Surface areaThe surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces.
ShapeA shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type. In geometry, shape excludes information about the object's position, size, orientation and chirality. A figure is a representation including both shape and size (as in, e.g., figure of the Earth).
LengthLength is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system, the base unit for length is the metre. Length is commonly understood to mean the most extended dimension of a fixed object.
Measure (mathematics)In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge.
Surface (mathematics)In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved (this is analogous to a curve generalizing a straight line). An example of a non-flat surface is the sphere. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space.Domain (mathematical analysis)In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space. In particular, it is any non-empty connected open subset of the real coordinate spaceR or the complex coordinate spaceC. A connected open subset of coordinate space is frequently used for the domain of a function.Solid geometrySolid geometry or stereometry is the geometry of three-dimensionalEuclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensionalclosed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms, cubes (and other polyhedrons), cylinders, cones (including truncated) and other solids of revolution.Plane curveIn mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions.
Planar laminaMathematical model of a thin, flat object In mathematics, a planar lamina (or plane lamina) is a plane figure representing a thin, usually uniform, flat layer of a solid. It serves also as an idealized model of a planar cross section of a solid body in integration. Planar laminas can be used to determine moments of inertia, or center of mass of figures, as well as an aid in corresponding calculations for 3D bodies.
Surface (topology)In topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensionalsolid 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.
PaintPaint is a material or mixture of colored liquid that, when applied to a solid material and allowed to dry, adds a film-like layer. As art, this is used to create an image or images known as a painting. Paint can be made in many colors and types. Most paints are either oil-based or water-based, and each has distinct characteristics. Primitive forms of paint were used tens of millennia ago in cave paintings.
Boundary (topology)In topology and mathematics in general, the boundary of a subset S of a topological spaceX is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set. Notations used for boundary of a set S include bd(S),fr(S),{\displaystyle \operatorname {bd} (S),\operatorname {fr} (S),} and ∂S{\displaystyle \partial S}.
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