Degrees of FreedomDate: 12/17/2002 at 18:28:52 From: Duane Swacker Subject: Degrees of freedom What is meant by "degrees of freedom"? A friend's son named his band "Three Degrees of Freedom." I asked him about it and he said it was a math term. I searched my gray matter archives and there is a fuzzy response that says I learned about degrees of freedom somewhere along the way, but am currently baffled as to what it means. Please enlighten! Date: 12/17/2002 at 18:40:27 From: Doctor Tom Subject: Re: Degrees of freedom Hi Duane, It's a math/physics term. "N degrees of freedom" means a situation requires N numbers to identify exactly what condition it is in. For example, if you just want to identify the location of a point in our three-dimensional space, you need three coordinates. The interesting thing is that, in a sense, you need three coordinates no matter what coordinate system you use. For example, in standard Cartesian coordinates you need the x, y, and z coordinates. In spherical coordinates you need a radius, an azimuth, and an altitude. In cylindrical coordinates, you need an angle, a radius, and a z-coordinate, etc. If you want to identify the location and time of an event, there are four degrees of freedom: three for the location and one for the time. If you want to identify the location of an object on a two-dimensional surface (even a curved one), you essentially need two numbers: imagine a curvy grid over the surface for coordinates. If you want to identify an airplane's location and orientation, that has six degrees of freedom. Three to get the coordinates of the center of the plane, and three for roll, pitch, and yaw. If you are trying to figure out the situation completely in a dogfight between two planes, there are 12 degrees of freedom: six for each plane. The number of degrees of freedom in a situation basically tells you how many independent equations you'll need to completely understand the situation from a mathematical point of view. This is not necessarily just for location/position kinds of things - the concept is totally general. For example, if a chemical process is going on with a number of chemicals reacting, to know the final concentrations of all of them, you'll need to know a certain number of concentrations, or maybe temperatures, or pressures, etc. But whatever number it takes to figure it out, that's the number of degrees of freedom in the system. - Doctor Tom, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/