.02 +/- 0.02.

Flatness refers to the shape of a liquid's free surface. On planet Earth, the flatness of a liquid is a function of the curvature of the Earth, and from trigonometry, can be found to deviate from true flatness by approximately 19.6 nanometers over an area of 1 square meter, a deviation which is dominated by the effects of surface tension. This calculation using the Earth's mean radius at sea level, however a liquid will be slightly flatter at the poles.

In manufacturing and mechanical engineering, flatness is an important geometric condition for workpieces and tools.

In the manufacture of precision parts and assemblies, especially where parts will be required to be connected across a surface area in an air-tight or liquid-tight manner, flatness is a critical quality of the manufactured surfaces. Such surfaces are usually machined or ground to achieve the required degree of flatness. High-definition metrology, such as digital holographic interferometry, of such a surface to confirm and ensure that the required degree of flatness has been achieved is a key step in such manufacturing processes. Flatness may be defined in terms of least squares fit to a plane ("statistical flatness"), worst-case or overall flatness (the distance between the two closest parallel planes within).

Two parts that are flat to about 1 helium light band (HLB) can be "wrung" together, which means they will cling to each other when placed in contact. This phenomenon is commonly used with gage blocks.

Geometric dimensioning and tolerancing has provided geometrically defined, quantitative ways of defining flatness operationally.

In art criticism of the 1960s and 1970s, flatness described the smoothness and absence of curvature or surface detail of a two-dimensional work of art. Critic Clement Greenberg believed that flatness, or two-dimensional, was an essential and desirable quality in painting, a criterion which implies rejection of painterliness and impasto. The valorization of flatness led to a number of art movements, including minimalism and post-painterly abstractionism.

Modernism of the arts happened during the second half of the 19th century and extended into most of the 20th. This period of art is identified by art forms consisting of an image on a flat two-dimensional surface. This art evolution began in the 1860s and culminated 50 years later. By this time almost all three-dimensional works had been eliminated. This new approach to painting was to create a visual appearance of realism. Looking at a surface with only two-dimensions our perception of depth is an illusion. The reduction of depth in painting was the consequence of investigation. This new essence of self-analysis attempted to establish an experience or effect from the viewer of the painting.

The term flatness can be used to describe much of the popular American art work of the 1950s and 1960s. The art of this period had a basic yet colorful design that held a degree of two dimensional form. Thus the term flatness is used to describe this medium. The ground work idea for Minimalism began in Russia in 1913 when Kazimir Malevich placed a black square on a white background claiming that: “Art no longer cares to serve the state and religion it no longer wishes to illustrate the history of manners, it wants to have nothing further to do with the object as such, and believes that it can exist in and for itself without things.”

One of the first Minimalism artworks was created in 1964 by Dan Flavin. He produced a neon sculpture titled Monument for V. Tatlin. This work was a simplistic assembly of neon tubes that were not carved or constructed in any way. The idea was that they were not supposed to symbolize anything but to just merely exist. The Minimalist approach to art was to conceive by the mind before execution. Traditional modes of art composition were looked away from in favor of improvisation, spontaneity and automatism. This new expressionist style consisted of improvised pattern making where every stroke of the brush was viewed as expression and subjective freedom.

This concept inspired a whole new art form called Pop Art. It retained the color scheme and simplicity of Minimalism, but it borrowed images from pop culture to become relatable. The works now in question held a meaning for the viewer with familiar imagery but it still retained the avant-garde approach of Minimalism. Pop Art is a well-recognized movement for 1960s culture. This type of art was very free form fashionable and rebellious. It was wild and colorful but many works retained the idea of two dimensional flatness.

Pop Art fell out of fashion and a new movement came into being. Op Art or Optic Art was now the latest trend in home décor and fashion. This form of modern art shares a strong relationship with the culture thought and design of the 1960s. This new art form focused on non-objective painting that focused on design, color, form, and line. These paintings where hand drawn or created with a mechanical aid. They featured a flat looking two dimensional design that could appear to pop out in an almost three dimensional form. Some pieces look as if they are moving due to shape and line placement creating a trick of the eye. This form of art was created to test the limits of the conscious perception of the viewer.

Bright colors were no longer favored as much of Op Art is black and white with little use of color. The designs presented migrated back to the Minimalist idea of art simply existing and not representing an ideal. A well noted artist of this style is Bridget Riley who shaped the contemporary art scene of the early 50s and 70s. Her works are designed to pull the eye in such a way to stretch and disorder the perceptual sense. She is considered a ground breaking artist in the realm of modern art. Her work mainly consists of detailed line and circle patterns to create an optical challenge for the viewer.

Riley composes her art with the thought in mind; that we all have a narrow view on how we see things and our vision is rarely stretched to new abilities. Her work confronts the observer with new imaginative sensations, and the overall purpose of the artist’s disappears and is replaced with what the viewer conceives. This form of art has no clear outlined theme therefore it allows total freedom for one to compose their imagination. Riley’s work ignores object and instead focuses on movement to create a seemingly endless pattern. Riley’s art appeared in the fashion of that era. Similar patterns still remain popular in clothing today.