CylinderA cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces.
Dandelin spheresIn geometry, the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of the cone and the plane is a conic section, and the point at which either sphere touches the plane is a focus of the conic section, so the Dandelin spheres are also sometimes called focal spheres. The Dandelin spheres were discovered in 1822. They are named in honor of the French mathematician Germinal Pierre Dandelin, though Adolphe Quetelet is sometimes given partial credit as well.
Rotational spectroscopyRotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The spectra of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy.
SpeedIn everyday use and in kinematics, the speed (commonly referred to as v) of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
Homotopy groups of spheresIn the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure of spheres viewed as topological spaces, forgetting about their precise geometry. Unlike homology groups, which are also topological invariants, the homotopy groups are surprisingly complex and difficult to compute.
Diminishing returnsIn economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal (ceteris paribus). The law of diminishing returns (also known as the law of diminishing marginal productivity) states that in productive processes, increasing a factor of production by one unit, while holding all other production factors constant, will at some point return a lower unit of output per incremental unit of input.
Arms industryThe arms industry, also known as the defence industry (or defense industry), the military industry, or the arms trade, is a global industry which manufactures and sells weapons and military technology. Public sector and private sector firms conduct research and development, engineering, production, and servicing of military material, equipment, and facilities. Customers are the armed forces of states, and civilians. An arsenal is a place where arms and ammunition – whether privately or publicly owned – are made, maintained and repaired, stored, or issued, in any combination.
Rotation matrixIn linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: If x and y are the endpoint coordinates of a vector, where x is cosine and y is sine, then the above equations become the trigonometric summation angle formulae.
Speed of lightThe speed of light in vacuum, commonly denoted c, is a universal physical constant that is exactly equal to ). According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects.
Rate of returnIn finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return.
Speed of soundThe speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as well as the medium through which a sound wave is propagating. At , the speed of sound in air is about . More simply, the speed of sound is how fast vibrations travel. The speed of sound in an ideal gas depends only on its temperature and composition.
Marginal utilityIn economics, utility refers to the satisfaction or benefit that consumers derive from consuming a product or service. Marginal utility, on the other hand, describes the change in pleasure or satisfaction resulting from an increase or decrease in consumption of one unit of a good or service. Marginal utility can be positive, negative, or zero. For example, when eating pizza, the second piece brings more satisfaction than the first, indicating positive marginal utility.
