Welcome to the ToeQuest.
Page 1 of 3 123 LastLast
Results 1 to 10 of 27

Thread: elegant proofs

  1. #1
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    elegant proofs

    Scientific or mathematical theories or theorems are considered as elegant if their proofs are simple, succinct, and concise. However, elegance could not possibly apply to the underlying postulates or assumptions of every theory. On the other hand, could a theorem with the less number of assumptions or axioms be considered as elegant?

    In Euclidean geometry there are 5 assumptions. In non-Euclidean geometries (both Riemannian and Gaussian) there are also 5 assumptions. Their differences were stated in the 5th postulate of parallels: through a point not on a line (1) one and only one parallel, (2) no parallels, and (3) infinite parallels can be drawn. These three geometries are used in cosmology to determine the shape or topology of the whole universe. To date the winner remains undecided as a result of certain dimensional uncertainty. How many dimensions do the whole universe needs? In general relativity there are only 4 dimensions, 3 of space and 1 of time. In quantum mechanics there are only 3 of space with time-dimension reserved as a free parameter. In a quantum field theory, if the same as degrees of freedom then there are infinite number of dimensions. However, it is theoretically logical to formulate a physical theory base only on the 8 directional invariance properties of local infinitesimal uniform accelerated motion.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  2. #2
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: elegant proofs

    Reality is the utmost elegence,you only have to think about it.




    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  3. #3
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: elegant proofs

    but there are a lot of inelegant proofs in mathematics for example the 4 colors map theorem http://mathworld.wolfram.com/Four-ColorTheorem.html
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  4. #4
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: elegant proofs

    Quote Originally Posted by AntonioLao View Post
    but there are a lot of inelegant proofs in mathematics for example the 4 colors map theorem http://mathworld.wolfram.com/Four-ColorTheorem.html

    Well then just ignore them,they are not essential to life.





    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  5. #5
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: elegant proofs

    On the contrary they make life easier and simplier such as internet.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  6. #6
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: elegant proofs

    Quote Originally Posted by AntonioLao View Post
    On the contrary they make life easier and simplier such as internet.
    Oh I was forgetting that!Old age creeping up.



    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  7. #7
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: elegant proofs

    Without math life would just be hunters and gatherers.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  8. #8
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: elegant proofs

    Quote Originally Posted by AntonioLao View Post
    Without math life would just be hunters and gatherers.

    Is that so bad,the Kalahari bushmen need only hunt (work) for two hours per day to fufil their needs,can you do that?



    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  9. #9
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: elegant proofs

    Are they using cellphones?
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  10. #10
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: elegant proofs

    Quote Originally Posted by AntonioLao View Post
    Are they using cellphones?

    Certainly not!they use bow and arrow with a small spear.




    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

 

 
Page 1 of 3 123 LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Back to top