A coordinate-free, or component-free, treatment of a scientific theory or mathematical topic develops its concepts on any form of manifold without reference to any particular coordinate system.
https://en.wikipedia.org/wiki/Coordinate-free
Benefits[edit]
Coordinate-free treatments generally allow for simpler systems of equations and inherently constrain certain types of inconsistency, allowing greater mathematical elegance at the cost of some abstraction from the detailed formulae needed to evaluate these equations within a particular system of coordinates.
History[edit]
Coordinate-free treatments were the only available approach to geometry (and are now known as synthetic geometry) before the development of analytic geometry by Descartes. After several centuries of generally coordinate-based exposition, the modern tendency is generally to introduce students to coordinate-free treatments early on, and then to derive the coordinate-based treatments from the coordinate-free treatment, rather than vice versa.
Applications[edit]
Fields that are now often introduced with coordinate-free treatments include vector calculus, tensors, differential geometry, and computer graphics.[1]
In physics, the existence of coordinate-free treatments of physical theories is a corollary of the principle of general covariance.
See also[edit]
- General covariance
- Foundations of geometry
- Change of basis
- Coordinate conditions
- Component-free treatment of tensors
- Background independence
References[edit]
- ^ DeRose, Tony D. Three-Dimensional Computer Graphics: A Coordinate-Free Approach. Retrieved 25 September 2017.
neutronium
Neutronium (sometimes shortened to neutrium,[1] also referred to as neutrite[2]) is a hypothetical substance composed purely of neutrons. The word was coined by scientist Andreas von Antropoff in 1926 (before the 1932 discovery of the neutron) for the hypothetical "element of atomic number zero" (with zero protons in its nucleus) that he placed at the head of the periodic table (denoted by dash, no element symbol).[3][4] However, the meaning of the term has changed over time, and from the last half of the 20th century onward it has been also used to refer to extremely dense substances resembling the neutron-degenerate matter theorized to exist in the cores of neutron stars; hereinafter "degenerate neutronium" will refer to this.
Science fiction and popular literature have used the term "neutronium" to refer to an imaginary highly dense phase of matter composed primarily of neutrons, with properties useful to the story.
https://en.wikipedia.org/wiki/Neutronium
Preon
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