Minimal surfaceIn mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame.
Differential geometry of surfacesIn mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface.
ContractA contract is an agreement that specifies certain legally enforceable rights and obligations pertaining to two or more mutually agreeing parties. A contract typically involves the transfer of goods, services, money, or a promise to transfer any of those at a future date. In the event of a breach of contract, the injured party may seek judicial remedies such as damages or rescission. A binding agreement between actors in international law is known as a treaty.
Contract of saleIn contract law, a contract of sale, sales contract, sales order, or contract for sale is a legal contract for the purchase of assets (goods or property) by a buyer (or purchaser) from a seller (or vendor) for an agreed upon value in money (or money equivalent). An obvious ancient practice of exchange, in many common law jurisdictions, it is now governed by statutory law. See commercial law. Contracts of sale involving goods are governed by Article 2 of the Uniform Commercial Code in most jurisdictions in the United States and Canada.
Surface (topology)In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
