Page 17 of 20 FirstFirst ... 71516171819 ... LastLast
Results 161 to 170 of 200
Like Tree15Likes

Thread: Fermat's last, and mine too.

  1. #161
    Moderator grapes's Avatar
    Join Date
    Nov 2010
    Location
    NC USA
    Posts
    4,004

    Default Re: Proof of Fermat's Theorem

    Quote Originally Posted by BuleriaChk View Post


    -------------------------------
    case n=2
    --------------
    ab=0 (Pythagorean Triple

    ,

    ,
    --------------------------------


    , ,
    The vectors a and b are perpendicular to each other, so of course their dot product is *equal* to zero. But even that doesn't mean that 2ab equals zero.




    Therefore, c' cannot be an integer
    -----------------------------------
    case n>2
    ----------------


    ------------------------------

    -------------------------

    ---------------------------

    --------------------------
    QED
    Math is not your strong suit.

  2. #162
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,761

    Default Re: Proof of Fermat's Theorem

    Quote Originally Posted by grapes View Post
    The vectors a and b are perpendicular to each other, so of course their dot product is *equal* to zero. But even that doesn't mean that 2ab equals zero.
    No shit, Dick Tracy.

    (check the cross product where a and b commute in my pdf)....

    Now all you have to do is imagine n>2....
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle Updates 03/02/2017 12:07 PM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  3. #163
    Moderator grapes's Avatar
    Join Date
    Nov 2010
    Location
    NC USA
    Posts
    4,004

    Default Re: Proof of Fermat's Theorem

    Quote Originally Posted by BuleriaChk View Post
    Quote Originally Posted by grapes View Post
    The vectors a and b are perpendicular to each other, so of course their dot product is *equal* to zero. But even that doesn't mean that 2ab equals zero.
    No shit, Dick Tracy.
    And yet, you say in your post, that it is *not equal* to zero
    (check the cross product where a and b commute in my pdf)....

    Now all you have to do is imagine n>2....

  4. #164
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,761

    Default Re: Proof of Fermat's Theorem

    Quote Originally Posted by grapes View Post
    And yet, you say in your post, that it is *not equal* to zero
    The dot product is zero only if there is no interaction (multiplication) - (i.e. ). If there is interaction, then both the dot products and the cross product exists.



    Pythagorean triples model no interaction. The Binomial Expansion always includes interaction.

    Interaction means multiplication of two independent variables ab=ba (the factor of 2 exists because the variables commute).

    Fermat's expression lacks multiplication, but his expression is only valid for n=2 if no interaction (multiplication) is involved (which is why he specified n>2 in his theorem).
    Last edited by BuleriaChk; 03-18-2017 at 06:29 PM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle Updates 03/02/2017 12:07 PM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  5. #165
    Moderator grapes's Avatar
    Join Date
    Nov 2010
    Location
    NC USA
    Posts
    4,004

    Default Re: Proof of Fermat's Theorem

    Quote Originally Posted by BuleriaChk View Post

    Look how you defined these vectors! See above
    Quote Originally Posted by BuleriaChk View Post
    The dot product is zero only if there is no interaction (multiplication) - (i.e. ). If there is interaction, then both the dot products and the cross product exists.
    No, their dot product is always zero.


    Pythagorean triples model no interaction. The Binomial Expansion always includes interaction.

    Interaction means multiplication of two independent variables ab=ba (the factor of 2 exists because the variables commute).

    Fermat's expression lacks multiplication, but his expression is only valid for n=2 if no interaction (multiplication) is involved (which is why he specified n>2 in his theorem).

  6. #166
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,761

    Default Re: Proof of Fermat's Theorem

    Quote Originally Posted by grapes View Post
    Look how you defined these vectors! See above

    No, their dot product is always zero.


    ,
    ,


    ,


    ,

    is the angle between the vectors (for those who are just beginning high school math).
    Last edited by BuleriaChk; 03-18-2017 at 11:31 PM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle Updates 03/02/2017 12:07 PM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  7. #167
    Moderator grapes's Avatar
    Join Date
    Nov 2010
    Location
    NC USA
    Posts
    4,004

    Default Re: Fermat's last, and mine too.

    Quote Originally Posted by BuleriaChk View Post

    This is how you defined these vectors, a and b are positive integers.
    Quote Originally Posted by BuleriaChk View Post
    The dot product is zero only if there is no interaction (multiplication) - (i.e. ). If there is interaction, then both the dot products and the cross product exists.
    The dot product will always be zero. That means will *never* equal .

  8. #168
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,761

    Default Re: Fermat's last, and mine too.

    Quote Originally Posted by grapes View Post
    This is how you defined these vectors, a and b are positive integers.

    The dot product will always be zero. That means will *never* equal .
    Hey, you may be on to something, Dick Tracy..

    (That is why c can never be an integer unless it is part of a Pythagorean Triple.... in the general Binomial Expansion for the case n=2. )

    But the equation is true for all real numbers.



    What does it mean for ? (think Cartesian Coordinate system - Wiki article)

    Well, ok, that may too complex Math Is Fun

    (Play with the interactive graph awhile... it might help you as an introduction to more advanced math)..

    (if you get confused about the Binomial Expansion, scroll down to the bottom where they introduce three dimensions).
    Then go back to the Wiki article....

    (Hint: the set {c,a,b,2ab} is not a triangle. Neither is the set {z,x,y,2xy},

    Then consult the institution that taught you your advanced math and physics and see if you can get a refund ....

    (Follow, Follow the links, and they will lead you to freedom... some day... maybe...)

    From the Wiki article (w.r.t. John Gabriel)"

    "The development of the Cartesian coordinate system would play a fundamental role in the development of the Calculus by Isaac Newton and Gottfried Wilhelm Leibniz.[3] The two-coordinate description of the plane was later generalized into the concept of vector spaces.[4]"
    Last edited by BuleriaChk; 03-19-2017 at 11:24 AM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle Updates 03/02/2017 12:07 PM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

  9. #169
    Moderator grapes's Avatar
    Join Date
    Nov 2010
    Location
    NC USA
    Posts
    4,004

    Default Re: Fermat's last, and mine too.

    Quote Originally Posted by BuleriaChk View Post
    Hey, you may be on to something, Dick Tracy..
    I was just pointing out one of the mistakes that invalidate your "proof" of Fermat's Last Theorem.

  10. #170
    Senior Member
    Join Date
    Jun 2012
    Location
    Santa Barbara, CA
    Posts
    2,761

    Default Re: Fermat's last, and mine too.

    Quote Originally Posted by grapes View Post
    I was just pointing out one of the mistakes that invalidate your "proof" of Fermat's Last Theorem.
    Doesn't invalidate the proof at all. The proof specifies n>2.

    The dot product is only valid for for the Pythagorean triple.

    It is NOT valid for terms in rem(a,b,n) for n>2 Consider the case n=3, which has terms like and



    In the terms containing products of a and b ( ), and , are NEVER orthogonal, and rem(a,b,3) only vanishes if a = 0 or b= 0.

    (the terms only intersect at (0,0).

    Village idiot...
    Last edited by BuleriaChk; 03-19-2017 at 11:18 AM.
    _______________________________________
    "Flamenco Chuck" Keyser
    The Relativistic Unit Circle Updates 03/02/2017 12:07 PM PST
    Proof of Fermat's Last Theorem Updates 03/19/2017 8:23 PM PST
    Ignore List -The Peanut Gallery.

Page 17 of 20 FirstFirst ... 71516171819 ... LastLast

Bookmarks

Posting Permissions

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