Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. 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 (written as 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.

Arbeit macht frei

"Arbeit macht frei" (German pronunciation: [ˈaɐ̯baɪt ˈmaxt ˈfʁaɪ]) is a German phrase meaning "work sets you free." The slogan is known for appearing on the entrance of Auschwitz and other concentration camps.

Origin

The expression comes from the title of a novel by German philologist Lorenz Diefenbach, Arbeit macht frei: Erzählung von Lorenz Diefenbach (1873), in which gamblers and fraudsters find the path to virtue through labour. The phrase was also used in French ("le travail rend libre!") by Auguste Forel, a Swiss entomologist, neuroanatomist and psychiatrist, in his "Fourmis de la Suisse" ["Ants of Switzerland"] (1920). In 1922, the Deutsche Schulverein of Vienna, an ethnic nationalist "protective" organization of Germans within the Austrian empire, printed membership stamps with the phrase Arbeit macht frei.

Use by the Nazis

The slogan "Arbeit macht frei" was placed at the entrances to a number of Nazi concentration camps. The slogan's use in this instance was ordered by SS General Theodor Eicke, inspector of concentration camps and second commandant of Dachau Concentration Camp.