Degrees of freedom
 | This article needs additional citations for verification. (November 2021) |
Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or other physical processes are possible. This relates to the philosophical concept to the extent that people may be considered to have as much freedom as they are physically able to exercise.[citation needed]
Applications
Statistics
In statistics, degrees of freedom refers to the number of variables in a statistic calculation that can vary. It can be calculated by subtracting the number of estimated parameters from the total number of values in the sample.[1] For example, a sample variance calculation based on n samples will have n-1 degrees of freedom, because sample variance is calculated using the sample mean as an estimate of the actual mean.[2]
Mathematics
In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that models the system is only implicitly defined.
Mechanics
In mechanics, degrees of freedom describes the number of independent motions that are allowed to a body. In the case of a mechanism made of several bodies, it refers to the number of possible independent relative motions between the pieces of the mechanism. Ball-and-socket joints, such as the human wrist or hip, can freely rotate and have three degrees of freedom.[3] A free, rigid object, such as a ship at sea, has six degrees of freedom: three rotations and three translations about each perpendicular axis.[4]
In the study of complex motor control, there may be so many degrees of freedom that a given action can be achieved in many different ways. The brain must select and combine movements with different degrees of freedom.[5] This issue is sometimes called the degrees of freedom problem.
Physics and chemistry
In physics and chemistry, degrees of freedom refers to the parameters used to describe a physical system, such as chemical composition and pressure. The minimum number of fixed parameters required to define a system, or the dimension of its phase space, is known as its degrees of freedom.[6]
See also
- Phase (matter) – Region of uniform physical properties
- Component (thermodynamics) – Chemically inert constituent of a system
- Phase rule – General principle in thermodynamics regarding pVT systems in equilibrium
References
- ^ Lane, David M. "Online Statistics Education: A Multimedia Course of Study". onlinestatbook.com. Archived from the original on 2006-07-06. Retrieved 2021-11-23.
- ^ "Degrees of Freedom (df)". www.animatedsoftware.com. Archived from the original on 2018-09-17. Retrieved 2021-11-23.
- ^ Diversity of Muscle - Britannica. Archived from the original on 2021-11-22. Retrieved 2021-11-23.
{{cite encyclopedia}}:|website=ignored (help) - ^ "Summary of Ship Movement" (PDF). Archived (PDF) from the original on 2011-11-25. Retrieved 2021-11-23.
- ^ "Degrees of freedom problem". APA Dictionary of Psychology. Washington, DC: American Psychological Association. n.d. Retrieved 2021-11-23.
{{cite encyclopedia}}: CS1 maint: year (link) Archived from the original on 2022-10-05 - ^ "phase | Definition & Facts | Britannica". www.britannica.com. Archived from the original on 2021-11-22. Retrieved 2021-11-23.
 | This science article is a stub. You can help Wikipedia by expanding it. |