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Volume Volume Volume is the quantity of threedimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.[1] Volume Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straightedged, and circular shapes can be easily calculated using arithmetic formulas [...More...] 


Invariant (mathematics) In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually indicated by the context in which the term is used. For example, the area of a triangle is an invariant with respect to isometries of the Euclidean plane. The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class. Invariants are used in diverse areas of mathematics such as geometry, topology and algebra [...More...] 


Solid Solid Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). In solids molecules are closely packed. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice) or irregularly (an amorphous solid such as common window glass). Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because in gases molecules are loosely packed. The branch of physics that deals with solids is called solidstate physics, and is the main branch of condensed matter physics (which also includes liquids) [...More...] 


Displacement (fluid) In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, and from this, the volume of the immersed object can be deduced (the volume of the immersed object will be exactly equal to the volume of the displaced fluid). An object that sinks displaces an amount of fluid equal to the object's volume. Thus buoyancy is expressed through Archimedes' principle, which states that the weight of the object is reduced by its volume multiplied by the density of the fluid. If the weight of the object is less than this displaced quantity, the object floats; if more, it sinks. The amount of fluid displaced is directly related (via Archimedes' Principle) to its volume. In the case of an object that sinks (is totally submerged), the volume of the object is displaced [...More...] 


Square (geometry) In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90degree angles, or (100gradian angles or right angles).[1] It can also be defined as a rectangle in which two adjacent sides have equal length [...More...] 


Arithmetic Arithmetic Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the toplevel divisions of modern mathematics, along with algebra, geometry, and analysis [...More...] 


Centimetre A centimetre (international spelling as used by the International Bureau of Weights and Measures; symbol cm) or centimeter (American spelling) is a unit of length in the metric system, equal to one hundredth of a metre, centi being the SI prefix SI prefix for a factor of 1/100.[1] The centimetre was the base unit of length in the now deprecated centimetre–gram–second (CGS) system of units. Though for many physical quantities, SI prefixes for factors of 103—like milli and kilo—are often preferred by technicians, the centimetre remains a practical unit of length for many everyday measurements [...More...] 


Gill (unit) The gill (pronounced[1] /ˈdʒɪl/ ( listen)) or teacup is a unit of measurement for volume equal to a quarter of a pint.[2] It is no longer in common use, except in regard to the volume of alcoholic spirits measures.In imperial units1 imperial gill ≡ 5 imperial fluid ounces≡ 1⁄32 imperial gallon≡ 1⁄4 imperial pint≡ 142.0653125 ml[3]≈ 142 ml≈ 1.2 US gillsIn United States customary units1 US gill ≡ 4 US fl oz≡ 1⁄32 US gallon≡ 1⁄4 US pint≡ 1⁄2 US cup≡ 8 tablespoons≡ 24 teaspoons≡ 32 US fluid drams≡ 77⁄32 in3≡ 118.29411825 ml[4]≈ 118 ml≈ 5⁄6 imperial gillsIn Great Britain, the standard single measure of spirits in a pub was 1⁄6 gill (23.7 ml) in England, and 1⁄5 gill (28.4 ml) in Scotland; after metrication th [...More...] 


Plasma (physics) Plasma (from Ancient Greek Ancient Greek πλάσμα, meaning 'moldable substance'[1]) is one of the four fundamental states of matter, and was first described by chemist Irving Langmuir[2] in the 1920s.[3]. Unlike the other three states, solid, liquid, and gas, plasma does not exist freely on the Earth's surface under normal conditions [...More...] 


Teaspoon A teaspoon is an item of cutlery, a measuring instrument, of approximately 5ml, or a unit of measurement of volume (usually abbreviated tsp.).[1][2]Contents1 Cutlery 2 Measure of volume2.1 History 2.2 United States customary teaspoon 2.3 Metric teaspoon 2.4 Alternative definitions3 See also 4 References 5 External linksCutlery[edit]A cup of coffee with coffee spoonA teaspoon is a small spoon suitable for stirring and sipping the contents of a cup of tea or coffee, or adding a portion of loose sugar to it. These spoons have heads more or less oval in shape. Teaspoons are a common part of a place setting. Teaspoons with longer handles, such as iced tea spoons, are commonly used also for ice cream desserts or floats. Similar spoons include the tablespoon and the dessert spoon, the latter intermediate in size between a teaspoon and a tablespoon, used in eating dessert and sometimes soup or cereals [...More...] 


Fluid Dram The dram (alternative British spelling drachm; apothecary symbol ʒ or ℨ; abbreviated dr)[1][2]:C6–C7[3] is a unit of mass in the avoirdupois system, and both a unit of mass and a unit of volume in the apothecaries' system.[2] It was originally both a coin and a weight in ancient Greece.[4] The unit of volume is more correctly called a fluid dram, fluid drachm, fluidram or fluidrachm (abbreviated fl dr, ƒ 3, or fʒ).[1][2]:C17[3][5][6][7]Contents1 Ancient unit of mass 2 British unit of mass 3 Modern unit of mass 4 Unit of volume 5 In popular culture 6 References 7 External linksAncient unit of mass[edit]Silver Drachm from Dyrrhachium, Illyria dated circa 229 BC. Obverse: ΞΕΝΩΝ,(XENON) cow standing right, looking back at calf which it suckles, eagle standing right above; Reverse: DUR PURBA, square containing double stellate pattern, club to left [...More...] 


Gill (volume) The gill (pronounced[1] /ˈdʒɪl/ ( listen)) or teacup is a unit of measurement for volume equal to a quarter of a pint.[2] It is no longer in common use, except in regard to the volume of alcoholic spirits measures.In imperial units1 imperial gill ≡ 5 imperial fluid ounces≡ 1⁄32 imperial gallon≡ 1⁄4 imperial pint≡ 142.0653125 ml[3]≈ 142 ml≈ 1.2 US gillsIn United States customary units1 US gill ≡ 4 US fl oz≡ 1⁄32 US gallon≡ 1⁄4 US pint≡ 1⁄2 US cup≡ 8 tablespoons≡ 24 teaspoons≡ 32 US fluid drams≡ 77⁄32 in3≡ 118.29411825 ml[4]≈ 118 ml≈ 5⁄6 imperial gillsIn Great Britain, the standard single measure of spirits in a pub was 1⁄6 gill (23.7 ml) in England, and 1⁄5 gill (28.4 ml) in Scotland; after metrication th [...More...] 


Additive Map In algebra an additive map, Zlinear map or additive function is a function that preserves the addition operation: f ( x + y ) = f ( x ) + f ( y ) displaystyle f(x+y)=f(x)+f(y) for every pair of elements x and y in the domain. For example, any linear map is additive. When the domain is the real numbers, this is Cauchy's functional equation. For a specific case of this definition, see additive polynomial. More formally, an additive map is a Zmodule homomorphism. Since an abelian group is a Zmodule, it may be defined as a group homomorphism between abelian groups. Typical examples include maps between rings, vector spaces, or modules that preserve the additive group [...More...] 


Cubic Foot The cubic foot (symbol ft3)[1] is an imperial and US customary (nonmetric) unit of volume, used in the United States, and partially in Canada, and the United Kingdom. It is defined as the volume of a cube with sides of one foot (0.3048 m) in length [...More...] 


Cubic Inch The cubic inch (symbol in3)[1] is a unit of measurement for volume in the Imperial units Imperial units and United States customary units United States customary units systems [...More...] 


Tablespoon A tablespoon is a large spoon used for serving or eating. In many Englishspeaking regions, the term now refers to a large spoon used for serving,[1] however, in some regions, including parts of Canada, it is the largest type of spoon used for eating. By extension, the term is used as a measure of volume in cooking. In this capacity, it is most commonly abbreviated tbsp or T, and occasionally referred to as a tablespoonful to distinguish it from the utensil [...More...] 
