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 picture info Length In Euclidean geometry, length is measured along straight lines unless otherwise specified. Pythagoras's theorem relating the length of the sides of a right triangle is one of many applications in Euclidean geometry. Length may also be measured along other types of curves and is referred to as Einstein's special relativity, length can no longer be thought of as being constant in all reference frames. Thus a ruler that is one metre long in one frame of reference will not be one metre long in a reference frame that is moving relative to the first frame [...More Info...]       [...Related Items...] Great Circles A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. A great circle is the largest circle that can be drawn on any given sphere. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same center and circumference as each other. This special case of a circle of a sphere is in opposition to a small circle, that is, the intersection of the sphere and a plane that does not pass through the center. Every circle in Euclidean 3-space is a great circle of exactly one sphere. For most pairs of distinct points on the surface of a sphere, there is a unique great circle through the two points. The exception is a pair of antipodal points, for which there are infinitely many great circles. The minor arc of a great circle between two points is the shortest surface-path between them [...More Info...]       [...Related Items...] Boundary (of A Manifold) In topology, a branch of mathematics, a topological manifold is a topological space which locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold (e.g. differentiable manifolds are topological manifolds equipped with a differential structure). Every manifold has an "underlying" topological manifold, obtained by simply "forgetting" the added structure.[1] A topological space X is called locally Euclidean if there is a non-negative integer n such that every point in X has a neighbourhood which is homeomorphic to real n-space Rn.[2] A topological manifold is a locally Euclidean Hausdorff space. It is common to place additional requirements on topological manifolds [...More Info...]       [...Related Items...] picture info Solid Solid is one of the four fundamental states of matter (the others being liquid, gas and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural rigidity and resistance to a force applied to the surface. 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 available volume like a gas. The atoms in a solid are 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 the molecules in a gas are loosely packed. The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids) [...More Info...]       [...Related Items...] Base (geometry) In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure.[1] This term is commonly applied to triangles, parallelograms, trapezoids, cylinders, cones, pyramids, parallelepipeds and frustums. Bases are commonly used (together with heights) to calculate the areas and volumes of figures. In speaking about these processes, the measure (length or area) of a figure's base is often referred to as its "base." By this usage, the area of a parallelogram or the volume of a prism or cylinder can be calculated by multiplying its "base" by its height; likewise, the areas of triangles and the volumes of cones and pyramids are fractions of the products of their bases and heights [...More Info...]       [...Related Items...] picture info Altitude (triangle) In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the extended base of the altitude. The intersection of the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. Thus, the longest altitude is perpendicular to the shortest side of the triangle [...More Info...]       [...Related Items...] picture info Intensive And Extensive Properties Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system[1] whereas an extensive quantity is one whose magnitude is additive for subsystems.[2] This reflects the corresponding mathematical ideas of mean and measure, respectively. An intensive property is a bulk property, meaning that it is a local physical property of a system that does not depend on the system size or the amount of material in the system [...More Info...]       [...Related Items...] picture info Triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ${\displaystyle \triangle ABC}$.[1] In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ${\displaystyle \triangle ABC}$.[1] In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space) [...More Info...]       [...Related Items...] Measurement System A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units (SI), the modern form of the metric system, the British imperial system, and the United States customary system. The French Revolution gave rise to the metric system, and this has spread around the world, replacing most customary units of measure. In most systems, length (distance), mass, and time are base quantities. Later science developments showed that either electric charge or electric current could be added to extend the set of base quantities by which many other metrological units could be easily defined. (However, electrical units are not necessary for such a set [...More Info...]       [...Related Items...]