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Thread: Equations that changed the world - photo

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    Supporting Member mklotz's Avatar
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    Forgot a very important one, Euler's formula...

    e^ix = cos x + i sin x

    which, when evaluated for x = π, yields the amazing relation...

    e^iπ + 1 = 0

    An irrational number raised to an irrational, imaginary value yields an integer - astounding.

    And here's one way to prove it...

    Equations that changed the world - photo-euler-proof.jpg

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    Last edited by mklotz; Nov 25, 2022 at 09:25 AM.
    ---
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    Supporting Member Toolmaker51's Avatar
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    Quote Originally Posted by mklotz View Post
    Forgot a very important one, Euler's formula...
    That's because Euler didn't have a good publicist or agent;
    or
    the convening board felt a third revolutionary concept per mathematician an excess.
    Last edited by Toolmaker51; Nov 26, 2022 at 09:56 PM.
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    ...we'll learn more by wandering than searching...

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    the chemists secrets are freely told to the carpenter ( emerson)

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    Supporting Member Toolmaker51's Avatar
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    Quote Originally Posted by 2wheelcharlie View Post
    the chemists secrets are freely told to the carpenter (emerson)
    Note those who needing an exclusive vocabulary to restrain such occurrence.
    Sincerely,
    Toolmaker51
    ...we'll learn more by wandering than searching...

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    Supporting Member mwmkravchenko's Avatar
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    Leibnitz independently founded calculus. And there was even a Precursor to Fourier. With even a derivation of the FFT. ( I watched this on YouTube. My Math skills are there on the far back recesses of my shelf of clapping brain cells, rusty and get lubricated only when required )

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    Whew! Thought I was the one making all that noise.
    Sincerely,
    Toolmaker51
    ...we'll learn more by wandering than searching...

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    Jon
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    Don't forget the critical mathematical contributions of the American woke movement in the past few years:


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    Supporting Member mklotz's Avatar
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    Quote Originally Posted by mwmkravchenko View Post
    Leibnitz independently founded calculus. And there was even a Precursor to Fourier. With even a derivation of the FFT. ( I watched this on YouTube. My Math skills are there on the far back recesses of my shelf of clapping brain cells, rusty and get lubricated only when required )
    Leibniz (note spelling, Leibnitz is a city in Austria) is responsible for the notation we still use in calculus. Our integral sign is the script form of the letter 's' used in those days. As such, it stood for continuous Summation, much as we now use the Greek capital sigma for discrete summations.

    This picture shows this form of the letter as used in the mid 1700s; other examples can be seen in Washington's diaries preserved at Mount Vernon.

    Equations that changed the world - photo-congress.jpg
    ---
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    Supporting Member mwmkravchenko's Avatar
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    Quote Originally Posted by mklotz View Post
    Leibniz (note spelling, Leibnitz is a city in Austria) is responsible for the notation we still use in calculus. Our integral sign is the script form of the letter 's' used in those days. As such, it stood for continuous Summation, much as we now use the Greek capital sigma for discrete summations.

    This picture shows this form of the letter as used in the mid 1700s; other examples can be seen in Washington's diaries preserved at Mount Vernon.

    Click image for larger version. 

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    Yup, my spelling prowess is slipping little by little. Funny how language changes, is Old English they even used similar spelling to German. Roots of English being German and French for a great part, and a lot of Greek too. Pays to do a little appreciating of how things we use regularly come to be. It's called history. Some of it is even honest!

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