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In materials science, an intrinsic property is independent of how much of a material is present and is independent of the form of the material, e.g., one large piece or a collection of small particles. Intrinsic properties are dependent mainly on the fundamental chemical composition and structure of the material. [1]
For example, the property of being an aunt is extrinsic while the property of having a mass of 60 kg is intrinsic. [11] [12] If the identity of indiscernibles is defined only in terms of intrinsic pure properties, one cannot regard two books lying on a table as distinct when they are intrinsically identical. But if extrinsic and impure ...
An intrinsic property is a property that a thing has itself, including its context. An extrinsic (or relational ) property is a property that depends on a thing's relationship with other things. For example, mass is an intrinsic property of any physical object , whereas weight is an extrinsic property that varies depending on the strength of ...
The mean curvature is an extrinsic invariant. In intrinsic geometry, a cylinder is developable, meaning that every piece of it is intrinsically indistinguishable from a piece of a plane since its Gauss curvature vanishes identically. Its mean curvature is not zero, though; hence extrinsically it is different from a plane.
For example, mass is a physical intrinsic property of any physical object, whereas weight is an extrinsic property that varies depending on the strength of the gravitational field in which the respective object is placed. Another example of a relational property is the name of a person (an attribute given by the person's parents).
The Riemann Hypothesis. Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize ...
Such a surface would, in modern terminology, be called a manifold; and in modern terms, the theorem proved that the curvature of the surface is an intrinsic property. Manifold theory has come to focus exclusively on these intrinsic properties (or invariants), while largely ignoring the extrinsic properties of the ambient space.
These two points of view can be reconciled, i.e. the extrinsic geometry can be considered as a structure additional to the intrinsic one. (See the Nash embedding theorem.) In the formalism of geometric calculus both extrinsic and intrinsic geometry of a manifold can be characterized by a single bivector-valued one-form called the shape operator ...