My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum


Thanks Tree3Thanks
  • 1 Post By mathman
  • 1 Post By studiot
  • 1 Post By SDK
Reply
 
LinkBack Thread Tools Display Modes
October 15th, 2017, 04:32 PM   #1
Newbie
 
Joined: Oct 2017
From: Toronto

Posts: 6
Thanks: 0

Degrees of (Freedom?)

If a 2D circle has 360 degrees (of freedom?), how many degrees (of freedom) does a sphere have? 360^2 ? or more?
nietzscheswoman is offline  
 
October 15th, 2017, 05:37 PM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,659
Thanks: 964

Math Focus: Elementary mathematics and beyond
As far as I know, "degrees of freedom" pertains to systems, usually statistical ones.
greg1313 is offline  
October 15th, 2017, 05:51 PM   #3
Newbie
 
Joined: Oct 2017
From: Toronto

Posts: 6
Thanks: 0

Got it. Thanks. I'll just stick with "degrees" then.
nietzscheswoman is offline  
October 16th, 2017, 02:17 PM   #4
Global Moderator
 
Joined: May 2007

Posts: 6,397
Thanks: 546

A sphere has a solid angle of 4π.
Thanks from nietzscheswoman
mathman is offline  
October 16th, 2017, 04:02 PM   #5
Senior Member
 
Joined: Jun 2015
From: England

Posts: 704
Thanks: 202

Quote:
Originally Posted by nietzscheswoman View Post
If a 2D circle has 360 degrees (of freedom?), how many degrees (of freedom) does a sphere have? 360^2 ? or more?

Got it. Thanks. I'll just stick with "degrees" then.
Degrees and degrees of freedom are measures of quite different things.

A degree (by itself) is a measure of angle and there are indeed 360 degrees to make up a circle.

But there are other forms of angular measure for instance revolutions and it takes one revolution to make a circle.

Mathematicians use radians and it takes $\displaystyle 2\pi $ of these to make a circle.

In some European countries they use that grad or gradien which divides the circle into 400 grads, and therefore a quarter circle into 100 degrees.
This compares with degrees which divide the circle into 90 degrees.

The quarter circle is important and called a quadrant.


On the other hand, the degree of freedom is roughly speaking the number of independent values (called coordinates) we require to specify something.

So in 2D we require 2 numbers, say an x coordinate and a y coordinate.

However, a circle is only part of the whole two dimensional plane and obeys a particular relationship between the x and the y so that if we know one we can calculate the other. This is also called a constraint.

So any particular circle only has one degree of freedom.

Does this help?
Thanks from nietzscheswoman

Last edited by skipjack; October 16th, 2017 at 05:17 PM.
studiot is offline  
October 16th, 2017, 06:46 PM   #6
Newbie
 
Joined: Oct 2017
From: Toronto

Posts: 6
Thanks: 0

This jogs my memory and I'm thankful for the clarification.

But what I have in mind is this -- 2D circles filling up a sphere, how many of them would fit?


Visualizing it right now...it seems the answer is 180. Is that how many degrees a sphere has? Or are degrees irrelevant to spheres?
nietzscheswoman is offline  
October 16th, 2017, 07:15 PM   #7
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 223
Thanks: 120

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
Originally Posted by nietzscheswoman View Post
This jogs my memory and I'm thankful for the clarification.

But what I have in mind is this -- 2D circles filling up a sphere, how many of them would fit?


Visualizing it right now...it seems the answer is 180. Is that how many degrees a sphere has? Or are degrees irrelevant to spheres?
Degrees are irrelevant to spheres and also every other shape. They are a completely arbitrary choice off measurement. For example, for some applications people use mils of which they are 6400 per circle. The point is, a circle can be arbitrarily divided into how ever many pieces you like and the resulting unit can be defined. It doesn't mean it is instrinsically important whatsoever.

The question of how many circles makeup a sphere is a much more meaningful one. It is the same as the number of points on the line segment $[0,1]$ and also the same as the number off rays inscribed in the circle. This is equal to the cardinality of the continuum.
Thanks from nietzscheswoman
SDK is offline  
October 17th, 2017, 03:31 AM   #8
Senior Member
 
Joined: Jun 2015
From: England

Posts: 704
Thanks: 202

Good to see someone maintaining an interest resulting in a productive discussion.



Your original question took us from 2D to 3D.

If we divide the sphere up into patches of unit area, each patch subtends a cone to the centre with the solid angle at the vertex being measured in steradians.

https://en.wikipedia.org/wiki/Solid_angle

https://en.wikipedia.org/wiki/Steradian

There are $\displaystyle 4\pi $ steradians to make up the complete sphere, as already noted.
studiot is offline  
October 21st, 2017, 12:10 PM   #9
Newbie
 
Joined: Oct 2017
From: Toronto

Posts: 6
Thanks: 0

Quote:
Originally Posted by SDK View Post
Degrees are irrelevant to spheres and also every other shape. They are a completely arbitrary choice off measurement. For example, for some applications people use mils of which they are 6400 per circle. The point is, a circle can be arbitrarily divided into how ever many pieces you like and the resulting unit can be defined. It doesn't mean it is instrinsically important whatsoever.

The question of how many circles makeup a sphere is a much more meaningful one. It is the same as the number of points on the line segment $[0,1]$ and also the same as the number off rays inscribed in the circle. This is equal to the cardinality of the continuum.
Wow. What an incredible answer. I get it. Thank you.
nietzscheswoman is offline  
October 23rd, 2017, 12:10 AM   #10
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 786
Thanks: 294

If you were to rotate about the diameter of the circle and lay a copy every 1 degree of rotation, it would indeed start to copy over itself after 180 1 degree rotations. There would be gaps but it would approximate a sphere or a Christmas decoration.
weirddave is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
degrees, freedom, geometry



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Applying offsets to six degrees of freedom defunktlemon Linear Algebra 2 July 21st, 2015 03:30 AM
Finding vector potential: "degrees of freedom" uint Calculus 1 May 19th, 2015 05:09 AM
chi sqr degrees of freedom Kinroh Algebra 0 November 29th, 2013 08:51 PM
Minimum degrees of freedom fotoni Algebra 0 July 21st, 2013 05:45 AM
Easy degrees of freedom question blabla Advanced Statistics 6 May 9th, 2012 09:16 PM





Copyright © 2017 My Math Forum. All rights reserved.