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  • Re: If you love Pythagoras and hate Trigonometry [Loomis]

    From Mild Shock@21:1/5 to Mild Shock on Sun Nov 26 19:43:02 2023
    Ok, ChatGPT got smarter:

    Apply the angle sum/difference identity for cosine:
    cos(A - B) = cos(A) * cos(B) + sin(A) * sin(B)

    Substitute A = B into the equation:
    cos(0) = cos^2(B) + sin^2(B)

    Simplify further:
    1 = cos^2(B) + sin^2(B)

    Does this count?

    https://chat.openai.com/share/c1b17dfd-8c4d-4633-9081-8bdc62b338f1

    Mild Shock schrieb am Montag, 27. November 2023 um 04:32:14 UTC+1:
    Somebody really loved Pythagoras, and
    compiled 370 proofs or somesuch.

    But then made a bold claim that no
    trigonometric proofs are possible.

    Loomis, Elisha Scott - 1940 ff https://files.eric.ed.gov/fulltext/ED037335.pdf

    Fact or fiction?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mild Shock@21:1/5 to All on Sun Nov 26 19:32:12 2023
    Somebody really loved Pythagoras, and
    compiled 370 proofs or somesuch.

    But then made a bold claim that no
    trigonometric proofs are possible.

    Loomis, Elisha Scott - 1940 ff
    https://files.eric.ed.gov/fulltext/ED037335.pdf

    Fact or fiction?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Ross Finlayson@21:1/5 to Mild Shock on Tue Nov 28 00:03:45 2023
    On Sunday, November 26, 2023 at 7:43:05 PM UTC-8, Mild Shock wrote:
    Ok, ChatGPT got smarter:

    Apply the angle sum/difference identity for cosine:
    cos(A - B) = cos(A) * cos(B) + sin(A) * sin(B)

    Substitute A = B into the equation:
    cos(0) = cos^2(B) + sin^2(B)

    Simplify further:
    1 = cos^2(B) + sin^2(B)

    Does this count?

    https://chat.openai.com/share/c1b17dfd-8c4d-4633-9081-8bdc62b338f1
    Mild Shock schrieb am Montag, 27. November 2023 um 04:32:14 UTC+1:
    Somebody really loved Pythagoras, and
    compiled 370 proofs or somesuch.

    But then made a bold claim that no
    trigonometric proofs are possible.

    Loomis, Elisha Scott - 1940 ff https://files.eric.ed.gov/fulltext/ED037335.pdf

    Fact or fiction?

    Sounds like "identity dimension".

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)